Variable particle number on a quantum computer

by Felipe J. Llanes-Estrada

Thursday 10 Oct 2024, 10:00 → 11:00 Europe/Zurich

4/2-037 - TH meeting room (CERN)

We develop theoretical methods for the implementation of creation and destruction operators in separate registers of a quantum computer, allowing for a transparent and dynamical creation and destruction of particle modes in second quantization in problems with variable particle number, of interest for few-body physics.  I will sketch commutation (anticommutation) relations on a finite memory bank, symmetrizing and antisymmetrizing operators, and unitary evolution under conventional two- and four-body Hamiltonian terms, as well as terms varying the particle number.

To codify n particles with N_p modes each one needs O(n log (N_p)) qubits. Such scaling seems more efficient than the Jordan-Wigner transformation (of O(N_p) qubits as long as n does not saturate N_p), whenever there are a modest number of particles with a large number of states available to each (and less advantageous for a large number of particles with few states available to each). And although less efficient, it is also less cumbersome than optimal compact encodings.

 

CERNLlanesViruet.pdf