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The 9th edition of the conference Quantum Information in Spain (ICE), supported by the Spanish Network on Quantum Information and Quantum Technologies, aims to provide a gathering for discussion to researchers working in quantum information science and technologies in Spain to bring together academia and industry.
ICE covers the fields of quantum communication and cryptography, quantum computation and simulation, quantum metrology and sensing, quantum information theory, quantum thermodynamics, photonics, trapped ions, and enabling technologies.
We strongly encourage junior researchers to contribute.
In the talk I will present examples of projects which have leveraged fundamental quantum physics for developing technologies that have gone into products for cybersecurity, large-scale computation and biological detection
In recent years, quantum key distribution (QKD) has become a fully fledged application of quantum information science, and QKD services are being supplied by different companies/institutions around the world. However, the practical security of QKD is not well-established yet, mainly due to the difficulty of guaranteeing that real QKD implementations stick to the assumptions and models on which theoretical security proofs rely.
A particularly conflictive assumption present in most QKD security proofs is that no information is undesirably leaked outside the users’ locations. In fact, optical QKD systems typically rely on the use of active modulators to encode the key information, and these modulators may be a source of side-channels in different ways. For instance, an eavesdropper may actively tamper with a QKD module to gain information about the protocol settings or, more simply, the information can be inadvertently encoded in undesired degrees of freedom.
A candidate solution to overcome this problem is to consider passive (rather than active) state preparation, which rules out all possible modulator side-channels by avoiding the use of active modulation of any kind. Precisely, a passive QKD transmitter generates the quantum states prescribed by a QKD protocol at random, combining a fixed quantum mechanism and a post-selection step. Putting the security upgrade aside, getting rid of all actively driven elements could be very appealing for QKD in practice, because it may allow to boost the frequency of operation of QKD systems while reducing the complexity (and thereby the cost) of QKD infrastructures. Needless to say, this would entail an advantage in many practical situations, for instance, when it comes to deploying QKD on a satellite. Notably though, these advantages come at the price of decreasing the key generation rate because of two main reasons. On the one hand, in a passive transmitter, additional sifting is required to discard those protocol rounds where the randomly generated settings do not lie in certain acceptance intervals. On the other hand, the quantum states post-selected in a passive transmitter are in a mixed polarization state. This represents an inherent source of noise not present in the active case, where one typically considers perfectly prepared pure states.
In a recent collaboration, we presented the first linear optics scheme suitable for fully passive QKD, and analyzed its expected performance within two sharply different approaches for polarization encoding and secret-key-rate estimation. However, these analyses addressed the asymptotic limit of infinite signals, and in both cases the distillable key rate was limited by the inherent noise of the mixed polarization states. Here, we report on a novel parameter estimation technique that surpasses this limitation ---in so reaching tighter bounds on the secret key rate--- and address the practical scenario where a finite number of signals is exchanged. Furthermore, the developed techniques for the estimation of the secret key parameters might be of independent interest for the field of quantum cryptography.
We implemented a simplified time-bin BB84 quantum key distribution protocol with the purpose of achieving the highest possible secret key rate at short distances. The sender Alice emits signals at a rate of 2.5 GHz. In the key-generating basis, we use a superconducting nanowire single photon detector (SNSPD) with a novel design optimized for fast count rates. The in-house designed and fabricated NbTiN detector consists of 14 nanowires which are arranged in an interleaved pattern. Together with the in-house made readout electronics, the detector shows a jitter below 60 ps and simultaneously an efficiency of 64\% at a count rate of 320 Mcps, which represents the operating point of the detector for our shortest-distance key exchange. We performed real-time error correction with a low-density parity check algorithm implemented on a dedicated field-programmable gate array. This algorithm has a leakage of 17% at the highest quantum bit error rate found in our experiment, which was 0.4%. The privacy amplification was performed in real time on a consumer-grade GPU. We achieved a secret key rate of 64 Mbps over a distance of 10.0 km of ultra-low-loss (ULL) single-mode fiber (0.16 dB/km) and 3.0 Mbps over 102.4 km of ULL single-mode fiber . Additionally, we monitored the secret key rate over a longer time over 10.0 km ULL SMF, showing that the secret key rate can be maintained at a similar value for more than 1000 consecutive privacy amplification blocks.
We consider a heterogeneous network of quantum computing modules, sparsely connected via Bell states. Operations across these connections constitute a computational bottleneck and they are likely to add more noise to the computation than operations performed within a module. We introduce several techniques for transforming a given quantum circuit into one implementable on a network of the aforementioned type, minimising the number of Bell states required to do so.
We extend previous works on circuit distribution over fully connected networks to the case of heterogeneous networks. On one hand, we extend the hypergraph approach of [Andres-Martinez & Heunen. 2019] to arbitrary network topologies, making use of Steiner trees to find efficient realisations of the entanglement sharing within the network, reusing already established connections as often as possible. On the other hand, we extend the embedding techniques of [Wu, et al. 2022] to networks with more than two modules. Furthermore, we discuss how these two seemingly incompatible approaches can be made to cooperate. Our proposal is implemented and benchmarked; the results confirm that, when orchestrated, the two approaches complement each other's weaknesses.
In recent years, the study of Bell-type nonlocality on networks has led to an array of intriguing foundational results. Nonetheless the field still faces difficulties in finding a justified application. One of the key barriers for this is the assumption of independent sources in network nonlocality, which is difficult to enforce. In our work we examine a possible operational interpretation for such independent sources. In particular, in networks without inputs, parties connected with a common classical source can be interpreted as malicious parties working together. We explore the first steps in this framework and show that there exist nonlocal distributions which are robust against the topology of the network, i.e. in the spirit of decentralized protocols, the overall distributions are nonlocal even if one is unsure which parties are collaborating. In fact, we show that in large random networks this is quite typical. We further examine the relation to randomness generation and highlight some remaining challenges in developing protocols based on network nonlocality.
Quantum technologies promise interesting new approaches to areas such as computing and communication. A branch that is becoming increasingly interesting is that of quantum networks. The technological assets for quantum networks have been developing rapidly in recent years and many implementations, often geared towards quantum cryptography, have been reported. In order to demonstrate security of quantum cryptographic protocols, a necessary condition is to guarantee that the observations of the parties cannot be reproduced when classical systems are distributed instead (i.e., to observe non-locality). However, in contrast with traditional bipartite scenarios, the standard notion of multipartite non-locality only guarantees that something quantum is happening somewhere in the network. In contrast, recently a new notion of non-locality in networks has been introduced, called full network nonlocality, that allows to guarantee that non-classical behavior is present everywhere in the network. Moreover, this notion does not assume quantum mechanics. Therefore, proofs of security based on full network nonlocality will not break if, in the future, we ever find physical systems that go beyond quantum mechanics.
In this talk I will describe several experimental observations of full network nonlocality in scenarios that are specially relevant as building blocks of large-scale quantum communication networks. The first one is a star-shaped network where three branch parties share each a bipartite quantum state with a central node that performs tripartite entanglement swapping. This is an important scenario to realize multipartite quantum cryptographic protocols mediated by a central authority. The second one is a quantum repeater scenario where we strictly enforce the network structure via space-like separation of its components. The fact that full network nonlocality is observed in a significant manner, in demanding scenarios, and with state-of-the-art technology, strongly motivates the development of multipartite quantum cryptographic protocols in networks and proofs of security based on full network nonlocality.
In a Mach-Zehnder-type light pulse atom interferometer, matter waves are split, mirrored, and recombined using coherent atom optics. With the leading order phase shift scaling with the enclosed space-time area, the momentum transfer induced by the atom optics light pulses as well as the free evolution time are key to significantly enhanced sensitivity to inertial forces and motivate ground-based 10m-scale facilities as well as space-borne experiments. Beyond fundamental physics, the ability to provide long-term stable, accurate measurements gives rise to applications in inertial navigation.
In this talk we will introduce the field of atom interferometric inertial sensing, provide an overview of state-of-the-art experiments, and present current activities at Leibniz University Hannover. In particular, we will provide an overview on the Hannover VLBAI facility (Very Long Baseline Atom Interferometry). With shot noise-limited instabilities better than 10−9 m/s2 at 1 s at the horizon it may compete with state-of-the-art superconducting gravimeters, while providing absolute instead of relative gravity measurements. Operated with rubidium and ytterbium simultaneously, tests of the universality of free fall at a level of parts in 1013 and beyond are in reach. We will finally discuss strategies mitigating vibration noise, which is the dominant noise source in absolute acceleration sensing using atom interferometry. To this end, we report on hybrid inertial sensing by correlating novel opto-mechanical accelerometers with atom interferometers and describe a path towards state-of-the-art inertial sensing in the field without the need for seismic attenuation.
Continuous variable quantum key distribution with discrete modulation has the potential to provide unconditional security using widely available optical elements and existing telecom infrastructure, while allowing for the use of well studied error correction protocols. However, proving finite-size security against coherent attacks poses a challenge. In this work we apply the entropy accumulation theorem, a tool that has previously been used in the setting of discrete variables, to prove finite-size security against coherent attacks for a discretely modulated QKD protocol involving four coherent states and heterodyne detection, under a realistic photon number cutoff assumption. Our analysis provides non-trivial key rates for $n=10^{12}$ rounds.
In quantum metrology, the usefulness of a quantum state is determined by how much it outperforms separable states. For the maximal metrological usefulness genuine multipartite entanglement (GME) is required. In order to improve the usefulness of a quantum state we consider a scheme of having several of its copies. With this scheme, it is possible to find a large class of practically important entangled states that can achieve maximal metrological performance in the limit of many copies, whereas in the single copy case these states can even be non-useful. Thus, we essentially activate quantum metrologically useful GME. Moreover, this maximal usefulness is attained exponentially fast with the number of copies and it can be achieved by measurements of simple correlation observables. We also give examples of improving the usefulness outside of the above mentioned class.
In this contribution I will present ideas and ongoing project to enhance the capabilities of particle detectors using quantum systems [1]. The presented technologies could not only improve the accuracy of measurements but also provide a new dimension by directly sensing properties as spin of individual particles. The level of maturity and applicability of ideas range from those already proved they basic principles to others which are an exercise of what future detectors might look like.
I will start from defining concepts of what is considered in this approach a quantum sensor. Then, the focus will be on detectors for tracking, calorimetry, and timing using nanostructured materials, atoms, molecules and ions and spin-based sensors.
[1] Doser M, Auffray E, Brunbauer FM, Frank I, Hillemanns H, Orlandini G and Kornakov G (2022) Quantum Systems for Enhanced High Energy Particle Physics Detectors. Front. Phys. 10:887738. doi: 10.3389/fphy.2022.887738
As important branches in quantum technologies, quantum sensing and quantum metrology have experienced significant progress, placing themselves at the forefront of the new generation of technologies harnessing quantum effects. In this presentation, different quantum magnetometers assisted by neural networks are introduced. Our results show that neural networks are valuable in distinct quantum systems for quantum sensing leading to adaptive protocols for quantum detection with broad working regime and high accuracy.
The benefits to integrate neural networks are illustrated to decipher the information contained in the sensor responses at the data processing stage of general quantum sensing tasks. We experimentally demonstrate that the combination of 171Yb+ atomic sensors with adequately trained neural networks enables to investigate target fields in the presence of large shot noise, including using the limit case of continuous data acquisition via single-shot measurements [1]. We significantly extend the working regime of atomic magnetometers into scenarios in which the RF driving induces responses beyond their standard harmonic behaviour [2].
The way for the practical use of quantum many-body systems as black-box sensors exploiting quantum resources to improve precision estimation is also demonstrated [3]. Entangled quantum many-body systems can be used as sensors that enable the estimation of parameters with a precision larger than that achievable with ensembles of individual quantum detectors. Neural networks faithfully reproduce the dynamics of quantum many-body sensors, thus allowing for an efficient Bayesian analysis. We exemplify with an XXZ model driven by magnetic fields and demonstrate that our method is capable to yield an estimation of field parameters beyond the standard quantum limit scaling.
References:
[1] Y. Chen, Y. Ban, R. He, et al., A neural network assisted 171Yb+ quantum magnetometer. npj Quantum Inf. 8, 152 (2022).
[2] Y. Ban, J. Echanobe, Y. Ding, et al. Neural-network-based parameter estimation for quantum detection, Quantum Sci. Technol. 6, 045012 (2021).
[3] Y. Ban, J. Casanova, R. Puebla, Neural networks for Bayesian quantum many-body magnetometry, arXiv: 2212.12058 (2022).
We present a method to identify energy shifts which contain structural information in solid-state systems using Nitrogen-Vacancy (NV) centers combined with synchronization techniques. To achieve this, we have developed a theory for Lee-Goldburg based decoupling schemes in microscale-NMR scenarios with NV centers at large static magnetic fields. The introduced RF fields serve two purposes: (i) nuclear decoupling and (ii) bridging the interaction between NV sensors and fast-rotating spins. We have created a theory to track the thermal signal (i.e., the magnetization vector) when driven by decoupling fields. This allows us to obtain coherent signals even in highly protonated samples with strong internuclear couplings.
Rydberg atoms in arrays of optical tweezers offer a new perspective for quantum simulation of many body problems. In this talk, I will give a brief overview about this platform and describe our efforts to control Rydberg interactions to explore different types of spin Hamiltonians. I will report on our recent implementations of the 2D Ising Hamiltonian [1] and the dipolar XY model [2] with more than 100 spins to study quantum magnetism. Furthermore, I will illustrate how the dipolar XY model can be used to generate scalable spin squeezing [3], which could be exploited for metrological applications. Finally, I will show our first steps to scale up the atom numbers in our platform by using a cryogenic environment [4].
References:
[1] Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms, Scholl et al., Nature 595, 233 (2021).
[2] Continuous symmetry breaking in a two-dimensional Rydberg array, Chen et al., Nature (2023).
[3] Scalable spin squeezing in a dipolar Rydberg atom array, Bornet et al., arXiv:2303.08053
[4] Single atoms with 6000-second trapping lifetimes in optical-tweezer arrays at cryogenic temperatures, Schymik et al., Phys. Rev. Applied 16, 034013 (2021).
The well-known spin squeezing coefficient efficiently quantifies the sensitivity and entanglement of Gaussian states [1,2]. However, this coefficient is insufficient to characterize the much wider class of non-Gaussian quantum states that can generate even larger sensitivity gains. In this talk, we present a non-Gaussian extension of spin squeezing based on reduced variances of nonlinear observables that can be optimized under relevant constraints [3]. We determine the scaling of the sensitivity enhancement that is made accessible from increasingly complex quantum states generated by one-axis-twisting in the presence of relevant noise processes [4,5]. Our analytical results provide recipes for optimal non-Gaussian spin squeezing in atomic experiments.
[1] D. J. Wineland, J. J. Bollinger, W. M. Itano, F. L. Moore, and D. J. Heinzen, Spin squeezing and reduced quantum noise in spectroscopy, Phys. Rev. A 46, R6797 (1992).
[2] L. Pezzè, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein, Quantum metrology with nonclassical states of atomic ensembles, Rev. Mod. Phys. 90, 035005 (2018).
[3] M. Gessner, A. Smerzi, and L. Pezzè, Metrological Non-linear Squeezing Parameter, Phys. Rev. Lett. 122, 090503 (2019).
[4] Y. Baamara, A. Sinatra, M. Gessner, Scaling laws for the sensitivity enhancement of non-Gaussian spin states, Phys. Rev. Lett. 127, 160501 (2021).
[5] Y. Baamara, A. Sinatra, M. Gessner, Squeezing of nonlinear spin observables by one axis twisting in the presence of decoherence: An analytical study, Comptes Rendus. Physique 23, 1 (2022).
Measurements take a singular role in quantum theory. While they are often idealized as an instantaneous process, this is in conflict with all other physical processes in nature. Here, we adopt a standpoint where the interaction with an environment is a crucial ingredient for the occurrence of a measurement. Within this framework, we derive a general lower bound on the time needed for a measurement to occur with minimal assumptions and without specifying any physical model.
We evaluate our bound in two examples where the environment is modeled by harmonic oscillators and the measurement apparatus is modeled by spins or bosons. We further discuss possible experimental implementations of the dynamics of a measurement induced by complex environment.
I present two approaches for closing the detection loophole in Bell experiments. Both exploit that high-dimensional entanglement allows for loophole-free experiments with low detection efficiency.
The "penalized N-product Bell inequalities" [1] is a method for, starting from any qudit-qudit correlation violating a Bell inequality with a certain critical detection efficiency, identifying correlations and Bell inequalities for which the critical detection efficiency decays exponentially with N, where N is the number of qudits encoded in each entangled particle.
The "graph-based Bell inequalities" [2] are a family of Bell inequalities for which the critical detection efficiency for maximally entangled states is a function of some invariants of a class of graphs. By exploring this class, we identify correlations with low detection efficiency and relatively low local dimension.
[1] N. Miklin, A. Chaturvedi, M. Bourennane, M. Pawłowski and A. Cabello,
Phys. Rev. Lett. 129, 230403 (2022).
[2] Z.-P. Xu, J. Steinberg, J. Singh, A. J. López-Tarrida, J. R. Portillo and A. Cabello,
Quantum 7, 922 (2023).
We present a method to detect bipartite entanglement based on number-phase-like uncertainty relations in split spin ensembles. First, we derive an uncertainty relation that plays the role of a number-phase uncertainty for spin systems. It is important that the relation is given with well-defined and easily measurable quantities, and that it does not need assuming infinite dimensional systems. Based on this uncertainty relation, we show how to detect bipartite entanglement in an unpolarized Dicke state of many spin-1/2 particles. The particles are split into two subensembles, then collective angular momentum measurements are carried out locally on the two parts. First, we present a bipartite Einstein-Podolsky-Rosen (EPR) steering criterion. Then, we present an entanglement condition that can detect bipartite entanglement in such systems. We demonstrate the utility of the criteria by applying them to a recent experiment given in K. Lange et al. [Science 360, 416 (2018)] realizing a Dicke state in a Bose-Einstein condensate of cold atoms, in which the two subensembles were spatially separated from each other.
[1] G. Vitagliano, M. Fadel, I. Apellaniz, M. Kleinmann, B. Lücke, C. Klempt, and G. Tóth, Quantum 7, 914 (2023).
While current research in quantum theory focuses on the exploitation of quantum effects in communication and computation scenarios, quantum systems are also known to be advantageous for some mechanical tasks. The most known effect is that of tunneling, but there are other less well known effects. One of those is quantum backflow [1], a phenomenon in which a free quantum particle with positive momentum can be observed to propagate backwards. More recently, Tsirelson [2] studied the probability of observing a positive value when we measure the position of a harmonic oscillator with period $T$ at times $0,T/3,2T/3$. He found that a quantum harmonic oscillator can exhibit a bigger probability of success than a classical harmonic oscillator - for which such a probability is bounded by $2/3$. This effect was recently followed up to devise novel tests for quantumness and entanglement [3,4].
We consider a scenario where a (non-relativistic) particle is evolving freely in $\mathbb{R}$. Initially confined in some region $[0,L]$, we measure its position after some time $\Delta T$ has elapsed, to determine if we can find it in the region $[a,\infty)$. We show that a quantum particle can exhibit a bigger probability of success than a classical particle with the same distribution of momentum, thus finding a new mechanical quantum effect, which we name quantum projectiles. We relate the maximum possible advantage of a quantum projectile to the so-called Bracken-Melloy constant $c_{bm}$, which is the maximal possible quantum backflow. We use this relation and an integration technique from Werner [5] to compute for the first time new upper bounds for $c_{bm}$. We study several related mechanical problems and extensions of quantum projectiles. For more details, please see [6].
References
[1] A.J.Bracken, G.F.Mellow Probability backflow and a new dimensionaless quantum number J.Phys.A:Math.Gen.27 2197 (1994).
[2]B.S.Tsirelson How often is the coordinate of a harmonic oscillator positive? quant-ph/0611147 (2006)
[3]L.H.Zaw, C.C.Aw, Z.Lasmar, V.Scarani Detecting quantumness in uniform precessions Phys.Rev.A 106, 032222 (2022)
[4]P.Jayachandran, L.H.Zaw, V.Scarani Dynamic-based entanglement witnesses for harmonic oscillators quant-ph/2210.10357
[5]R.F:Werner Wigner quantusation of arrival time and oscillator phase J.Phys. A:Math.Gen. 21, 4565 (1988)
[6]D.Trillo, T.P.Le, M.Navascués, Quantum supremacy in mechanical tasks: projectiles, rockets and quantum backflow, quant-ph/2209.00725
To achieve efficient and reliable control of microscopic systems one should look for driving protocols that mitigate both the average dissipation and stochastic fluctuations in work. This is especially important in fast driving regimes in which the system is driven far out of equilibrium, potentially creating large amounts of unwanted entropy production. Here we characterise these optimal protocols in rapidly driven classical and quantum systems and prove that they consist of two discontinuous jumps in the full set of control variables. These jumps can be tuned to interpolate between processes with either minimal dissipation or minimal fluctuations, and in some situations allow for simultaneous minimisation. We illustrate our general results with rapidly driven closed quantum systems, classical bit erasure and a dissipative Ising chain driven close to a quantum phase transition.
Quantum machine learning (QML) is often put forward as one of the most likely quantum applications to bring about useful advantages, perhaps even in the near term.
Large-scale quantum computers, once available, will give definite answers to whether this is true, but to make the most out of the significant investments in experimental quantum computing, it is important to try to learn as much as possible already now. And much can be done both using theory, and empirical approaches.
At present, we can work on identifying when (and if) advantages can be already theoretically proven; in parallel we can also investigate how to probe the performance of quantum methods experimentally, even beyond the small sizes current devices allow.
In this talk we will review recent progress in answering these questions; we will present results proving superpolynomial speed-ups and learning advantages in data analysis tasks, specifically well suited for analyzing highly correlated (i.e. genuinely quantum) systems. Regarding more empirical approaches, we will reflect on recent ideas on how to simulate larger and deeper quantum machine learning algorithms which may give us glimpses of what larger quantum computers will bring.
Quantum Key Distribution (QKD) has the potential to play a significant role in improving security in communication networks in the near future. Since the first experimental demonstration [1], multiple QKD experiments have been carried out, the majority of which were proof-of-concept demonstrations that continually broke new records in terms of transmission distance, in both fibre [2,3] and free space [4], and secret key rate (SKR) [5]. However, for large-scale applications of this technology in communication networks, compact, scalable and robust integrated receivers and transmitters are needed. To pursue this effort, we developed a compact, portable, ready-to-use high-speed (1.25 GHz) QKD platform based on Photonic Integrated Circuits (PIC), for both the transmitter and the receiver unit. Our practical integrated QKD system can generate secret keys at high speeds and with low Quantum Bit Error Rates (QBER) implementing the 3-state, one-decoy BB84 protocol with time-bin encoding [6,7].
Regarding the transmitter unit, a silicon-based Photonic Integrated Circuit (PIC) is responsible for producing the three states needed for the protocol [8]. A distributed feedback laser, which is external to the chip, generates phase-randomised laser pulses. An in-house-made PCB that actively controls all the previously mentioned components. The experimental setup is further supported by a field programmable gate array (FPGA). The totality of the transmitter unit is placed inside a 1U 19’’ frame.
The receiver’s PIC is based on silica, features low loss and is polarization-insensitive [8,9]. The receiver’s unit comprises two Negative-Feedback Single-Photon Detectors (NFADs), a PCB and an FPGA. The NFADs are integrated into a compact package resulting in a total volume of 125 cm3 per detection unit. The NFADs are cooled to -50ºC, with a standard Peltier, and achieve timing jitters smaller than 120ps, dark count rates below 600cps and afterpulsing probabilities of 3% at a detection efficiency of 25%. The totality of the transmitter unit is placed inside a 2U 19’’ frame.
As preliminary results, we obtained a QBERZ = 1.8% and QBERX= 3%. These were obtained with a receiver PIC that was not optimized for this application, therefore, we expect significant improvement in QBERX once a fitting receiver is assembled. With such low QBERs, we expect to obtain SKRs of more than 1 kbps, over 100km of fibre, and we look forward to presenting our newest results at the conference.
The biggest challenge that quantum computing and quantum machine learning are currently facing is the presence of noise in quantum devices. As a result, big efforts have been put into correcting or mitigating the induced errors. But, can these two fields benefit from noise? Surprisingly, we demonstrate that under some circumstances, quantum noise can be used to improve the performance of quantum reservoir computing, a prominent and recent quantum machine learning algorithm. Our results show that certain noise types can be beneficial to machine learning, while others should be prioritized for correction.
This critical result sheds new light on the physical mechanisms underlying quantum devices, providing solid practical prescriptions for the successful implementation of quantum information processing in nowadays hardware.
In recent years, there has been a growing interest in utilizing hole spins in silicon and germanium for quantum information processing. One reason for this is the strong spin-orbit interaction present in the valence band of these materials, which allows for versatile interactions with electric fields. As a result, there have been demonstrations of fast electrical manipulation of hole spin qubits [1] and strong spin-photon interactions [2], which are useful for generating long-range entanglement. While these experimental advances are well-established, there is still much to learn on the theoretical side. For example, Ge hole qubits can be operated with in-plane magnetic fields [3], which cannot be easily explained by the expected spin-orbit mechanisms like cubic Rashba or g-tensor modulation resonance.
In this work, we go beyond the usual models for electrical spin manipulation in semiconductor quantum dots. We perform simulations of realistic Ge devices and find that both the electrostatics [4] and the strain [5] display inhomogeneities that heavily affect the performance of hole spin qubits. In particular, we identify overlooked spin-orbit mechanisms that enable manipulation under in-plane magnetic fields and enhance the expected Rabi frequencies. Our simulations show that these mechanisms are dominating the physics of isotropic hole spin qubits.
[1] G. Scappucci et al., Nat. Rev. Mater 6, 926-943 (2021)
[2] C. Yu et al., arXiv:2206.14082 (2022)
[3] N. Hendrickx et al., Nature 591, 580–585 (2021)
[4] B. Martínez et al., Phys. Rev. B 106, 235426 (2022)
[5] J. C. Abadillo-Uriel et al., arXiv:2212.03691 (2022).
Combinatorial optimization problems (CO) have a strong impact on a wide range of disciplines such as finance, machine learning, logistics, etc. In addition to finding a solution with minimum cost, problems of high relevance involve a number of constraints that the solution must satisfy. Variational quantum algorithms (VQA) have emerged as promising candidates for solving these problems in the noisy intermediate-scale quantum stage [1]. However, the constraints are often complex enough to make their efficient mapping to quantum hardware difficult or even infeasible. An alternative standard approach is to transform the optimization problem to include these constraints as penalty terms, but this method involves additional hyperparameters and has several shortcomings [2].
Our work introduces the Multi-Objective Variational Constrained Optimizer (MOVCO), a new method for solving CO with challenging constraints [3]. MOVCO combines the quantum variational framework with a genetic multi-objective optimization to simultaneously optimize the projection of the variational wave function onto the subspace of solutions satisfying all constraints, and the energy of the feasible solutions. This procedure allows the algorithm to progressively sample states within the in-constraints space, while optimizing the energy of these states. We test our proposal on a real-world problem with great relevance in finance: the Cash Management problem. We introduce a novel mathematical formulation for this problem, and compare the performance of MOVCO versus a penalty-based optimization. Our empirical results show a significant improvement in terms of the cost of the achieved solutions, but especially in the avoidance of local minima that do not satisfy any of the mandatory constraints.
References
[1] M.Cerezo et al., Nature Reviews Physics, 3 (2021).
[2] Andrew Lucas, Front.Phys., 2 (2014).
[3] Pablo Díez-Valle et al., arxiv preprint 2302:04196 (2023).
We present a variational algorithm to solve ground states of atomic nuclei within the nuclear shell model. The strategy is based on the implementation of ADAPT-VQE, an adaptive version of the variational quantum eigensolver algorithm, on a digital quantum computer. Exact ground energies are found up to medium-mass nuclei by implementing and simulating ADAPT-VQE on quantum circuits using the QIBO simulator and HPC resources. We also discuss the main challenges the algorithm faces on its implementation to heavier nuclei.
Enhanced coherence in HoW$_{10}$ molecular spin qubits has been demonstrated by use of clock-transitions (CTs) . More recently it was shown by some of us that, while operating at the CTs, it was possible to use an electrical field to selectively address HoW$_{10}$ molecules pointing in a given direction, within a crystal that contains two kinds of identical but inversion-related molecules [2]. Herein we theoretically explore the possibility of employing the electric field to effect entangling two-qubit quantum gates within a 2-qubit Hilbert space resulting from dipolar coupling of two CT-protected HoW$_{10}$ molecules in a diluted crystal. We estimate the thermal evolution of T$_1$, T$_2$, find that CTs are also optimal operating points from the point of view of phonons, and lay out how to combine a sequence of microwave and electric field pulses to achieve coherent control within a switchable two-qubit operating space between symmetric and asymmetric qubit states that are protected both from spin-bath and from phonon-bath decoherence. This two-qubit gate approach presents an elegant correspondence between physical stimuli and logical operations, meanwhile avoiding any spontaneous unitary evolution of the qubit states. Finally, we found a highly protected 1-qubit subspace resulting from the interaction between two clock molecules [3].
1 Shiddiq, Muhandis, et al. "Enhancing coherence in molecular spin qubits via atomic clock transitions." Nature 531.7594 (2016): 348-351.
[2] Liu, Junjie, et al. "Quantum coherent spin–electric control in a molecular nanomagnet at clock transitions." Nature Physics 17.11 (2021): 1205-1209.
[3] Ullah, Aman, et al. "Electrical two-qubit gates within a pair of clock-qubit magnetic molecules." npj Quantum Information 8.1 (2022): 133.
Quantum illumination is one of the main paradigms for implementing quantum radar in the low-frequency spectrum. Here, we contribute towards an open-air application of the protocol, by notably easing its experimental requirements. We first define an experimentally feasible receiver for an entangled signal-idler transmitter. This consists in measuring heterodyne the received signal and adaptively measuring homodyne the idler, reaching a maximal quantum advantage of 3 dB in the error probability exponent with respect to the optimal classical strategy. Our receiver requires only a single tunable JPA. In order to relax the bandwidth requirement at the transmitter level, we discuss a sequential protocol that uses patches of modes sequentially to probe the target region. We show that, in a practical scenario, the sequential protocol needs two orders of magnitude less bandwidth with respect to the non-sequential protocol, while keeping the same quantum advantage.
We calculate precision bounds for estimating the gradient of the magnetic field based on the quantum Fisher information for various types of ensembles, such as for example, a single atomic ensemble with an arbitrary density profile, where the atoms cannot be addressed individually and which is a very relevant case for experiments.
We present a method to find spin states for gradient magnetometry with two spatially separated atomic ensembles based on states for sensing a global phase shift, such as the GHZ state or the Dicke state.
[1] I. Apellaniz et al., Phys. Rev. A, 97 053603 (2018)
[2] G. Vitagliano et al., arXiv:2104.05663 (2021)
In recent years, hole spins in silicon and germanium have attracted increasing interest for quantum information processing. In this talk, I will describe recent advances in hole spin qubits for both silicon and germanium towards intermediate- or large-scale quantum processors.
First, I will present the coherent interaction of a hole spin in silicon with a microwave photon. This coupling scheme enables long-range, on-chip qubit connectivity. Second, I will show our progress on a 10-qubit system in planar germanium, structured in a 3-4-3 array. Finally, I will highlight other efforts towards large quantum dot arrays in germanium, such as device homogeneity and coherent shuttling of spin qubits
I will review the recent advances of TN algorithms that allow to compute the out-of-equilibrium dynamics of local observables after a quantum quench and discuss entropies, generalized entropies and coherence of the states generated.
Shortcuts to adiabaticity [1] are well-known methods for controlling the quantum dynamics beyond the adiabatic criteria, where counter-diabatic (CD) driving provides a promising means to speed up quantum many-body systems. In this talk, we show the applicability of CD driving to enhance the digitized adiabatic quantum computing paradigm in terms of fidelity and total simulation time. Firstly, we begin with the state evolution of an Ising spin chain using the digitized CD driving derived from the variational approach [2]. We apply this technique in the preparation of Bell and Greenberger-Horne-Zeilinger states with high fidelity using a very shallow quantum circuit, demonstrating the acceleration of adiabatic quantum computing in noisy intermediate-scale quantum devices. Secondly, we focus on quantum approximate optimization algorithm (QAOA), an effective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ground state of many-body quantum systems. Since QAOA is an ansatz-dependent algorithm, there is always a need to design ansatz for better optimization. To this end, we propose a digitized version of QAOA enhanced via the use of shortcuts to adiabaticity [3]. Specifically, we use a CD driving term to design a better ansatz, along with the Hamiltonian and mixing terms, enhancing the global performance. We apply our digitized CD QAOA extensively to Ising models, classical optimization problems, and the P-spin model, demonstrating that it outperforms standard QAOA in all cases that we study. Finally, our talk will end up with different applications in quantum factorization [4], portfolio optimization [5], and protein folding [6]. It is concluded that the polynomial enhancement of digitized-counterdiabatic quantum optimization (DCQO) is accomplished by CD terms, severing as non-stoquastic catalyst [7].
References
[1] D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga, Shortcuts to adiabaticity: Concepts, methods, and applications, Rev. Mod. Phys. 91, 045001 (2019).
[2] N. N. Hegade, K. Paul, Y. Ding, M. Sanz, F. Albarrán-Arriagada, E. Solano, and X. Chen, Shortcuts to adiabaticity in digitized adiabatic quantum Computing, Phys. Rev. Applied 15, 024038 (2021).
[3] P. Chandarana, N. N. Hegade, K. Paul, F. Albarrán-Arriagada, E. Solano, A. del Campo, and X. Chen, Digitized-counterdiabatic quantum approximate optimization algorithm, Phys. Rev. Research 4, 013141 (2022),
[4] N. N. Hegade, K. Paul, F. Albarrán-Arriagada, X. Chen, and E. Solano, Digitized adiabatic quantum factorization, Phys. Rev. A 104, L050403 (2021).
[5] N. N. Hegade, P. Chandarana, K. Paul, X. Chen, F. Albarrán-Arriagada, and E. Solano, Portfolio optimization with digitized-counterdiabatic quantum algorithms, Phys. Rev. Research 4, 043204 (2022).
[6] Pranav Chandarana, Narendra N. Hegade, Iraitz Montalban, Enrique Solano, and X. Chen, Digitized-Counterdiabatic Quantum Algorithm for Protein Folding, arXiv:2212.13511.
[7] N. N. Hegade, X. Chen, and E. Solano, Digitized counterdiabatic quantum optimization, Phys. Rev. Research 4, L042030 (2022).
Variational Quantum Algorithms (VQAs) [1] use a classical optimizer to train a parametrized quantum circuit (PQC). These have emerged as a practical way to exploit state-of-the-art quantum computers. Currently, most VQAs have been designed for fully digital approaches, in which the error ends up accumulating for circuits with many parameters. A possible way out is the use of analogue quantum simulators (AQS) instead, that allow a global evolution of the system and are more resilient to errors. This is why they have been recently pointed out as one of the most promising directions to achieve “practical quantum advantage” [2]. However, current proof-of-principle demonstrations with trapped ions [3] or cold atoms [4], like it occurs with fully digital VQAs, are ultimately limited by the connectivities that can be achieved with these devices.
In this work we discuss a variational AQS inspired by the type of interactions that can be obtained in waveguide-QED platforms [5]. In these setups, quantum emitters are coupled to one-dimensional photonic band-gap materiales, leading to tunable long-range interactions among them [6]. We show how using the range of the interaction as a variational parameter one can design a novel class of PQCs. We compare their performance against state-of-the-art VQAs with fixed connectivities and demonstrate that they can accurately capture the ground state of critical spin models with fewer gates and variational parameters. Our results highlight the benefits of exploiting the tunable connectivity as a resource when designing PQCs and show the potential of variational waveguide-QED quantum simulators as a promising platform for implementing VQAs.
[1] M. Cerezo et al., Nature Review Physics 3, 625-644 (2020).
[2] A. J. Daley et al., Nature 607, 667–676 (2022).
[3] C. Kokail et al., Nature 569, 355 (2019).
[4] C. Kaubruegger et al., Phys. Rev. X 11, 041045 (2021).
[5] C. Tabares et al., arXiv:2302.01922 (2023).
[6] D. E. Chang et al., Rev. Mod. Phys. 90, 031002 (2018).
Theoretical and algorithmic advances, availability of data, and computing power have opened the door to exceptional perspectives for application of classical Machine Learning in the most diverse fields of science, business and society at large, and notably in High Energy Physics (HEP). In particular, Machine Learning is among the most promising approaches to analyse and understand the data the next generation HEP detectors will produce.
Machine Learning is also a promising task for quantum devices that can leverage compressed high dimensional representations and use the stochastic nature of quantum measurements as random source. Several architectures are being investigated. Quantum implementations of Boltzmann Machines, classifiers or Auto-Encoders, among the most popular classical approaches, are being proposed for different applications. Born machines are purely quantum models that can generate probability distributions in a unique way, inaccessible to classical computers. This talk will give an overview of the current state of the art in terms of Machine Learning on quantum computers with focus on their application to HEP.
We present our first steps towards the coherent coupling between inhomogeneous magnon excitations and resonant photons living in a superconducting cavity. Using a coplanar superconducting transmission line, we perform broad-band ferromagnetic resonance of thin-film mesoscopic magnets. This allows identifying the low-energy Kittel spin-wave excitation (with infinite wavelength). By patterning gap capacitors, we transform this transmission line into a cavity where resonant photons strong couple to the Kittel mode, as evidenced by the observation of an anti-crossing in the transmission spectra. We also develop the theory for coupling between magnetic textures (vortices and skyrmions) and microwave photons.
Quantum machine learning (QML) is recently gaining interest in both theory and experiment thanks to variational circuits implemented in the noisy intermediate-scale quantum computers (NISQs) [1]. Since we are in such an era, algorithms capable of being implemented in small circuits are of great interest. In pursuit of this objective, we explore QML algorithms that are implementable in circuits involving a single qudit, a system with d > 2 levels, instead of the traditional qubit (d = 2). Molecules with large electronic and/or nuclear spins provide a natural platform with multiple operational levels [2], being a suitable choice for implementing our qudits. Operations are driven by electromagnetic pulses resonant with the allowed transitions, which can be realized with EPR techniques or by coupling them to superconducting circuits [3]. It has been shown that this type of control in a single qudit is sufficient to implement any d-dimensional unitary operation [4], thus being an universal quantum processing unit. Specifically, we explore supervised learning [5] and classification problems of databases comprising more classes than levels are accessible in our qudit, forcing the development of tools to find maximally orthogonal states [6].
References
[1] J. Preskill, Quantum 2, 79 (2018)
[2] I. Gimeno, A. Urtizberea, J. Román-Roche et al., Chemical science 12(15), 5621-5630 (2021)
[3] V. Rollano, M. C. de Ory, C. D. Buch et al., Communications Physics, 5(1), 1-9 (2022)
[4] A. Castro, A. G. Carrizo, S. Roca et al., Physical Review Applied 17(6), 064028 (2022)
[5] M. Schuld and N. Killoran, Physical Review Letters 122, 040504 (2019)
[6] A. Pérez-Salinas, A. Cervera-Lierta, E. Gil-Fuster, and J. I. Latorre, Quantum 4, 226 (2020)
Variational quantum algorithms (VQAs) are one of the most promising NISQ-era algorithms due to their feasibility for their application in vastly diverse fields. Machine learning, quantum chemistry, mathematics, finance or combinatorial problems can be tackled through VQAs. However, the underlying optimization processes within these algorithms usually deal with local minima and barren plateau problems, preventing them to scale efficiently.
Here, we demonstrate how an optimization based on Differential Evolution can help to avoid or drastically reduce the effect of these issues in cost function minimization. Starting from a 1D Ising model, we show that while some common gradient-based and gradient-free optimizers tend to significantly fail when increasing the chain length, Differential Evolution always outperforms them when finding the ground state of the system. Our results demonstrate that non-exponential multiparticle strategies can help to increase the accuracy of these algorithms in large-scale applications.
Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this problem in order to benchmark quantum simulators and to delineate the regime of quantum advantage. Here we present classical algorithms for approximating the dynamics of local observables and nonlocal quantities such as the Loschmidt echo, where the evolution is governed by a local Hamiltonian. For short times, their computational cost scales polynomially with the system size and the inverse of the approximation error. In the case of local observables, the proposed algorithm has a better dependence on the approximation error than algorithms based on the Lieb–Robinson bound. Our results use cluster expansion techniques adapted to the dynamical setting, for which we give a novel proof of their convergence. This has important physical consequences besides our efficient algorithms. In particular, we establish a novel quantum speed limit, a bound on dynamical phase transitions, and a concentration bound for product states evolved for short times.
In recent years, a lot of effort has been put into expanding established jet-quenching formalisms to account for higher-order or energy-suppressed medium-induced effects. Understanding how such contributions emerge is important to have a more complete picture of jet evolution in the medium and to extract more detailed properties of the underlying matter. However, such efforts are in general plagued by technical difficulties related to the complexity of the calculations. In this talk, we show that quantum computers can be used as alternative theoretical labs to simulate jet evolution in the quark-gluon plasma. Based on the light-front Hamiltonian formalism, we construct a digital quantum circuit that tracks the evolution of a multi-particle jet probe within the $\ket{q}+\ket{qg}+\ket{qgg}$ Fock sectors in the presence of a stochastic color background, which is computationally expensive for classical simulation. Using the quantum simulation algorithm, we show that th!
e jet evolution in the medium can be properly captured employing small lattices. Importantly, the simulations can be run in general stochastic backgrounds, surpassing many of the simplifying assumptions usually taken. We will also show that efficient qubit encoding strategies can be used to simplify the quantum simulation.
We propose a new variational ansatz for the ground state preparation of the two-dimensional $\mathbb{Z}_2$ lattice gauge theory in digital quantum computers. It is similar to the well known QAOA, but it contains half Trotter step of an imaginary time propagator, which increases the fidelities reached around the phase transition of the gauge theory. We propose a non-probabilistic implementation for this non-unitary operation. The performance of this ansatz is demonstrated by showing its ability to approximate the critical exponents of the $\mathbb{Z}_2$ lattice theory apart from the usual fidelity arguments. A lattice with the geometry of the rotated surface code is used in the simulation in order to introduce ground state degeneracy in the topological phase for finite lattices. The proposed ansatz is able to prepare any of the degenerated ground states.
This talk explores the integration of Quantum Computers (QCs) within High-Performance Computing (HPC) environments and its significance for Italy and Europe. Representing CINECA, the largest Italian supercomputing center and an EuroHPC selected quantum computer hosting entity, we will discuss about the EuroQCS initiative, an European collaboration involving different countries (including Spain) that aims to facilitate the sharing of quantum computing resources across Europe.
We delve into the potential benefits of integrating quantum accelerators with HPC infrastructures. Challenges such as hardware compatibility, programming models, and software stack optimizations are addressed. Emphasizing hybrid approaches that leverage the strengths of both quantum and classical computing, we highlight the need for seamless integration
Analog quantum processors hold a high potential to show quantum advantage
in the near future. These systems may be programmed to operate as quantum
annealers to address optimisation problems, as well as variational quantum
algorithms and quantum simulations. The technology to build coherent analog quantum processors is still in a premature stage and requires dedicated efforts to be able to scale up into large-scale processors to address real-world problems.
The AVaQus (Annealing-Based Variational Quantum Processors) program coordinated by IFAE is the largest-scale European effort to develop the technology and functionality to operate analog quantum processors as coherent quantum annealers and variational processors. The focus of the project is on both the hardware as well as the theoretical sides, to yield a small-scale prototype representing the unit cell of a larger-scale processor that will succeed project AVaQus in the future.
In this talk, I will report on the current state of project AVAQus, focusing on the most recent developments particularly at IFAE on fabricating and characterizing superconducting flux qubits for coherent quantum annealing applications.
Classical simulation of quantum dynamics from many-body systems with tensor networks is hindered by the exponential growth of entanglement contained at the bonds of a chosen wavefunction factorization (typically Matrix Product States). Modern algorithms try to overcome this entanglement barrier by folding and contracting transversely the network [1], or optimizing schemes to exploit only physical subset of nodes participating in the light cone of local observables [2].
All current proposals are still trying to handle the full entanglement content of the many-body wavefunction. Our target will be the study of thermalization in generic quantum spin chains; in this specific type of evolution, reduced density matrices lose purity and coherence as they converge to the thermal one. At the present stage of our work, we focus on showing that there exists a network predicting local observables for any time which includes insertions that we call decoherers/mixers (equivalent to the disentanglers in MERA). These mixers are structured as 2-spin rotations followed by a total decoherence and a back rotation, and are alternated in the time evolution à la Trotter, emulating a depolarizing channel. We will explain how to optimize them in order to faithfully reproduce the relaxation of local observables, and study the entanglement properties of this auxiliary network, which by construction can be envisioned as a classical stochastic system.
[1] Müller-Hermes, A., Cirac, J. I., & Banuls, M. C. (2012). Tensor network techniques for the computation of dynamical observables in one-dimensional quantum spin systems. New Journal of Physics, 14(7), 075003.
[2] Frías-Pérez, M., & Bañuls, M. C. (2022). Light cone tensor network and time evolution. arXiv preprint arXiv:2201.08402.
The field of cavity qed materials seeks to modify the properties of bulk materials by coupling them to an electromagnetic cavity at equilibrium. When the material is, e.g., composed of magnetic dipoles, the resulting system is described by a generalized Dicke model. Under certain conditions, the cavity modes can be traced out, leaving a spin Hamiltonian with cavity-mediated (effective) spin-spin interactions [1]. Here, we leverage this result to study the relationship between the effective spin model and the underlying Dicke model. We reverse the mapping and use it as a generalized Hubbard–Stratonovich transformation. We show that long-range quantum models can be mapped exactly to generalized Dicke models and use this result to provide an analytical solution in the thermodynamic limit. We illustrate the method on the Ising chain in transverse field. The critical behaviour is found to be universal for all strong long-range models and lattice dimensionalities, in agreement with previous numerical results [2]. The expression for the order parameter is equivalent to the one provided by mean-field theory, proving the exactness of the later. Finally, we study the algebraic decay of correlations and characterize its dependence on the range of interactions in the full phase diagram.
References:
[1] J. Román-Roche and D. Zueco, SciPost Phys. Lect. Notes, 50 (2022).
[2] E. Gonzalez Lazo, M. Heyl, M. Dalmonte and A. Angelone, SciPost Phys. 11, 076 (2021).
Quantum computers in the NISQ era (noisy, intermediate-scale, quantum) still offer a relatively small amount of qubits. The largest quantum computers so far, dedicated to binary optimization, do not surpass a few thousands qubits. We nevertheless are willing and able to probe such computers in real-life tasks with their high demand in number of variables to optimize over.
We tackle a binary optimization problem and discuss the problems around its conversion to a QUBO (quadratic unconstrained binary optimization), which is the kind of problem treated by quantum annealers such as the D-Wave quantum computers. Among these problems are the use of penalties and, importantly, quadratization (reduction of higher-order polynomials to binary ones) that typically requires (scarcely available) extra variables. Different encodings of the same problem are discussed, and, surprisingly, encoding the original problem's variables as densely as possible into fewer binary variables becomes counterproductive after a certain degree in the context of QUBO optimization. We show how this result comes about in the context of different forms of quadratization and discuss their advantages and disadvantages for use in a quantum computer.
Quantum walks (QWs) play an important role in quantum computing. On the one hand, some algoritmical problems can be recast as a QW. On the other hand, many physical phenomena can be simulated with the help of a QW. Here we concentrate on discrete-time QWs, and we discuss quantum circuits that can implement discrete-time quantum walks having an arbitrary position-dependent coin operator [1]. The position of the walker is encoded in base 2: with n qubits, we encode $2^n$ position states. We first propose a circuit implementing the position-dependent coin operator, that is naive, in the sense that it has exponential depth and implements sequentially all appropriate position-dependent coin operators. We then propose a circuit that “transfers” all the depth into ancillae, yielding a final depth that is linear in n at the cost of an exponential number of ancillae. The main idea of this linear-depth circuit is to implement in parallel all coin operators at the different positions. Finally, we extend the result of [2] from position-dependent unitaries which are diagonal in the position basis to position-dependent $2 \times 2$-block-diagonal unitaries: indeed, we show that for a position dependence of the coin operator (the block-diagonal unitary) which is smooth enough, one can find an efficient quantum-circuit implementation approximating the coin operator up to an error $\epsilon$ (in terms of the spectral norm), the depth and size of which scale as $O(1/\epsilon)$. Applications of a coin-dependent QW range from the quantum simulation of a relativistic spin-1/2 particle on a lattice, coupled to a smooth external gauge field, to spatial noise on the coin operator.
[1] https://arxiv.org/abs/2211.05271.
[2] J. Welch, D. Greenbaum, S. Mostame, and A. AspuruGuzik, “Efficient quantum circuits for diagonal unitaries without ancillas,” New J. Phys. 16, 033040 (2014).
Hybrid quantum-classical algorithms emerge as one promising approach to improve the performance of current quantum computers. In this work, we consider the method to execute general quantum algorithms on two different QPUs connected via classical communication. The optimal protocol for such computation consists of two steps: First, a quasi-probabilistic simulation scheme generates the required number of entangling gates among the two QPUs. Second, the entangling gates are distributed across the circuit by gate teleportation. To perform this protocol, we propose the set of quantum circuits and the classical postprocessing required to simulate $k$ CNOT gates. We show that the extra sampling overhead required to execute this parallelization protocol is $2^{k+1}-1$. Our method can be directly adapted to parallelize widely used algorithms such as variational quantum algorithms. This work serves as an intermediate step towards a distributed quantum architecture in which an array of connected QPUs via quantum communication perform the execution of a quantum algorithm jointly.
In this talk I will provide a tutorial introduction to quantum simulation with quantum computers. I will review the failure of conventional computing to address many-body problems and how this prevents progress in many scientific areas. I will discuss whether and how quantum computers, either fault tolerant in the future or noisy intermediate scale state of the art, can help to solve many-body problems. I will present the main challenges for quantum simulation algorithms: quantum state preparation, dynamical evolution and post-processing, including some recent work of my group [1,2,3]
[1] Preparing valence-bond-solid states on noisy intermediate-scale quantum computers
Bruno Murta, Pedro M. Q. Cruz, and J. Fernández-Rossier,
Phys. Rev. Research 5, 013190 (2023)
[2] Gutzwiller wave function on a digital quantum computer
Bruno Murta and J. Fernández-Rossier
Phys. Rev. B 103, L241113 (2021)
[3] Optimizing quantum phase estimation for the simulation of Hamiltonian eigenstates
P. M. Queiroz da Cruz, G. Catarina, R. Gautier and J. Fernández-Rossier
Quantum Science and Technology 5, 044005 (2020)
Quantum reservoir computing (QRC) is a machine learning technique where complex quantum systems are exploited to solve temporal tasks, such as predicting chaotic time series and complex spatiotemporal dynamics. Most existing results in the analysis of QRC systems with classical inputs have been obtained using the density matrix formalism. This paper shows that alternative representations can provide better insights when dealing with design and assessment questions. More explicitly, system isomorphisms have been established that unify the density matrix approach to QRC with the representation in the space of observables using Bloch vectors associated with Gell-Mann bases. It has been shown that these vector representations yield state-affine systems (SAS) previously introduced in the classical reservoir computing literature and for which numerous theoretical results have been established. This connection has been used to show that various statements in relation to the fading memory (FMP) and the echo state (ESP) properties are independent of the representation, and also to shed some light on fundamental questions in QRC theory in finite dimensions. Our conclusions can be summarized as: the necessary and sufficient condition that makes a quantum reservoir valuable is strictly contractive dynamics towards input-dependent fixed points.
Pattern matching of quantum circuits, the task of finding sub-circuits of a quantum circuit that match a given pattern, is an essential tool of quantum circuit compilation. It can be used for instance to find redundant gate sequences that can be rewritten as more efficient computations. We propose an algorithm that performs this task for many patterns simultaneously, independently of the number of patterns. After a pre-computation step, in which the patterns are compiled into a decision tree, all pattern matches can be enumerated in time linear in the size of the input quantum circuit and in the size of the output. More precisely, given a set of patterns with at most $N$ qubits and circuit depth $\delta$, we enumerate all $m$ pattern matches of a circuit with $|C|$ gates in time $O(N)^{N + \frac{1}{2}} \cdot \delta \log \delta \cdot |C| + O(m)$.
We present a general strategy for mapping fermionic systems to quantum hardware with square qubit connectivity which yields low-depth quantum circuits, counted in the number of native two-qubit fSIM gates. We achieve this by leveraging novel operator decomposition and circuit compression techniques paired with specifically chosen fermion-to-qubit mappings that allow for a high degree of gate cancellations and parallelism. Our mappings retain the flexibility to simultaneously optimize for qubit counts or qubit operator weights and can be used to investigate arbitrary fermionic lattice geometries. We showcase our approach by investigating the tight-binding model, the Fermi-Hubbard model as well as the multi-orbital Hubbard-Kanamori model. We report unprecedentedly low circuit depths per single Trotter layer with up to a factor 3.2 improvement upon previous state-of-the-art. Additionally, we show that our decomposition and compression formalism produces favourable circuits even when no native parameterized two-qubit gates are available.