Digital quantum simulation of molecular vibrations

McArdle, Sam; Mayorov, Alexander; Xiao, Shan; Benjamin, Simon C.; Yuan, Xiao

doi:10.1039/c9sc01313j

Cited by 89 publications

(128 citation statements)

References 71 publications

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“…The advent of variational methods, most notably the variational quantum eigensolver [1,2], inspires hope that useful contributions to our understanding of strongly correlated physical and chemical systems might be achievable in pre-error-corrected quantum devices [3]. Following this initial work, much progress has gone into lowering the coherence requirements of variational methods [4], calculating system properties beyond ground state energies [5][6][7], and experimental implementation [8][9][10][11]. However, extracting data from an exponentially complex quantum state is a critical bottleneck for such applications.…”

Section: Introductionmentioning

confidence: 99%

Nearly Optimal Measurement Scheduling for Partial Tomography of Quantum States

2020

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Many applications of quantum simulation require one to prepare and then characterize quantum states by efficiently estimating k-body reduced density matrices (k-RDMs), from which observables of interest may be obtained. For instance, the fermionic 2-RDM contains the energy, charge density, and energy gradients of an electronic system, while the qubit 2-RDM contains the spatial correlation functions of magnetic systems. Naive estimation of such RDMs requires repeated state preparations for each matrix element, which makes for prohibitively large computation times. However, commuting matrix elements may be measured simultaneously, allowing for a significant cost reduction. In this work, we design schemes for such a parallelization with near-optimal complexity in the system size N. We first describe a scheme to sample all elements of a qubit k-RDM using only Oð3 k log k−1 NÞ unique measurement circuits, an exponential improvement over prior art. We then describe a scheme for sampling all elements of the fermionic 2-RDM using only OðN 2 Þ unique measurement circuits, each of which requires only a local OðNÞ-depth measurement circuit. We prove a lower bound of Ωðϵ −2 N k Þ on the number of state preparations, Clifford circuits, and measurement in the computational basis required to estimate all elements of a fermionic k-RDM, making our scheme for sampling the fermionic 2-RDM asymptotically optimal. We finally construct circuits to sample the expectation value of a linear combination of ω anticommuting two-body fermionic operators with only OðωÞ gates on a linear array. These circuits allows for sampling any linear combination of fermionic 2-RDM elements in OðN 4 =ωÞ time, with a significantly lower measurement circuit complexity than prior art. Our results improve the viability of near-term quantum simulation of molecules and strongly correlated material systems.

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Section: Introductionmentioning

confidence: 99%

Nearly Optimal Measurement Scheduling for Partial Tomography of Quantum States

2020

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“…All these features are sufficiently distinct from the usual quantum chemical scenarios that quantum algorithms are likely to require additional innovation to be useful in the nuclear problem. Some steps in this direction have recently appeared [88][89][90]. One simplification is that many nuclei are distinguishable avoiding the need to consider indistinguishable particles.…”

Section: B Quantum Molecular Spectroscopymentioning

confidence: 99%

Quantum Algorithms for Quantum Chemistry and Quantum Materials Science

et al. 2020

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As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a theoretical possibility, recent advances in hardware mean that quantum computing devices now exist that can carry out quantum computation on a limited scale. Thus, it is now a real possibility, and of central importance at this time, to assess the potential impact of quantum computers on real problems of interest. One of the earliest and most compelling applications for quantum computers is Feynman’s idea of simulating quantum systems with many degrees of freedom. Such systems are found across chemistry, physics, and materials science. The particular way in which quantum computing extends classical computing means that one cannot expect arbitrary simulations to be sped up by a quantum computer, thus one must carefully identify areas where quantum advantage may be achieved. In this review, we briefly describe central problems in chemistry and materials science, in areas of electronic structure, quantum statistical mechanics, and quantum dynamics that are of potential interest for solution on a quantum computer. We then take a detailed snapshot of current progress in quantum algorithms for ground-state, dynamics, and thermal-state simulation and analyze their strengths and weaknesses for future developments.

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“…We note that a bosonic ONV can be represented with a smaller number of qubits by adopting the compact mapping proposed in the literature. 31,32 However, the representation of the elementary raising and lowering operators within such mapping is more complex than in the direct one leading to an increase in the circuit depth and in the number of terms in the Hamiltonian. As we will highlight in the following, current hardware limitations impose short circuit depths because of the accumulation of gate errors, while the possibility of executing gates in parallel favours the use of more qubits.…”

Section: Wavefunction Parametrizationmentioning

confidence: 99%

“…Two key limitations hinder the application of the theory presented in ref. 31 to complex vibrational Hamiltonians. First, the algorithm can be applied only to vibrational ground states and, therefore, does not allow to access vibrational excitation energies that are key for vibrational spectroscopy.…”

Section: Introductionmentioning

confidence: 99%