Solving quantum statistical mechanics with variational autoregressive networks and quantum circuits

Abstract

We extend the ability of an unitary quantum circuit by interfacing it with a classical autoregressive neural network. The combined model parametrizes a variational density matrix as a classical mixture of quantum pure states, where the autoregressive network generates bitstring samples as input states to the quantum circuit. We devise an efficient variational algorithm to jointly optimize the classical neural network and the quantum circuit to solve quantum statistical mechanics problems. One can obtain thermal observables such as the variational free energy, entropy, and specific heat. As a byproduct, the algorithm also gives access to low energy excitation states. We demonstrate applications of the approach to thermal properties and excitation spectra of the quantum Ising model with resources that are feasible on near-term quantum computers.

Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design

“…The implementation of the AD engine is generic so that it works automatically with symbolic computation. We show an example of calculating the symbolic derivative of gate parameters in Appendix G. One can also integrate Yao.AD with classical automatic differentiation engines such as Zygote to handle mixed classical and quantum computational graphs, see [55].…”

“…The batched register is a collection of quantum wave functions. It can be samples of classical data for quantum machine learning tasks [66] or an ensemble of pure quantum states for thermal state simulation [55]. For both applications, having the batch dimension not only provides convenience but may also significantly speed up the simulations.…”

“…A recent project extending VQE [56] to thermal quantum states [55] integrates Yao seamlessly with the differentiable programming package Zygote [87]. Yao's efficient AD engine and batched quantum register support allow joint training of quantum circuit and classical neural network effortlessly.…”

A quantum convolutional neural network on NISQ devices

“…Quantum information processing (QIP) [1,2], which exploits quantum-mechanical phenomena such as quantum superpositions and quantum entanglement, allows one to overcome the limitations of classical computation and reaches higher computational speed for certain problems [3][4][5]. Quantum machine learning, as an interdisciplinary study between machine learning and quantum information, has undergone a flurry of developments *Correspondence: gllong@tsinghua.edu.cn 1 Beijing Academy of Quantum Information Sciences, Beijing 100193, China 2 State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China Full list of author information is available at the end of the article in recent years [6][7][8][9][10][11][12][13][14][15]. Machine learning algorithm consists of three components: representation, evaluation and optimization, and the quantum version [16][17][18][19][20] usually concentrates on realizing the evaluation part, the fundamental construct in deep learning [21].…”

Ab-initio study of interacting fermions at finite temperature with neural canonical transformation

“…However, unitary transformations are not considered in these ansatzes, since only a single wavefunction, instead of a whole basis, is needed in this situation. Second, there have been quantum algorithms for thermal properties of model Hamiltonians [32][33][34], which rely on quantum circuits to construct the unitary transformation. However, they still demand advances in quantum technologies to be practically useful.…”