1
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Rocca D, Cortes CL, Gonthier JF, Ollitrault PJ, Parrish RM, Anselmetti GL, Degroote M, Moll N, Santagati R, Streif M. Reducing the Runtime of Fault-Tolerant Quantum Simulations in Chemistry through Symmetry-Compressed Double Factorization. J Chem Theory Comput 2024; 20:4639-4653. [PMID: 38788209 PMCID: PMC11403611 DOI: 10.1021/acs.jctc.4c00352] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/26/2024]
Abstract
Quantum phase estimation based on qubitization is the state-of-the-art fault-tolerant quantum algorithm for computing ground-state energies in chemical applications. In this context, the 1-norm of the Hamiltonian plays a fundamental role in determining the total number of required iterations and also the overall computational cost. In this work, we introduce the symmetry-compressed double factorization (SCDF) approach, which combines a CDF of the Hamiltonian with the symmetry shift technique, significantly reducing the 1-norm value. The effectiveness of this approach is demonstrated numerically by considering various benchmark systems, including the FeMoco molecule, cytochrome P450, and hydrogen chains of different sizes. To compare the efficiency of SCDF to other methods in absolute terms, we estimate Toffoli gate requirements, which dominate the execution time on fault-tolerant quantum computers. For the systems considered here, SCDF leads to a sizable reduction of the Toffoli gate count in comparison to other variants of DF or even tensor hypercontraction, which is usually regarded as the most efficient approach for qubitization.
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Affiliation(s)
- Dario Rocca
- QC Ware Corporation, Palo Alto, California 94306, United States
| | | | | | | | | | | | - Matthias Degroote
- Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany
| | - Nikolaj Moll
- Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany
| | | | - Michael Streif
- Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany
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2
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Asthana A, Kumar A, Abraham V, Grimsley H, Zhang Y, Cincio L, Tretiak S, Dub PA, Economou SE, Barnes E, Mayhall NJ. Quantum self-consistent equation-of-motion method for computing molecular excitation energies, ionization potentials, and electron affinities on a quantum computer. Chem Sci 2023; 14:2405-2418. [PMID: 36873839 PMCID: PMC9977410 DOI: 10.1039/d2sc05371c] [Citation(s) in RCA: 14] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Accepted: 01/26/2023] [Indexed: 01/30/2023] Open
Abstract
Near-term quantum computers are expected to facilitate material and chemical research through accurate molecular simulations. Several developments have already shown that accurate ground-state energies for small molecules can be evaluated on present-day quantum devices. Although electronically excited states play a vital role in chemical processes and applications, the search for a reliable and practical approach for routine excited-state calculations on near-term quantum devices is ongoing. Inspired by excited-state methods developed for the unitary coupled-cluster theory in quantum chemistry, we present an equation-of-motion-based method to compute excitation energies following the variational quantum eigensolver algorithm for ground-state calculations on a quantum computer. We perform numerical simulations on H2, H4, H2O, and LiH molecules to test our quantum self-consistent equation-of-motion (q-sc-EOM) method and compare it to other current state-of-the-art methods. q-sc-EOM makes use of self-consistent operators to satisfy the vacuum annihilation condition, a critical property for accurate calculations. It provides real and size-intensive energy differences corresponding to vertical excitation energies, ionization potentials and electron affinities. We also find that q-sc-EOM is more suitable for implementation on NISQ devices as it is expected to be more resilient to noise compared with the currently available methods.
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Affiliation(s)
- Ayush Asthana
- Department of Chemistry, Virginia Tech Blacksburg 24061 VA USA
- Virginia Tech Center for Quantum Information Science and Engineering Blacksburg 24061 VA USA
| | - Ashutosh Kumar
- Theoretical Division, Los Alamos National Laboratory Los Alamos 87545 NM USA
| | - Vibin Abraham
- Department of Chemistry, University of Michigan Ann Arbor 48109 MI USA
| | - Harper Grimsley
- Department of Chemistry, Virginia Tech Blacksburg 24061 VA USA
- Virginia Tech Center for Quantum Information Science and Engineering Blacksburg 24061 VA USA
| | - Yu Zhang
- Theoretical Division, Los Alamos National Laboratory Los Alamos 87545 NM USA
| | - Lukasz Cincio
- Theoretical Division, Los Alamos National Laboratory Los Alamos 87545 NM USA
| | - Sergei Tretiak
- Theoretical Division, Los Alamos National Laboratory Los Alamos 87545 NM USA
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory Los Alamos 87545 NM USA
| | - Pavel A Dub
- Chemistry Division, Los Alamos National Laboratory Los Alamos 87545 NM USA
| | - Sophia E Economou
- Department of Physics, Virginia Tech Blacksburg 24061 VA USA
- Virginia Tech Center for Quantum Information Science and Engineering Blacksburg 24061 VA USA
| | - Edwin Barnes
- Department of Physics, Virginia Tech Blacksburg 24061 VA USA
- Virginia Tech Center for Quantum Information Science and Engineering Blacksburg 24061 VA USA
| | - Nicholas J Mayhall
- Department of Chemistry, Virginia Tech Blacksburg 24061 VA USA
- Virginia Tech Center for Quantum Information Science and Engineering Blacksburg 24061 VA USA
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3
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Ryabinkin IG, Jena AJ, Genin SN. Efficient Construction of Involutory Linear Combinations of Anticommuting Pauli Generators for Large-Scale Iterative Qubit Coupled Cluster Calculations. J Chem Theory Comput 2023; 19:1722-1733. [PMID: 36820812 DOI: 10.1021/acs.jctc.2c01155] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/24/2023]
Abstract
We present an efficient method for construction of a fully anticommutative set of Pauli generators (elements of the Pauli group) from a commutative set of operators that are composed exclusively from Pauli x̂ operators (purely X generators) and sorted by an associated numerical measure, such as absolute energy gradients. Our approach uses the Gauss-Jordan elimination applied to a binary matrix that encodes the set of X generators to bring it to the reduced row-echelon form, followed by the construction of an anticommutative system in a standard basis by means of a modified Jordan-Wigner transformation and returning to the original basis. The algorithm complexity is linear in the size of the X set and quadratic in the number of qubits. The resulting anticommutative sets are used to construct the qubit coupled cluster Ansatz with involutory linear combinations of anticommuting Paulis (QCC-ILCAP) proposed in J. Chem. Theory Comput. 2021, 17 (1), 66-78. We applied the iterative qubit coupled cluster method with the QCC-ILCAP Ansatz to calculations of ground-state potential energy curves for symmetric stretching of the water molecule (36 qubits) and dissociation of N2 (56 qubits).
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Affiliation(s)
- Ilya G Ryabinkin
- OTI Lumionics Inc., 3415 American Drive Unit 1, Mississauga, Ontario L4V 1T4, Canada
| | - Andrew J Jena
- Combinatorics & Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Scott N Genin
- OTI Lumionics Inc., 3415 American Drive Unit 1, Mississauga, Ontario L4V 1T4, Canada
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4
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Kang C, Bauman NP, Krishnamoorthy S, Kowalski K. Optimized Quantum Phase Estimation for Simulating Electronic States in Various Energy Regimes. J Chem Theory Comput 2022; 18:6567-6576. [PMID: 36201845 DOI: 10.1021/acs.jctc.2c00577] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
While quantum algorithms for simulations exhibit better asymptotic scaling than their classical counterparts, they currently cannot be accurately implemented on real-world devices. Instead, chemists and computer scientists rely on costly classical simulations of these quantum algorithms. In particular, the quantum phase estimation (QPE) algorithm is among several approaches that has attracted much attention in recent years due to its genuine quantum character. However, it is memory-intensive to simulate and intractable for moderate system sizes. This paper discusses the performance and applicability of QPESIM, a new simulation of the QPE algorithm designed to take advantage of modest computational resources. In particular, we demonstrate the versatility of QPESIM in simulating various electronic states by examining the ground and core-level states of H2O. For these states, we also discuss the effect of the active-space size on the quality of the calculated energies. For the high-energy core-level states, we demonstrate that new QPE simulations for active spaces defined by 15 active orbitals significantly reduce the errors in core-level excitation energies compared to earlier QPE simulations using smaller active spaces.
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Affiliation(s)
- Christopher Kang
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington99354, United States.,University of Washington, Seattle, Washington98195, United States
| | - Nicholas P Bauman
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington99354, United States
| | - Sriram Krishnamoorthy
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington99354, United States
| | - Karol Kowalski
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington99354, United States
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5
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Reliably assessing the electronic structure of cytochrome P450 on today's classical computers and tomorrow's quantum computers. Proc Natl Acad Sci U S A 2022; 119:e2203533119. [PMID: 36095200 PMCID: PMC9499570 DOI: 10.1073/pnas.2203533119] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022] Open
Abstract
Chemical simulation is one of the most promising applications for future quantum computers. It is thought that quantum computers may enable accurate simulation for complex molecules that are otherwise impossible to simulate classically; that is, it displays quantum advantage. To better understand quantum advantage in chemical simulation, we explore what quantum and classical resources are required to simulate a series of pharmaceutically relevant molecules. Using classical methods, we show that reliable classical simulation of these molecules requires significant resources and therefore is a promising candidate for quantum simulation. We estimate the quantum resources, both in overall simulation time and the size. The insights from this study pave the way for future quantum simulation of complex molecules. An accurate assessment of how quantum computers can be used for chemical simulation, especially their potential computational advantages, provides important context on how to deploy these future devices. To perform this assessment reliably, quantum resource estimates must be coupled with classical computations attempting to answer relevant chemical questions and to define the classical algorithms simulation frontier. Herein, we explore the quantum computation and classical computation resources required to assess the electronic structure of cytochrome P450 enzymes (CYPs) and thus define a classical–quantum advantage boundary. This is accomplished by analyzing the convergence of density matrix renormalization group plus n-electron valence state perturbation theory (DMRG+NEVPT2) and coupled-cluster singles doubles with noniterative triples [CCSD(T)] calculations for spin gaps in models of the CYP catalytic cycle that indicate multireference character. The quantum resources required to perform phase estimation using qubitized quantum walks are calculated for the same systems. Compilation into the surface code provides runtime estimates to compare directly to DMRG runtimes and to evaluate potential quantum advantage. Both classical and quantum resource estimates suggest that simulation of CYP models at scales large enough to balance dynamic and multiconfigurational electron correlation has the potential to be a quantum advantage problem and emphasizes the important interplay between classical computations and quantum algorithms development for chemical simulation.
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6
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Wan K, Berta M, Campbell ET. Randomized Quantum Algorithm for Statistical Phase Estimation. PHYSICAL REVIEW LETTERS 2022; 129:030503. [PMID: 35905339 DOI: 10.1103/physrevlett.129.030503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Accepted: 06/15/2022] [Indexed: 06/15/2023]
Abstract
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyze a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent of the number of terms L in the Hamiltonian. Second, unlike previous L-independent approaches, such as those based on qDRIFT, all algorithmic errors in our method can be suppressed by collecting more data samples, without increasing the circuit depth.
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Affiliation(s)
- Kianna Wan
- AWS Center for Quantum Computing, Pasadena 91125, USA
- Stanford Institute for Theoretical Physics, Stanford University, Stanford 94305, USA
| | - Mario Berta
- AWS Center for Quantum Computing, Pasadena 91125, USA
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena 91125, USA
- Department of Computing, Imperial College London, London, SW7 2AZ, United Kingdom
| | - Earl T Campbell
- AWS Center for Quantum Computing, Cambridge, CB1 2GA, United Kingdom
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7
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Klco N, Roggero A, Savage MJ. Standard model physics and the digital quantum revolution: thoughts about the interface. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 85:064301. [PMID: 35213853 DOI: 10.1088/1361-6633/ac58a4] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2021] [Accepted: 02/25/2022] [Indexed: 06/14/2023]
Abstract
Advances in isolating, controlling and entangling quantum systems are transforming what was once a curious feature of quantum mechanics into a vehicle for disruptive scientific and technological progress. Pursuing the vision articulated by Feynman, a concerted effort across many areas of research and development is introducing prototypical digital quantum devices into the computing ecosystem available to domain scientists. Through interactions with these early quantum devices, the abstract vision of exploring classically-intractable quantum systems is evolving toward becoming a tangible reality. Beyond catalyzing these technological advances, entanglement is enabling parallel progress as a diagnostic for quantum correlations and as an organizational tool, both guiding improved understanding of quantum many-body systems and quantum field theories defining and emerging from the standard model. From the perspective of three domain science theorists, this article compilesthoughts about the interfaceon entanglement, complexity, and quantum simulation in an effort to contextualize recent NISQ-era progress with the scientific objectives of nuclear and high-energy physics.
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Affiliation(s)
- Natalie Klco
- Institute for Quantum Information and Matter and Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena CA 91125, United States of America
| | - Alessandro Roggero
- InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, Seattle, WA 98195, United States of America
| | - Martin J Savage
- InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, Seattle, WA 98195, United States of America
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8
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Motta M, Rice JE. Emerging quantum computing algorithms for quantum chemistry. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1580] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Mario Motta
- IBM Quantum, IBM Research‐Almaden San Jose California USA
| | - Julia E. Rice
- IBM Quantum, IBM Research‐Almaden San Jose California USA
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9
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Bauman NP, Kowalski K. Coupled Cluster Downfolding Methods: the effect of double commutator terms on the accuracy of ground-state energies. J Chem Phys 2022; 156:094106. [DOI: 10.1063/5.0076260] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Karol Kowalski
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, United States of America
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10
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Bauer B, Bravyi S, Motta M, Chan GKL. Quantum Algorithms for Quantum Chemistry and Quantum Materials Science. Chem Rev 2020; 120:12685-12717. [DOI: 10.1021/acs.chemrev.9b00829] [Citation(s) in RCA: 134] [Impact Index Per Article: 33.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Affiliation(s)
- Bela Bauer
- Microsoft Quantum, Station Q, University of California
, Santa Barbara, California 93106, United States
| | - Sergey Bravyi
- IBM Quantum, IBM T. J. Watson Research Center
, Yorktown Heights, New York 10598, United States
| | - Mario Motta
- IBM Quantum, IBM Research Almaden
, San Jose, California 95120, United States
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology
, Pasadena, California 91125, United States
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11
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Metcalf M, Bauman NP, Kowalski K, de Jong WA. Resource-Efficient Chemistry on Quantum Computers with the Variational Quantum Eigensolver and the Double Unitary Coupled-Cluster Approach. J Chem Theory Comput 2020; 16:6165-6175. [PMID: 32915568 DOI: 10.1021/acs.jctc.0c00421] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Applications of quantum simulation algorithms to obtain electronic energies of molecules on noisy intermediate-scale quantum (NISQ) devices require careful consideration of resources describing the complex electron correlation effects. In modeling second-quantized problems, the biggest challenge confronted is that the number of qubits scales linearly with the size of the molecular basis. This poses a significant limitation on the size of the basis sets and the number of correlated electrons included in quantum simulations of chemical processes. To address this issue and enable more realistic simulations on NISQ computers, we employ the double unitary coupled-cluster (DUCC) method to effectively downfold correlation effects into the reduced-size orbital space, commonly referred to as the active space. Using downfolding techniques, we demonstrate that properly constructed effective Hamiltonians can capture the effect of the whole orbital space in small-size active spaces. Combining the downfolding preprocessing technique with the variational quantum eigensolver, we solve for the ground-state energy of H2, Li2, and BeH2 in the cc-pVTZ basis using the DUCC-reduced active spaces. We compare these results to full configuration-interaction and high-level coupled-cluster reference calculations.
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Affiliation(s)
- Mekena Metcalf
- Lawrence Berkeley National Laboratory, 1 Cyclotron Rd, Berkeley, California 94720, United States
| | - Nicholas P Bauman
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Karol Kowalski
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Wibe A de Jong
- Lawrence Berkeley National Laboratory, 1 Cyclotron Rd, Berkeley, California 94720, United States
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12
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Stair NH, Huang R, Evangelista FA. A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons. J Chem Theory Comput 2020; 16:2236-2245. [DOI: 10.1021/acs.jctc.9b01125] [Citation(s) in RCA: 46] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Nicholas H. Stair
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Renke Huang
- 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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13
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Bauman NP, Low GH, Kowalski K. Quantum simulations of excited states with active-space downfolded Hamiltonians. J Chem Phys 2019; 151:234114. [DOI: 10.1063/1.5128103] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Nicholas P. Bauman
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
| | | | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
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14
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Kirby WM, Love PJ. Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers. PHYSICAL REVIEW LETTERS 2019; 123:200501. [PMID: 31809115 DOI: 10.1103/physrevlett.123.200501] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2019] [Revised: 09/23/2019] [Indexed: 06/10/2023]
Abstract
Contextuality is an indicator of nonclassicality, and a resource for various quantum procedures. In this Letter, we use contextuality to evaluate the variational quantum eigensolver (VQE), one of the most promising tools for near-term quantum simulation. We present an efficiently computable test to determine whether or not the objective function for a VQE procedure is contextual. We apply this test to evaluate the contextuality of experimental implementations of VQE, and determine that several, but not all, fail this test of quantumness.
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Affiliation(s)
- William M Kirby
- Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155, USA
| | - Peter J Love
- Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155, USA
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15
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Cao Y, Romero J, Olson JP, Degroote M, Johnson PD, Kieferová M, Kivlichan ID, Menke T, Peropadre B, Sawaya NPD, Sim S, Veis L, Aspuru-Guzik A. Quantum Chemistry in the Age of Quantum Computing. Chem Rev 2019; 119:10856-10915. [PMID: 31469277 DOI: 10.1021/acs.chemrev.8b00803] [Citation(s) in RCA: 283] [Impact Index Per Article: 56.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Abstract
Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging and complex landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chemistry, such as the electronic structure of molecules. In the past two decades, significant advances have been made in developing algorithms and physical hardware for quantum computing, heralding a revolution in simulation of quantum systems. This Review provides an overview of the algorithms and results that are relevant for quantum chemistry. The intended audience is both quantum chemists who seek to learn more about quantum computing and quantum computing researchers who would like to explore applications in quantum chemistry.
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Affiliation(s)
- Yudong Cao
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Jonathan Romero
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Jonathan P Olson
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Matthias Degroote
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Department of Chemistry , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada.,Department of Computer Science , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada
| | - Peter D Johnson
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Mária Kieferová
- Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States.,Department of Physics and Astronomy , Macquarie University , Sydney , NSW 2109 , Australia.,Institute for Quantum Computing and Department of Physics and Astronomy , University of Waterloo , Waterloo , Ontario N2L 3G1 , Canada
| | - Ian D Kivlichan
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Department of Physics , Harvard University , Cambridge , Massachusetts 02138 , United States
| | - Tim Menke
- Department of Physics , Harvard University , Cambridge , Massachusetts 02138 , United States.,Research Laboratory of Electronics , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States.,Department of Physics , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
| | - Borja Peropadre
- Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Nicolas P D Sawaya
- Intel Laboratories , Intel Corporation , Santa Clara , California 95054 United States
| | - Sukin Sim
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry , Academy of Sciences of the Czech Republic v.v.i. , Doleǰskova 3 , 18223 Prague 8, Czech Republic
| | - Alán Aspuru-Guzik
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States.,Department of Chemistry , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada.,Department of Computer Science , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada.,Canadian Institute for Advanced Research , Toronto , Ontario M5G 1Z8 , Canada.,Vector Institute for Artificial Intelligence , Toronto , Ontario M5S 1M1 , Canada
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16
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Bauman NP, Bylaska EJ, Krishnamoorthy S, Low GH, Wiebe N, Granade CE, Roetteler M, Troyer M, Kowalski K. Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms. J Chem Phys 2019; 151:014107. [PMID: 31272173 DOI: 10.1063/1.5094643] [Citation(s) in RCA: 32] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper, we discuss the extension of the recently introduced subsystem embedding subalgebra coupled cluster (SES-CC) formalism to unitary CC formalisms. In analogy to the standard single-reference SES-CC formalism, its unitary CC extension allows one to include the dynamical (outside the active space) correlation effects in an SES induced complete active space (CAS) effective Hamiltonian. In contrast to the standard single-reference SES-CC theory, the unitary CC approach results in a Hermitian form of the effective Hamiltonian. Additionally, for the double unitary CC (DUCC) formalism, the corresponding CAS eigenvalue problem provides a rigorous separation of external cluster amplitudes that describe dynamical correlation effects-used to define the effective Hamiltonian-from those corresponding to the internal (inside the active space) excitations that define the components of eigenvectors associated with the energy of the entire system. The proposed formalism can be viewed as an efficient way of downfolding many-electron Hamiltonian to the low-energy model represented by a particular choice of CAS. In principle, this technique can be extended to any type of CAS representing an arbitrary energy window of a quantum system. The Hermitian character of low-dimensional effective Hamiltonians makes them an ideal target for several types of full configuration interaction type eigensolvers. As an example, we also discuss the algebraic form of the perturbative expansions of the effective DUCC Hamiltonians corresponding to composite unitary CC theories and discuss possible algorithms for hybrid classical and quantum computing. Given growing interest in quantum computing, we provide energies for H2 and Be systems obtained with the quantum phase estimator algorithm available in the Quantum Development Kit for the approximate DUCC Hamiltonians.
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Affiliation(s)
- Nicholas P Bauman
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
| | - Eric J Bylaska
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
| | - Sriram Krishnamoorthy
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
| | - Guang Hao Low
- Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA
| | - Nathan Wiebe
- Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA
| | - Christopher E Granade
- Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA
| | - Martin Roetteler
- Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA
| | - Matthias Troyer
- Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA
| | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
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