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Instantaneous Quantum Circuits for Ising Models

Gavin Brennen, Macquarie University

(Session 1 : Thursday from 10:15 - 11:00)

Abstract. Statistical Mechanics has provided us with straightforward recipes to compute various physical quantities that can be experimentally probed on an interacting many-body system. But more often than not, the application of these recipes is computationally inefficient, as can be seen from very idealised systems. It may be expected that quantum algorithms could help in this regard. I will describe a scheme for measuring complex temperature partition functions of Ising models which, through appropriate Wick rotations, can be analytically continued to yield estimates for real ones. Notably, the kind of state preparations and measurements involved in this application can in principle be made "instantaneous", i.e. independent of the system size or the parameters being simulated. The estimation error is analysed numerically and analytically and shown to be compatible with prior art using larger depth quantum circuits. Also I'll describe some results on when the algorithm yields approximation scales with multiplicative rather than additive error which could have application in other contexts as well. Finally the dual problem concerning the BQP-hardness of computing partition functions for classical ferromagnetic and consistent Ising models in 2D a high but not perfect accuracy will be described.