A large body of work has demonstrated that parameterized artificial neural networks (ANNs) can efficiently describe ground states of numerous interesting quantum manybody Hamiltonians. However, the standard variational algorithms used to update or train the ANN parameters can get trapped in local minima, especially for frustrated systems and even if the representation is sufficiently expressive. We propose a parallel tempering method that facilitates escape from such local minima. This methods involves training multiple ANNs independently, with each simulation governed by a Hamiltonian with a different driver strength, in analogy to quantum parallel tempering, and it incorporates an update step into the training that allows for the exchange of neighboring ANN configurations. We study instances from two classes of Hamiltonians to demonstrate the utility of our approach using Restricted Boltzmann Machines as our parameterized ANN. The first instance is based on a permutationinvariant Hamiltonian whose landscape stymies the standard training algorithm by drawing it increasingly to a false local minimum. The second instance is four hydrogen atoms arranged in a rectangle, which is an instance of the second quantized electronic structure Hamiltonian discretized using Gaussian basis functions. We study this problem in a minimal basis set, which exhibits false minima that can trap the standard variational algorithm despite the problem’s small size. We show that augmenting the training with quantum parallel tempering becomes useful to finding good approximations to the ground states of these problem instances.
 Award ID(s):
 2120757
 NSFPAR ID:
 10423022
 Date Published:
 Journal Name:
 Science
 Volume:
 377
 Issue:
 6613
 ISSN:
 00368075
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
More Like this


Abstract Computing excitedstate properties of molecules and solids is considered one of the most important nearterm applications of quantum computers. While many of the current excitedstate quantum algorithms differ in circuit architecture, specific exploitation of quantum advantage, or result quality, one common feature is their rooting in the Schrödinger equation. However, through contracting (or projecting) the eigenvalue equation, more efficient strategies can be designed for nearterm quantum devices. Here we demonstrate that when combined with the Rayleigh–Ritz variational principle for mixed quantum states, the groundstate contracted quantum eigensolver (CQE) can be generalized to compute any number of quantum eigenstates simultaneously. We introduce two
excitedstate (antiHermitian) CQEs that perform the excitedstate calculation while inheriting many of the remarkable features of the original groundstate version of the algorithm, such as its scalability. To showcase our approach, we study several model and chemical Hamiltonians and investigate the performance of different implementations. 
Quantum linear system algorithms (QLSAs) have the potential to speed up algorithms that rely on solving linear systems. Interior point methods (IPMs) yield a fundamental family of polynomialtime algorithms for solving optimization problems. IPMs solve a Newton linear system at each iteration to compute the search direction; thus, QLSAs can potentially speed up IPMs. Due to the noise in contemporary quantum computers, quantumassisted IPMs (QIPMs) only admit an inexact solution to the Newton linear system. Typically, an inexact search direction leads to an infeasible solution, so, to overcome this, we propose an inexactfeasible QIPM (IFQIPM) for solving linearly constrained quadratic optimization problems. We also apply the algorithm to ℓ1norm soft margin support vector machine (SVM) problems, and demonstrate that our algorithm enjoys a speedup in the dimension over existing approaches. This complexity bound is better than any existing classical or quantum algorithm that produces a classical solution.more » « less

null (Ed.)Quantum computing is poised to dramatically change the computational landscape, worldwide. Quantum computers can solve complex problems that are, at least in some cases, beyond the ability of even advanced future classicalstyle computers. In addition to being able to solve these classical computerunsolvable problems, quantum computers have demonstrated a capability to solve some problems (such as prime factoring) much more efficiently than classical computing. This will create problems for encryption techniques, which depend on the difficulty of factoring for their security. Security, scientific, and other applications will require access to quantum computing resources to access their unique capabilities, speed and economic (aggregate computing time cost) benefits. Many scientific applications, as well as numerous other ones, use grid computing to provide benefits such as scalability and resource access. As these applications may benefit from quantum capabilities  and some future applications may require quantum capabilities  identifying how to integrate quantum computing systems into grid computing environments is critical. This paper discusses the benefits of gridconnected quantum computers and what is required to achieve this.more » « less

Groundstate entanglement governs various properties of quantum manybody systems at low temperatures and is the key to understanding gapped quantum phases of matter. Here we identify a structural property of entanglement in the ground state of gapped local Hamiltonians. This property is captured using a quantum information quantity known as the entanglement spread, which measures the difference between Rényi entanglement entropies. Our main result shows that gapped ground states possess limited entanglement spread across any partition of the system, exhibiting an arealaw scaling. Our result applies to systems with interactions described by any graph, but we obtain an improved bound for the special case of lattices. These interaction graphs include cases where entanglement entropy is known not to satisfy an area law. We achieve our results first by connecting the groundstate entanglement to the communication complexity of testing bipartite entangled states and then devising a communication scheme for testing ground states using recently developed quantum algorithms for Hamiltonian simulation.more » « less