ELFT HÍRADÓ

[Janos Asboth <asboth.janos AT ttk.bme.hu>]

Meghívó

BME Elméleti Fizika Szeminárium,

máj. 12. péntek 10h15,

1111 Budapest, Budafoki út 8., BME F III. magasföldszint 01.,
Elméleti Fizika Tanszék szemináriumi szoba

Gilyén András (Rényi Alfréd Matematikai Intézet):
Quantum Thermal State Preparation

Preparing ground states and thermal states is of key importance to
simulating quantum systems on a quantum computer. Despite the hope for
practical quantum advantage in quantum simulation, popular approaches like
variational circuits or adiabatic algorithms appear to face serious
difficulties. Monte-Carlo style quantum Gibbs samplers have emerged as an
alternative, but prior proposals have been unsatisfactory due to technical
obstacles related to energy-time uncertainty. We introduce [1] simple
continuous-time quantum Gibbs samplers that overcome these obstacles by
efficiently simulating Nature-inspired quantum Master Equations
(Liouvillians) utilizing the operator Fourier transform. In addition, we
construct the first provably accurate and efficient algorithm for preparing
certain purified Gibbs states (called thermal field double states in
high-energy physics) of rapidly thermalizing systems; this algorithm also
benefits from a Szegedy-type quadratic improvement with respect to the
mixing time. Our algorithms' cost has a favorable dependence on
temperature, accuracy, and the mixing time (or spectral gap) of the
relevant Liouvillians. We contribute to the theory of thermalization by
developing a general analytic framework that handles energy uncertainty
through non-asymptotic secular approximation and approximate detailed
balance, establishing our approximation guarantees and, as a byproduct
yielding the first rigorous proof of finite-time thermalization for
physically derived Liouvillians. Given the success of the classical
Metropolis algorithm and the ubiquity of thermodynamics, we anticipate that
quantum Gibbs sampling will become an indispensable tool in quantum
computing.

[1]: C-F Chen, MJ Kastoryano, FGSL Brandão, A Gilyen:
https://arxiv.org/abs/2303.18224

Minden érdeklődőt szeretettel várunk.
Asbóth János,
 szemináriumi koordinátor