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Filip MA. Fighting Noise with Noise: A Stochastic Projective Quantum Eigensolver. J Chem Theory Comput 2024; 20:5964-5981. [PMID: 38954827 PMCID: PMC11270749 DOI: 10.1021/acs.jctc.4c00295] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2024] [Revised: 06/13/2024] [Accepted: 06/14/2024] [Indexed: 07/04/2024]
Abstract
In the current noisy intermediate scale quantum era of quantum computation, available hardware is severely limited by both qubit count and noise levels, precluding the application of many current hybrid quantum-classical algorithms to nontrivial quantum chemistry problems. In this paper we propose applying some of the fundamental ideas of conventional Quantum Monte Carlo algorithms─stochastic sampling of both the wave function and the Hamiltonian─to quantum algorithms in order to significantly decrease quantum resource costs. In the context of an imaginary-time propagation based projective quantum eigensolver, we present a novel approach to estimating physical observables which can lead to an order of magnitude reduction in the required sampling of the quantum state to converge the ground state energy of a system relative to current state-of-the-art eigensolvers. The method can be equally applied to excited-state calculations and, combined with stochastic approximations of the system Hamiltonian, provides a promising near-term approach to Hamiltonian simulation for general chemistry on quantum devices.
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Affiliation(s)
- Maria-Andreea Filip
- Yusuf Hamied Department of
Chemistry, University of Cambridge, Cambridge CB2 1EW, U.K.
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2
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Sukurma Z, Schlipf M, Humer M, Taheridehkordi A, Kresse G. Toward Large-Scale AFQMC Calculations: Large Time Step Auxiliary-Field Quantum Monte Carlo. J Chem Theory Comput 2024; 20:4205-4217. [PMID: 38750634 PMCID: PMC11137827 DOI: 10.1021/acs.jctc.4c00304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2024] [Revised: 04/29/2024] [Accepted: 05/06/2024] [Indexed: 05/29/2024]
Abstract
We report modifications of the ph-AFQMC algorithm that allow the use of large time steps and reliable time step extrapolation. Our modified algorithm eliminates size-consistency errors present in the standard algorithm when large time steps are employed. We investigate various methods to approximate the exponential of the one-body operator within the AFQMC framework, distinctly demonstrating the superiority of Krylov methods over the conventional Taylor expansion. We assess various propagators within AFQMC and demonstrate that the Split-2 propagator is the optimal method, exhibiting the smallest time-step errors. For the HEAT set molecules, the time-step extrapolated energies deviate on average by only 0.19 kcal/mol from the accurate small time-step energies. For small water clusters, we obtain accurate complete basis-set binding energies using time-step extrapolation with a mean absolute error of 0.07 kcal/mol compared to CCSD(T). Using large time-step ph-AFQMC for the N2 dimer, we show that accurate bond lengths can be obtained while reducing CPU time by an order of magnitude.
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Affiliation(s)
- Zoran Sukurma
- University
of Vienna, Faculty of Physics and Center for Computational Materials
Science, Kolingasse 14-16, A-1090 Vienna, Austria
- University
of Vienna, Faculty of Physics
& Vienna Doctoral School in Physics, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Martin Schlipf
- VASP
Software GmbH, Berggasse
21/14, 1090 Vienna, Austria
| | - Moritz Humer
- University
of Vienna, Faculty of Physics and Center for Computational Materials
Science, Kolingasse 14-16, A-1090 Vienna, Austria
- University
of Vienna, Faculty of Physics
& Vienna Doctoral School in Physics, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Amir Taheridehkordi
- University
of Vienna, Faculty of Physics and Center for Computational Materials
Science, Kolingasse 14-16, A-1090 Vienna, Austria
| | - Georg Kresse
- University
of Vienna, Faculty of Physics and Center for Computational Materials
Science, Kolingasse 14-16, A-1090 Vienna, Austria
- VASP
Software GmbH, Sensengasse
8, 1090 Vienna, Austria
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3
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Magoulas I, Evangelista FA. Unitary Coupled Cluster: Seizing the Quantum Moment. J Phys Chem A 2023; 127:6567-6576. [PMID: 37523485 PMCID: PMC10424243 DOI: 10.1021/acs.jpca.3c02781] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2023] [Revised: 07/08/2023] [Indexed: 08/02/2023]
Abstract
Shallow, CNOT-efficient quantum circuits are crucial for performing accurate computational chemistry simulations on current noisy quantum hardware. Here, we explore the usefulness of noniterative energy corrections, based on the method of moments of coupled-cluster theory, for accelerating convergence toward full configuration interaction. Our preliminary numerical results relying on iteratively constructed ansätze suggest that chemically accurate energies can be obtained with substantially more compact circuits, implying enhanced resilience to gate and decoherence noise.
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Affiliation(s)
- Ilias Magoulas
- Department of Chemistry and
Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Francesco A. Evangelista
- Department of Chemistry and
Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
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4
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Magoulas I, Evangelista FA. Linear-Scaling Quantum Circuits for Computational Chemistry. J Chem Theory Comput 2023; 19:4815-4821. [PMID: 37410884 PMCID: PMC10413858 DOI: 10.1021/acs.jctc.3c00376] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2023] [Indexed: 07/08/2023]
Abstract
We have recently constructed compact, CNOT-efficient, quantum circuits for Fermionic and qubit excitations of arbitrary many-body rank [Magoulas, I.; Evangelista, F. A. J. Chem. Theory Comput. 2023, 19, 822]. Here, we present approximations of these circuits that substantially reduce the CNOT counts even further. Our preliminary numerical data, using the selected projective quantum eigensolver approach, show up to a 4-fold reduction in CNOTs. At the same time, there is practically no loss of accuracy in the energies compared to the parent implementation, while the ensuing symmetry breaking is essentially negligible.
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Affiliation(s)
- Ilias Magoulas
- Department of Chemistry and
Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Francesco A. Evangelista
- Department of Chemistry and
Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
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5
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Magoulas I, Evangelista FA. CNOT-Efficient Circuits for Arbitrary Rank Many-Body Fermionic and Qubit Excitations. J Chem Theory Comput 2023; 19:822-836. [PMID: 36656643 DOI: 10.1021/acs.jctc.2c01016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
Efficient quantum circuits are necessary for realizing quantum algorithms on noisy intermediate-scale quantum devices. Fermionic excitations entering unitary coupled-cluster (UCC) ansätze give rise to quantum circuits containing CNOT "staircases" whose number scales exponentially with the excitation rank. Recently, Yordanov et al. [Phys. Rev. A102, 062612 (2020); Commun. Phys.4, 228 (2021)] constructed CNOT-efficient quantum circuits for both Fermionic- (FEB) and qubit-excitation-based (QEB) singles and doubles and illustrated their usefulness in adaptive derivative-assembled pseudo-Trotterized variational quantum eigensolver (ADAPT-VQE) simulations. In this work, we extend these CNOT-efficient quantum circuits to arbitrary excitation ranks. To illustrate the benefits of these compact FEB and QEB quantum circuits, we perform numerical simulations using the recently developed selected projective quantum eigensolver (SPQE) approach, which relies on an adaptive UCC ansatz built from arbitrary-order particle-hole excitation operators. We show that both FEB- and QEB-SPQE decrease the number of CNOT gates compared to traditional SPQE by factors as large as 15. At the same time, QEB-SPQE requires, in general, more ansatz parameters than FEB-SPQE, in particular those corresponding to higher-than-double excitations, resulting in quantum circuits with larger CNOT counts. Although ADAPT-VQE generates quantum circuits with fewer CNOTs than SPQE, SPQE requires orders of magnitude less residual element evaluations than gradient element evaluations in ADAPT-VQE.
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Affiliation(s)
- Ilias Magoulas
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia30322, United States
| | - Francesco A Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia30322, United States
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Choy B, Wales DJ. Molecular Energy Landscapes of Hardware-Efficient Ansätze in Quantum Computing. J Chem Theory Comput 2023; 19:1197-1206. [PMID: 36749922 PMCID: PMC9979602 DOI: 10.1021/acs.jctc.2c01057] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/09/2023]
Abstract
Rapid advances in quantum computing have opened up new opportunities for solving the central electronic structure problem in computational chemistry. In the noisy intermediate-scale quantum (NISQ) era, where qubit coherence times are limited, it is essential to exploit quantum algorithms with sufficiently short quantum circuits to maximize qubit efficiency. The procedural construction of hardware-efficient ansätze provides one approach to design such circuits. However, refining the accuracy of the global minimum by increasing circuit depth may lead to a proliferation of local minima that hinders global optimization. To investigate this phenomenon, we explore the energy landscapes of hardware-efficient circuits to identify ground-state energies of the hydrogen, lithium hydride, and beryllium hydride molecules. We also propose a simple dimensionality reduction procedure that reduces quantum gate depth while retaining high accuracy for the global minimum, simplifying the energy landscape, and hence speeding up optimization from both software and hardware perspectives.
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Affiliation(s)
- Boy Choy
- School
of Chemistry, Chemical Engineering and Biotechnology, Nanyang Technological University, Block N1.2, B3-13, 62 Nanyang Drive, Singapore 637459,
| | - David J. Wales
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield
Road, Cambridge CB2 1EW, United Kingdom
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7
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Filip MA, Thom AJW. Erratum: "A stochastic approach to unitary coupled cluster" [J. Chem. Phys. 153, 214106 (2020)]. J Chem Phys 2022; 156:229902. [PMID: 35705401 DOI: 10.1063/5.0098911] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Alex J W Thom
- Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
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8
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Liu J, Matthews DA, Cheng L. Quadratic Unitary Coupled-Cluster Singles and Doubles Scheme: Efficient Implementation, Benchmark Study, and Formulation of an Extended Version. J Chem Theory Comput 2022; 18:2281-2291. [PMID: 35312299 DOI: 10.1021/acs.jctc.1c01210] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
An efficient implementation of the quadratic unitary coupled-cluster singles and doubles (qUCCSD) scheme for calculations of electronic ground and excited states using an unrestricted molecular spin-orbital formulation and an efficient tensor contraction library is reported. The accuracy of the qUCCSD scheme and the efficiency of the present implementation are demonstrated using extensive benchmark calculations of excitation energies and an application to S0 → S1 vertical excitation energies for cis- and trans-4a,4b-dihydrotriphenylene. The qUCCSD scheme has been shown to provide improved excitation energies compared with the UCC3 scheme formulated based on perturbation theory. A UCC truncation scheme that can provide excitation energies correct through the fourth order is also presented to further improve the accuracy of the qUCCSD scheme.
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Affiliation(s)
- Junzi Liu
- School of Chemistry and Biological Engineering, University of Science and Technology Beijing, Beijing, 100083, China
| | - Devin A Matthews
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States
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Anand A, Schleich P, Alperin-Lea S, Jensen PWK, Sim S, Díaz-Tinoco M, Kottmann JS, Degroote M, Izmaylov AF, Aspuru-Guzik A. A quantum computing view on unitary coupled cluster theory. Chem Soc Rev 2022; 51:1659-1684. [PMID: 35166276 DOI: 10.1039/d1cs00932j] [Citation(s) in RCA: 47] [Impact Index Per Article: 23.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
We present a review of the Unitary Coupled Cluster (UCC) ansatz and related ansätze which are used to variationally solve the electronic structure problem on quantum computers. A brief history of coupled cluster (CC) methods is provided, followed by a broad discussion of the formulation of CC theory. This includes touching on the merits and difficulties of the method and several variants, UCC among them, in the classical context, to motivate their applications on quantum computers. In the core of the text, the UCC ansatz and its implementation on a quantum computer are discussed at length, in addition to a discussion on several derived and related ansätze specific to quantum computing. The review concludes with a unified perspective on the discussed ansätze, attempting to bring them under a common framework, as well as with a reflection upon open problems within the field.
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Affiliation(s)
- Abhinav Anand
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
| | - Philipp Schleich
- Department of Computer Science, University of Toronto, 214 College St, Toronto, ONM5T 3A1, Canada. .,Applied and Computational Mathematics, Department of Mathematics, RWTH Aachen University, Aachen, Germany.,Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, Ontario M5G 1M1, Canada
| | - Sumner Alperin-Lea
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
| | - Phillip W K Jensen
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
| | - Sukin Sim
- Department of Chemistry and Chemical Biology, Harvard University, USA
| | - Manuel Díaz-Tinoco
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada. .,Department of Physical and Environmental Sciences, University of Toronto Scarborough, Canada
| | - Jakob S Kottmann
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada. .,Department of Computer Science, University of Toronto, 214 College St, Toronto, ONM5T 3A1, Canada.
| | - Matthias Degroote
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada. .,Department of Computer Science, University of Toronto, 214 College St, Toronto, ONM5T 3A1, Canada.
| | - Artur F Izmaylov
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada. .,Department of Physical and Environmental Sciences, University of Toronto Scarborough, Canada
| | - Alán Aspuru-Guzik
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada. .,Department of Computer Science, University of Toronto, 214 College St, Toronto, ONM5T 3A1, Canada. .,Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, Ontario M5G 1M1, Canada.,Lebovic Fellow, Canadian Institute for Advanced Research (CIFAR), 661 University Ave., Toronto, ON M5G 1M1, Canada
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10
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Liu J, Cheng L. Unitary coupled-cluster based self-consistent polarization propagator theory: A quadratic unitary coupled-cluster singles and doubles scheme. J Chem Phys 2021; 155:174102. [PMID: 34742195 DOI: 10.1063/5.0062090] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The development of a quadratic unitary coupled-cluster singles and doubles (qUCCSD) based self-consistent polarization propagator method is reported. We present a simple strategy for truncating the commutator expansion of the unitary version of coupled-cluster transformed Hamiltonian H̄. The qUCCSD method for the electronic ground state includes up to double commutators for the amplitude equations and up to cubic commutators for the energy expression. The qUCCSD excited-state eigenvalue equations include up to double commutators for the singles-singles block of H̄, single commutators for the singles-doubles and doubles-singles blocks, and the bare Hamiltonian for the doubles-doubles block. Benchmark qUCCSD calculations of the ground-state properties and excitation energies for representative molecules demonstrate significant improvement of the accuracy and robustness over the previous UCC3 scheme derived using Møller-Plesset perturbation theory.
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Affiliation(s)
- Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
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11
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Morales-Silva MA, Jordan KD, Shulenburger L, Wagner LK. Frontiers of stochastic electronic structure calculations. J Chem Phys 2021; 154:170401. [PMID: 34241059 DOI: 10.1063/5.0053674] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In recent years there has been a rapid growth in the development and application of new stochastic methods in electronic structure. These methods are quite diverse, from many-body wave function techniques in real space or determinant space to being used to sum perturbative expansions. This growth has been spurred by the more favorable scaling with the number of electrons and often better parallelization over large numbers of central processing unit (CPU) cores or graphical processing units (GPUs) than for high-end non-stochastic wave function based methods. This special issue of the Journal of Chemical Physics includes 33 papers that describe recent developments and applications in this area. As seen from the articles in the issue, stochastic electronic structure methods are applicable to both molecules and solids and can accurately describe systems with strong electron correlation. This issue was motivated, in part, by the 2019 Telluride Science Research Center workshop on Stochastic Electronic Structure Methods that we organized. Below we briefly describe each of the papers in the special issue, dividing the papers into six subtopics.
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Affiliation(s)
- Miguel A Morales-Silva
- Quantum Simulations Group, Lawrence Livermore National Laboratory, Livermore, California 94551, USA
| | - Kenneth D Jordan
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Luke Shulenburger
- HEDP Theory Department, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Lucas K Wagner
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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