Second Quantisation and Quantum Statistics

Ahana Ghoshal, Carlos de Gois, Kiara Hansenne +2 more

Simulating many-body fermionic systems in conventional qubit-based quantum computers poses significant challenges due to the overheads associated with the encoding of fermionic statistics in qubits, leading to the proposal of native fermionic simulators as an alternative. While allowing for fermionic problems to be simulated efficiently, this class of fermionic simulators carries also specific constraints with them and poses other challenges unfamiliar to qubit systems. Here, we propose to pair fermionic modes to form a so-called qubit in second quantisation representation. This allows fermionic gates to be represented as rotations of these second quantised qubits, enabling adaptation of methods for qubit systems. As an application, we use this pairing scheme to represent the measurement of two- and four-point correlators in fermionic simulators with its native gates as a graph problem. Optimising measurement settings is then analysed with various analytical and algorithmic methods.

Faqir Chand Auluck

Władysław Marcinek

GERALD RICKAYZEN

N N Bogolubov and N N Bogolubov Jr 1982 Singapore: World Scientific viii + 229 pp price £22.50 (£13 paperback) ISBN 9971 950 31 6 Hdbk, 9971 950 04 9 Pbk This book is based on lectures given at the Moscow State University and it is difficult to see at what readership it is aimed. It treats two disparate subjects, quantum statistical mechanics and second quantisation which, although they can be linked, are largely kept apart.

A K Mishra, G. Rajasekaran

Eric Jakeman, Terence J. Shepherd

The authors investigate the outcome of different monitoring schemes applied to small classical populations. Explicit calculation for a solvable model establishes the relationship between the statistical properties of the population and those of the counting processes. Parallels are drawn with operator ordering in the second quantised formulation of photodetection.