Speaker
Description
We present a quantum computing algorithm for fluid flows based on the Carleman-linearization of the Lattice Boltzmann (LB) method.
We demonstrate the convergence of the classical Carleman procedure at moderate Reynolds numbers, namely for Kolmogorov-like flows. Since the CLB procedure shows excellent convergence properties up to Reynolds numbers of order of hundreds, it is plausible to expect that once a viable CLB quantum algorithm is available, it can be readily extended to the quantum simulation of quark gluon plasmas.
We proceed to formulate the corresponding quantum algorithm, including the quantum circuit layout and analyze its computational viability.
We exploit the sparse nature of the CLB matrix to build a quantum circuit based on block-encoding techniques which make use of matrix oracles. The gate complexity of the algorithm is quadratic with the number of qubits, but the probability of success of the corresponding circuit is very low, due to the need of employing several ancilla qubits. It thus appears like the oracle formulation of the CLB procedure implies a tension between the depth of the circuit and its probability of success. To date, such tension does not result into any viable tradeoff, pinpointing the need of further developments in the block-encoding procedure. Finally we describe possible directions along this line.
Email Address of submitter
claudio.sanavio@iit.it
Short summary
We present an efficient quantum algorithm for fluid flows based on the Carleman-linearization of the Lattice Boltzmann (LB) method, which can be used for simulation of quark-gluon plasma. We show a trade-off between the efficiency of the algorithm and the success probability of the same.
