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arXiv:2004.04174 · Science

Hartree-Fock on a superconducting qubit quantum computer

Google AI Quantum and Collaborators, Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, R. Barends, Sergio Boixo, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, Yu Chen, Zijun Chen, Benjamin Chiaro, Roberto Collins, William Courtney, Sean Demura, Andrew Dunsworth, Edward Farhi, Austin G. Fowler, Brooks Foxen, Craig Gidney, Marissa Giustina, Rob Graff, Steve Habegger, Matthew P. Harrigan, Alan Ho, Sabrina Hong, Trent Huang, William J. Huggins, L. B. Ioffe, Sergei V. Isakov, Evan Jeffrey, Zhang Jiang, Cody Jones, Dvir Kafri, Kostyantyn Kechedzhi, Julian Kelly, Seon Kim, Paul V. Klimov, Alexander Korotkov, Fedor Kostritsa, David Landhuis, Pavel Laptev, Mike Lindmark, Erik Lucero, Orion Martin, John M. Martinis, Jarrod R. McClean, Matt McEwen, Anthony Megrant, Xiao Mi, Masoud Mohseni, Wojciech Mruczkiewicz, Josh Mutus, Ofer Naaman, Matthew Neeley, Charles Neill, Hartmut Neven, Murphy Yuezhen Niu, Thomas E. O’Brien, Eric Ostby, Andre Petukhov, Harald Putterman, Chris Quintana, Pedram Roushan, Nicholas C. Rubin, Daniel Sank, Kevin J. Satzinger, Vadim Smelyanskiy, Doug Strain, Kevin J. Sung, Marco Szalay, Tyler Y. Takeshita, Amit Vainsencher, Theodore White, Nathan Wiebe, Z. Jamie Yao, Ping Yeh, Adam Zalcman

Published Aug 28, 2020• 827 citations
arXivHTMLPDF

Abstract

Twelve-qubit quantum computing for chemistry Accurate electronic structure calculations are considered one of the most anticipated applications of quantum computing that will revolutionize theoretical chemistry and other related fields. Using the Google Sycamore quantum processor, Google AI Quantum and collaborators performed a variational quantum eigensolver (VQE) simulation of two intermediate-scale chemistry problems: the binding energy of hydrogen chains (as large as H 12 ) and the isomerization mechanism of diazene (see the Perspective by Yuan). The simulations were performed on up to 12 qubits, involving up to 72 two-qubit gates, and show that it is possible to achieve chemical accuracy when VQE is combined with error mitigation strategies. The key building blocks of the proposed VQE algorithm are potentially scalable to larger systems that cannot be simulated classically. Science , this issue p. 1084 ; see also p. 1054

DOI
10.1126/science.abb9811

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We report the first electronic structure calculation performed on a quantum computer without exponentially costly precompilation.We use a programmable array of superconducting qubits to compute the energy surface of molecular hydrogen using two distinct quantum algorithms.First, we experimentally execute the unitary coupled cluster method using the variational quantum eigensolver.Our efficient implementation predicts the correct dissociation energy to within chemical accuracy of the numerically exact result.Second, we experimentally demonstrate the canonical quantum algorithm for chemistry, which consists of Trotterization and quantum phase estimation.We compare the experimental performance of these approaches to show clear evidence that the variational quantum eigensolver is robust to certain errors.This error tolerance inspires hope that variational quantum simulations of classically intractable molecules may be viable in the near future.

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Twelve-qubit quantum computing for chemistry Accurate electronic structure calculations are considered one of the most anticipated applications of quantum computing that will revolutionize theoretical chemistry and other related fields. Using the Google Sycamore quantum processor, Google AI Quantum and collaborators performed a variational quantum eigensolver (VQE) simulation of two intermediate-scale chemistry problems: the binding energy of hydrogen chains (as large as H 12 ) and the isomerization mechanism of diazene (see the Perspective by Yuan). The simulations were performed on up to 12 qubits, involving up to 72 two-qubit gates, and show that it is possible to achieve chemical accuracy when VQE is combined with error mitigation strategies. The key building blocks of the proposed VQE algorithm are potentially scalable to larger systems that cannot be simulated classically. Science , this issue p. 1084 ; see also p. 1054
Quantum Computing Accurate electronic structure calculations are considered one of the most anticipated applications of quantum computing that will revolutionize theoretical chemistry and other related fields. Using the Google Sycamore quantum processor, Google AI Quantum and collaborators performed a variational quantum eigensolver (VQE) simulation of two intermediate-scale chemistry problems: the binding energy of hydrogen chains (as large as H12) and the isomerization mechanism of diazene (see the Perspective by Yuan). The simulations were performed on up to 12 qubits, involving up to 72 two-qubit gates, and show that it is possible to achieve chemical accuracy when VQE is combined with error mitigation strategies. The key building blocks of the proposed VQE algorithm are potentially scalable to larger systems that cannot be simulated classically. Science , this issue p. [1084][1]; see also p. [1054][2] [1]: /lookup/doi/10.1126/science.abb9811 [2]: /lookup/doi/10.1126/science.abd3880
Exponential scaling presents a significant challenge in electronic structure calculations performed on classical computers. This paper explores how quantum computer algorithms can accurately represent quantum systems. Variational Quantum Eigensolver (VQE) algorithm is used to compute the ground state energy of hydrogen and helium sequences by implementing variational principle and quantum gates as trial wavefunction. This technique combines classical optimization with quantum computing calculations to simulate quantum systems on noisy and resource-limited computers. The resulting calculated energy is highly consistent to the corresponding exact values and Hartree-Fock calculations with a trend of when the number of atoms increases the calculated energy becomes more negative, leading to a decrease in the percentage error. Moreover, the convergence of the ground state energy of hydrogen and helium atoms was effectively optimized. The desired energy was reached, proven by adjusting the expectation value, and gradually achieving unity in state overlap. These findings demonstrate the VQE method's accuracy in calculating simple quantum systems and its scalability for larger atomic and molecular system, such as those in quantum chemistry and material science. However, challenges in quantum computer simulations, such as limited in qubit numbers and the presence of noise, require further advancements. Therefore, implementing a larger basis sets, advanced qubit mapping, specific chemistry ansatz, and flexible optimization techniques is one way to improve overall calculation.
Quantum computing has emerged as a transformative approach for tackling complex problems in quantum chemistry, particularly in simulating multielectron systems and electron-phonon interactions. However, the current noisy intermediate-scale quantum (NISQ) devices face significant challenges in implementing practical quantum algorithms due to error accumulation caused by increased circuit depth, qubit counts, and gate operations. To address these challenges, we present TenCirChem, an open-source Python package specifically designed for implementing variational quantum algorithms in quantum computational chemistry. TenCirChem demonstrates exceptional performance in simulating unitary coupled-cluster circuits through its innovative use of compact representations for quantum states and excitation operators. This package supports noisy circuit simulation and provides advanced algorithms for variational quantum dynamics, enabling researchers to explore complex chemical phenomena. Its capabilities are exemplified in various applications, including the calculation of potential energy curves and the investigation of quantum gate error impacts on molecular systems. Moreover, TenCirChem’s seamless integration with real quantum hardware makes it a versatile tool for both simulation and experimentation. A key innovation developed within the TenCirChem framework is the Clifford-based Hamiltonian engineering approach for molecules (CHEM). This algorithm addresses the critical challenge of achieving chemical accuracy with shallow quantum circuits, a fundamental requirement for practical applications on NISQ devices. CHEM employs a sophisticated Clifford-based Hamiltonian transformation that operates within the variational quantum eigensolver (VQE) framework using hardware-efficient ansatz. The method ensures four crucial advantages: (1) generation of initial circuit parameters corresponding to Hartree-Fock energy, (2) maximization of initial energy gradients with respect to circuit parameters, (3) minimal classical processing overhead without additional quantum resource requirements, and (4) compatibility with any circuit topology. Through quantum hardware emulator demonstrations, CHEM has achieved chemical accuracy for systems up to 12 qubits with fewer than 30 two-qubit gates, representing a significant advancement in practical quantum computational chemistry. To enhance the efficiency of variational quantum algorithms, we developed the sequential optimization with approximate parabola (SOAP) method, specifically designed for parameter optimization in unitary coupled-cluster ansatz. SOAP addresses the critical bottleneck of measurement requirements in VQE by implementing an innovative optimization strategy that approximates the energy landscape as quadratic functions. This approach minimizes the number of energy evaluations while incorporating parameter correlations through the integration of average directions from previous iterations. Benchmark studies demonstrate SOAP’s superior performance, showing faster convergence and enhanced noise robustness compared to traditional optimization methods. The method’s scalability has been validated through numerical simulations of up to 20 qubits, and its practical efficacy has been confirmed through experiments on superconducting quantum computers. For simulating electron-phonon systems, we introduce a variational basis state encoding algorithm that significantly reduces resource requirements compared to conventional unary and binary encoding schemes. Our approach achieves smaller scaling than traditional methods for qubits and gates for systems obeying the area law of entanglement entropy, this remarkable reduction in resource requirements comes at the cost of a constant amount of additional measurements. The algorithm’s effectiveness has been validated through both numerical simulations and quantum hardware experiments, demonstrating that using just one or two qubits per phonon mode can produce quantitatively accurate results across various coupling regimes. The integration of these innovations within the TenCirChem library represents a significant advancement in quantum computational chemistry. The software package provides researchers with a comprehensive toolkit for developing, testing, and implementing quantum algorithms, while the novel methods address fundamental challenges in circuit depth, parameter optimization, and resource efficiency. These developments collectively enhance the practicality of quantum computing for addressing real-world chemical problems in the NISQ era, offering improved accuracy, efficiency, and noise robustness.
We report the first electronic structure calculation performed on a quantum computer without exponentially costly precompilation.We use a programmable array of superconducting qubits to compute the energy surface of molecular hydrogen using two distinct quantum algorithms.First, we experimentally execute the unitary coupled cluster method using the variational quantum eigensolver.Our efficient implementation predicts the correct dissociation energy to within chemical accuracy of the numerically exact result.Second, we experimentally demonstrate the canonical quantum algorithm for chemistry, which consists of Trotterization and quantum phase estimation.We compare the experimental performance of these approaches to show clear evidence that the variational quantum eigensolver is robust to certain errors.This error tolerance inspires hope that variational quantum simulations of classically intractable molecules may be viable in the near future.
However, accurately simulating molecular interactions constitutes the central, but open question of computer chemistry. This is a core task for efforts in drug development, catalyst design, and materials science. Most classical algorithms perform well on smaller systems, but incumbent exponential scaling penalties are unavoidable as models grow larger and more complex to describe quantum behaviour. An entirely new paradigm for this problem is now introduced by quantum computing: superposition and entanglement resources natively encode quantum states and model their electronic structures. The paper will thus take a high-level view of the leading quantum algorithms, with particular regard to those called Variational Quantum Eigensolver (VQE) and Quantum Phase Estimation (QPE), while evaluating their performance on today's Noisy Intermediate Scale Quantum (NISQ) devices. Next will follow discussions on algorithm design and current hardware capabilities, before which open challenges on scalability, error mitigation, and algorithm design will be outlined. Emphasis shall also be placed on the ethics and accessibility issues as well as the timelines with which quantum computing might gain a practical advantage. Linking together the recent advances and limitations, this paper posits how quantum computer implementation may change the face of chemical modelling and scientific discovery.
The Variational Quantum Eigensolver (VQE) is a promising quantum algorithm for applications in chemistry within the Noisy Intermediate-Scale Quantum (NISQ) era. The ability for a quantum computer to simulate electronic structures with high accuracy would have a profound impact on material and biochemical science with potential applications e.g., to the development of new drugs. However, considering the variety of quantum hardware architectures, it is still uncertain which hardware concept is most suited to execute the VQE for e.g., the simulation of molecules. Aspects to consider here are the required connectivity of the quantum circuit used, the size and the depth and thus the susceptibility to noise effects. Besides theo-retical considerations, empirical studies using available quantum hardware may help to clarify the question of which hardware technology might be better suited for a certain given application and algorithm. Going one step into this direction, within this work, we present results using the VQE for the simulation of the hydrogen molecule, comparing superconducting and ion trap quantum computers. The experiments are carried out with a standardized setup of ansatz and optimizer, selected to reduce the number of required iterations. The findings are analyzed considering different quantum processor types, calibration data as well as the depth and gate counts of the circuits required for the different hardware concepts after transpilation.