Quantum Algorithms for Quantum Chemistry and Quantum Materials Science

Abstract

As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a theoretical possibility, recent advances in hardware mean that quantum computing devices now exist that can carry out quantum computation on a limited scale. Thus, it is now a real possibility, and of central importance at this time, to assess the potential impact of quantum computers on real problems of interest. One of the earliest and most compelling applications for quantum computers is Feynman’s idea of simulating quantum systems with many degrees of freedom. Such systems are found across chemistry, physics, and materials science. The particular way in which quantum computing extends classical computing means that one cannot expect arbitrary simulations to be sped up by a quantum computer, thus one must carefully identify areas where quantum advantage may be achieved. In this review, we briefly describe central problems in chemistry and materials science, in areas of electronic structure, quantum statistical mechanics, and quantum dynamics that are of potential interest for solution on a quantum computer. We then take a detailed snapshot of current progress in quantum algorithms for ground-state, dynamics, and thermal-state simulation and analyze their strengths and weaknesses for future developments.

Quantum simulations of materials on near-term quantum computers

“…Quantum computers hold promise to enable efficient quantum mechanical simulations of weakly and strongly-correlated molecules and materials alike [8][9][10][11][12][13][14][15][16][17] ; in particular when using quantum computers, one is able to simulate systems of interacting electrons exponentially faster than using classical computers. Thanks to decades of successful experimental efforts, we are now entering the noisy intermediate-scale quantum (NISQ) era 18 , with quantum computers expected to have on the order of 100 quantum bits (qubits); unfortunately this limited number of qubits still prevents straightforward quantum simulations of realistic molecules and materials, whose description requires hundreds of atoms and thousands to millions of degrees of freedom to represent the electronic wavefunctions.…”

Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus

“…In recent years, hybrid quantum-classical algorithms are widely used in quantum chemistry [1][2][3][4], combinatorial optimization [5,6], and quantum machine learning [7][8][9][10][11][12]. In these hybrid quantumclassical algorithms, the goal is usually training parameterized quantum circuits (PQCs) with classical optimizers.…”

Qubit-efficient encoding schemes for binary optimisation problems

“…Going back to the example, x 3 is now connected to x 4 where the probabilities were ini-tiallyP 3,4 = (0.1, 0, 0, 0.9). Since the probability to sample x 3 = {0, 1} have been modified as exemplified in (3),P 3,4 is re-evaluated to (0.04, 0, 0, 0.96).…”

“…In recent years, important experimental breakthroughs have propelled quantum computing as one of the most thriving fields of research [3,8,44,48], with the long-term goal of building universal quantum computers capable of running algorithms with provable quantum speed-up [19,45]. As the first generations of quantum hardware, referred to as noisy intermediate-scale quantum (NISQ) devices [40], do not yet fulfill the technical requirements to implement error-corrected universal quantum computing, increasing efforts are dedicated to design near-term algorithms capable of performing computational tasks with imperfect and limited quantum resources [4,31]. Amongst the most promising paradigms are the variational quantum algorithms (VQA) [13,22,33,35,38].…”