Ground-State Preparation and Energy Estimation on Early Fault-Tolerant Quantum Computers via Quantum Eigenvalue Transformation of Unitary Matrices
Abstract
Under suitable assumptions, some recently developed quantum algorithms can estimate the ground-state energy and prepare the ground state of a quantum Hamiltonian with near-optimal query complexities. However, this is based on a block-encoding input model of the Hamiltonian, the implementation of which is known to require a large resource overhead. We develop a tool called quantum eigenvalue transformation of unitary matrices with real polynomials (QETU), which uses a controlled Hamiltonian evolution as the input model, a single ancilla qubit, and no multiqubit control operations and is thus suitable for early fault-tolerant quantum devices. This leads to a simple quantum algorithm that outperforms all previous algorithms with a comparable circuit structure for estimating the ground-state energy. For a class of quantum spin Hamiltonians, we propose a new method that exploits certain anticommutation relations and further removes the need to implement the controlled Hamiltonian evolution. Coupled with a Trotter-based approximation of the Hamiltonian evolution, the resulting algorithm can be very suitable for early fault-tolerant quantum devices. We demonstrate the performance of the algorithm using IBM qiskit for the transverse-field Ising model. If we are further allowed to use multiqubit Toffoli gates, we can then implement amplitude amplification and a new binary amplitude-estimationmore »
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); National Science Foundation (NSF); Google Quantum Research Award; Simons Foundation
- OSTI Identifier:
- 1892087
- Alternate Identifier(s):
- OSTI ID: 1994341
- Grant/Contract Number:
- AC02-05CH11231; OMA-2016245
- Resource Type:
- Published Article
- Journal Name:
- PRX Quantum
- Additional Journal Information:
- Journal Name: PRX Quantum Journal Volume: 3 Journal Issue: 4; Journal ID: ISSN 2691-3399
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; quantum algorithms; quantum computation; quantum simulation
Citation Formats
Dong, Yulong, Lin, Lin, and Tong, Yu. Ground-State Preparation and Energy Estimation on Early Fault-Tolerant Quantum Computers via Quantum Eigenvalue Transformation of Unitary Matrices. United States: N. p., 2022.
Web. doi:10.1103/PRXQuantum.3.040305.
Dong, Yulong, Lin, Lin, & Tong, Yu. Ground-State Preparation and Energy Estimation on Early Fault-Tolerant Quantum Computers via Quantum Eigenvalue Transformation of Unitary Matrices. United States. https://doi.org/10.1103/PRXQuantum.3.040305
Dong, Yulong, Lin, Lin, and Tong, Yu. Wed .
"Ground-State Preparation and Energy Estimation on Early Fault-Tolerant Quantum Computers via Quantum Eigenvalue Transformation of Unitary Matrices". United States. https://doi.org/10.1103/PRXQuantum.3.040305.
@article{osti_1892087,
title = {Ground-State Preparation and Energy Estimation on Early Fault-Tolerant Quantum Computers via Quantum Eigenvalue Transformation of Unitary Matrices},
author = {Dong, Yulong and Lin, Lin and Tong, Yu},
abstractNote = {Under suitable assumptions, some recently developed quantum algorithms can estimate the ground-state energy and prepare the ground state of a quantum Hamiltonian with near-optimal query complexities. However, this is based on a block-encoding input model of the Hamiltonian, the implementation of which is known to require a large resource overhead. We develop a tool called quantum eigenvalue transformation of unitary matrices with real polynomials (QETU), which uses a controlled Hamiltonian evolution as the input model, a single ancilla qubit, and no multiqubit control operations and is thus suitable for early fault-tolerant quantum devices. This leads to a simple quantum algorithm that outperforms all previous algorithms with a comparable circuit structure for estimating the ground-state energy. For a class of quantum spin Hamiltonians, we propose a new method that exploits certain anticommutation relations and further removes the need to implement the controlled Hamiltonian evolution. Coupled with a Trotter-based approximation of the Hamiltonian evolution, the resulting algorithm can be very suitable for early fault-tolerant quantum devices. We demonstrate the performance of the algorithm using IBM qiskit for the transverse-field Ising model. If we are further allowed to use multiqubit Toffoli gates, we can then implement amplitude amplification and a new binary amplitude-estimation algorithm, which increases the circuit depth but decreases the total query complexity. The resulting algorithm saturates the near-optimal complexity for ground-state preparation and energy estimation using a constant number of ancilla qubits (no more than three).},
doi = {10.1103/PRXQuantum.3.040305},
journal = {PRX Quantum},
number = 4,
volume = 3,
place = {United States},
year = {Wed Oct 12 00:00:00 EDT 2022},
month = {Wed Oct 12 00:00:00 EDT 2022}
}
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