Computing Ground State Properties with Early Fault-Tolerant Quantum Computers

Ruizhe Zhang1, Guoming Wang2, and Peter Johnson2

1Department of Computer Science, The University of Texas at Austin, Austin, TX 78712, USA.
2Zapata Computing Inc., Boston, MA 02110, USA.

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Abstract

Significant effort in applied quantum computing has been devoted to the problem of ground state energy estimation for molecules and materials. Yet, for many applications of practical value, additional properties of the ground state must be estimated. These include Green's functions used to compute electron transport in materials and the one-particle reduced density matrices used to compute electric dipoles of molecules. In this paper, we propose a quantum-classical hybrid algorithm to efficiently estimate such ground state properties with high accuracy using low-depth quantum circuits. We provide an analysis of various costs (circuit repetitions, maximal evolution time, and expected total runtime) as a function of target accuracy, spectral gap, and initial ground state overlap. This algorithm suggests a concrete approach to using early fault tolerant quantum computers for carrying out industry-relevant molecular and materials calculations.

Previously, there was no known way to use a near-term quantum computer to reliably compute many useful properties of quantum materials or molecules. Existing methods were either not reliable or not possible with a near-term quantum computer. This paper proposes a reliable, near-term method for computing useful properties beyond just the ground state energy of a Hamiltonian. Major applications of this work include the design of materials and molecules and solving linear systems of equations.

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Cited by

[1] Pablo A. M. Casares, Roberto Campos, and M. A. Martin-Delgado, "TFermion: A non-Clifford gate cost assessment library of quantum phase estimation algorithms for quantum chemistry", Quantum 6, 768 (2022).

[2] Yu Tong, "Designing algorithms for estimating ground state properties on early fault-tolerant quantum computers", Quantum Views 6, 65 (2022).

[3] Yulong Dong, Lin Lin, and Yu Tong, "Ground state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices", arXiv:2204.05955.

[4] Peter D. Johnson, Alexander A. Kunitsa, Jérôme F. Gonthier, Maxwell D. Radin, Corneliu Buda, Eric J. Doskocil, Clena M. Abuan, and Jhonathan Romero, "Reducing the cost of energy estimation in the variational quantum eigensolver algorithm with robust amplitude estimation", arXiv:2203.07275.

[5] Guoming Wang, Sukin Sim, and Peter D. Johnson, "State Preparation Boosters for Early Fault-Tolerant Quantum Computation", arXiv:2202.06978.

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