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 technology for entertainment, healthcare, 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 two examples of how to map a materials problem onto a DQC, with full code included in the Supplementary Material. 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.

46 pages, 6 figures, 1 table, Topical Review

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• Constant-Depth Circuits for Dynamic Simulations of Materials on Quantum Computers
• Avoiding symmetry roadblocks and minimizing the measurement overhead of adaptive variational quantum eigensolvers
• An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation
• Demonstration of a parity-time symmetry breaking phase transition using superconducting and trapped-ion qutrits
• Activating non-Hermitian skin modes by parity-time symmetry breaking
• Observing and braiding topological Majorana modes on programmable quantum simulators
• Adaptive variational simulation for open quantum systems
• Quantum computing critical exponents
• First-Order Phase Transition of the Schwinger Model with a Quantum Computer
• Variational dynamics as a ground-state problem on a quantum computer
• Extension of the Trotterized Unitary Coupled Cluster to Triple Excitations
• Dynamic Cooling on Contemporary Quantum Computers
• Narrow-line cooling of ${}^{87}$Rb using 5S${}_{1/2}\to$ 6P${}_{3/2}$ open transition at 420 nm
• EHA: Entanglement-variational Hardware-efficient Ansatz for Eigensolvers
• Trotter error with commutator scaling for the Fermi-Hubbard model
• Randomized measurement protocols for lattice gauge theories
• Quantum subspace expansion in the presence of hardware noise
• Workflow for practical quantum chemical calculations with quantum phase estimation algorithm: electronic ground and π-π* excited states of benzene and its derivatives†
• Real-time simulation of light-driven spin chains on quantum computers
• A Quantum Simulation Approach to Implementing Nuclear Density Functional Theory via Imaginary Time Evolution
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• Shaping Magnetic Order by Local Frustration for Itinerant Fermions on a Graph
• Toward Density Functional Theory on Quantum Computers?
• Variational decision diagrams for quantum-inspired machine learning applications
• Quantum-Classical Computing for Time-Dependent Ion-Atom Collision Dynamics: Applications to Charge Transfer Cross Section Simulations