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arXiv:2307.14607 · Physical Review Research

Demonstrating quantum computation for quasiparticle band structures

Takahiro Ohgoe, Hokuto Iwakiri, Masaya Kohda, Kazuhide Ichikawa, Yuya O. Nakagawa, Hubert Valencia, Sho Koh

Published Apr 25, 2024• 6 citations
arXivHTMLPDF

Abstract

Understanding and predicting the properties of solid-state materials from first principles has been a great challenge for decades. Owing to the recent advances in quantum technologies, quantum computations offer a promising way to achieve this goal. Here, we demonstrate the first-principles calculation of a quasiparticle band structure on actual quantum computers. This is achieved by hybrid quantum-classical algorithms in conjunction with qubit-reduction and error-mitigation techniques. Our demonstration will pave the way to practical applications of quantum computers. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.l022022

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Quasiparticle band structures are fundamental for understanding strongly correlated electron systems. While solving these structures accurately on classical computers is challenging, quantum computing offers a promising alternative. Specifically, the quantum subspace expansion (QSE) method, combined with the variational quantum eigensolver (VQE), provides a quantum algorithm for calculating quasiparticle band structures. However, optimizing the variational parameters in VQE becomes increasingly difficult as the system size grows, due to device noise, statistical noise, and the barren plateau problem. To address these challenges, we propose a hybrid approach that combines QSE with the quantum-selected configuration interaction (QSCI) method for calculating quasiparticle band structures. QSCI may leverage the VQE ansatz as an input state but, unlike the standard VQE, it does not require full optimization of the variational parameters, making it more scalable for larger quantum systems. Based on this approach, we demonstrate the quantum computation of the quasiparticle band structure of a silicon using 16 qubits on an IBM quantum processor.
Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates these two methods, inheriting their distinct features in efficient representation and manipulation of quantum states and overcoming their limitations. We first introduce non-stoquasticity indicators (NSIs) and their upper bounds, which measure the sign problem, the most notable limitation of QMC. We show that our algorithm could greatly mitigate the sign problem, which decreases NSIs with the assistance of quantum computing. Meanwhile, the use of quantum Monte Carlo also increases the expressivity of shallow quantum circuits, allowing more accurate computation that is conventionally achievable only with much deeper circuits. We numerically test and verify the method for the N2_22​ molecule (12 qubits) and the Hubbard model (16 qubits). Our work paves the way to solving practical problems with intermediate-scale and early-fault tolerant quantum computers, with potential applications in chemistry, condensed matter physics, materials, high energy physics, etc.
Abstract Quantum computers hold promise to enable efficient simulations of the properties of molecules and materials; however, at present they only permit ab initio calculations of a few atoms, due to a limited number of qubits. In order to harness the power of near-term quantum computers for simulations of larger systems, it is desirable to develop hybrid quantum-classical methods where the quantum computation is restricted to a small portion of the system. This is of particular relevance for molecules and solids where an active region requires a higher level of theoretical accuracy than its environment. Here, we present a quantum embedding theory for the calculation of strongly-correlated electronic states of active regions, with the rest of the system described within density functional theory. We demonstrate the accuracy and effectiveness of the approach by investigating several defect quantum bits in semiconductors that are of great interest for quantum information technologies. We perform calculations on quantum computers and show that they yield results in agreement with those obtained with exact diagonalization on classical architectures, paving the way to simulations of realistic materials on near-term 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.