Simulating quantum materials with digital quantum computers

Abstract

Quantum materials exhibit a wide array of exotic phenomena and practically useful properties. A better understanding of these materials can provide deeper insights into fundamental physics in the quantum realm as well as advance information processing technology and sustainability. The emergence of digital quantum computers (DQCs), which can efficiently perform quantum simulations that are otherwise intractable on classical computers, provides a promising path forward for testing and analyzing the remarkable, and often counter-intuitive, behavior of quantum materials. Equipped with these new tools, scientists from diverse domains are racing towards achieving physical quantum advantage (i.e. using a quantum computer to learn new physics with a computation that cannot feasibly be run on any classical computer). The aim of this review, therefore, is to provide a summary of progress made towards this goal that is accessible to scientists across the physical sciences. We will first review the available technology and algorithms, and detail the myriad ways to represent materials on quantum computers. Next, we will showcase the simulations that have been successfully performed on currently available DQCs, emphasizing the variety of properties, both static and dynamic, that can be studied with this nascent technology. Finally, we work through three examples of how to perform various materials simulation problems on DQCs, with full code included in the supplementary material (https://stacks.iop.org/QST/6/043002/mmedia). It is our hope that this review can serve as an organized overview of progress in the field for domain experts and an accessible introduction to scientists in related fields interested in beginning to perform their own simulations of quantum materials on DQCs.

MISTIQS: An open-source software for performing quantum dynamics simulations on quantum computers

“…In addition, MISTIQS also includes a domain-specific quantum circuit compiler for simulating a subgroup of the Heisenberg model known as the transverse field Ising model (TFIM) [22]. By lowering the gate count of the circuits for simulating the many-body dynamics, this special-purpose compiler allows for more accurate, longer-time simulations by reducing the compounding gate error [14], while also significantly reducing the wall-clock compilation time over backend-native general-purpose compilers.…”

Compact Molecular Simulation on Quantum Computers via Combinatorial Mapping and Variational State Preparation

“…Quantum computers promise to provide an advantage in chemistry and material simulation as molecular orbitals can be mapped to qubits [1][2][3]. This advantage is limited in the near term by the number of qubits and the quantity of operations required to capture correlation in the electronic wave function.…”

Mapping the metal-insulator phase diagram by algebraically fast-forwarding dynamics on a cloud quantum computer

“…In contrast, Shor's algorithm [1] for factoring large numbers will require thousands of nearly-noiseless qubits to become practically useful. Proposals for simulating correlated fermionic systems using quantum computers exist [2][3][4][5][6][7] but relatively few have been implemented or tested due to the noise of current devices [8][9][10].…”