A dynamical implementation of canonical second quantization on a quantum computer

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. We establish...

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Bibliographic Details
Published in:arXiv.org 2024-06
Main Authors: Gálvez-Viruet, Juan José, Llanes-Estrada, Felipe J
Format: Article
Language:English
Subjects:
Codification
Commutation
Operators
Quantum computers
Quantum computing
Qubits (quantum computing)
Online Access:Get full text
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Summary: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. We establish theorems for the commutation (anticommutation) relations on a finite memory bank and provide the needed symmetrizing and antisymmetrizing operators. Finally, we provide formulae in terms of these operators for unitary evolution under conventional two- and four-body Hamiltonian terms, as well as terms varying the particle number. In this formalism, the number of qubits needed to codify \(n\) particles with \(N_p\) modes each is of order \(n\log_2 N_p\). Such scaling is more efficient than the Jordan-Wigner transformation which requires \(O(N_p)\) qubits, 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 compact encoding.
ISSN:2331-8422