Quantum algorithm for obtaining the energy spectrum of molecular systems

Wang, Hefeng; Kais, Sabre; Aspuru‐Guzik, Alán; Hoffmann, Mark R.

doi:10.1039/b804804e

Cited by 119 publications

(150 citation statements)

References 32 publications

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“…Some of these results have already appeared in the quantum computation literature in the context of in depth studies of state preparation [24,25]. A general review of quantum simulation [26,27] and one on quantum computation for chemistry [28] cover these topics in more depth.…”

Section: Introductionmentioning

confidence: 99%

“…As a result, further developments in variational methods [13], quantum cooling [50], and adiabatic state preparation [7,25,51] will be of key importance in this area. Moreover improvements in the ansatze used to prepare the wave function such as multi-configurational self consistent field calculations(MCSCF) [24,25] or unitary coupled cluster (UCC) [10] will be integral parts of any practical quantum computing for quantum chemistry effort.…”

Section: Using Imperfect Oraclesmentioning

confidence: 99%

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Exploiting Locality in Quantum Computation for Quantum Chemistry

McClean

Babbush

Love

et al. 2014

J. Phys. Chem. Lett.

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127

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Accurate prediction of chemical and material properties from first principles quantum chemistry is a challenging task on traditional computers. Recent developments in quantum computation offer a route towards highly accurate solutions with polynomial cost, however this solution still carries a large overhead. In this perspective, we aim to bring together known results about the locality of physical interactions from quantum chemistry with ideas from quantum computation. We show that the utilization of spatial locality combined with the Bravyi-Kitaev transformation offers an improvement in the scaling of known quantum algorithms for quantum chemistry and provide numerical examples to help illustrate this point. We combine these developments to improve the outlook for the future of quantum chemistry on quantum computers.

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Section: Introductionmentioning

confidence: 99%

Section: Using Imperfect Oraclesmentioning

confidence: 99%

Exploiting Locality in Quantum Computation for Quantum Chemistry

McClean

Babbush

Love

et al. 2014

J. Phys. Chem. Lett.

Self Cite

127

190

View full text Add to dashboard Cite

show abstract

“…Quantum chemical state preparation is important in both the VQE approach, where it ultimately determines the state, energy, and properties measured, and in QPE, where it determines the success probability of the energy measurement 9,21,22 . Hence an understanding of the general effect of errors on state preparation is crucial to the success of both algorithms.…”

Section: Introductionmentioning

confidence: 99%

Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation

Sawaya

Smelyanskiy

McClean

et al. 2016

J. Chem. Theory Comput.

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Calculating molecular energies is likely to be one of the first useful applications to achieve quantum supremacy, performing faster on a quantum than a classical computer. However, if future quantum devices are to produce accurate calculations, errors due to environmental noise and algorithmic approximations need to be characterized and reduced. In this study, we use the high performance qHi PSTER software to investigate the effects of environmental noise on the preparation of quantum chemistry states. We simulated eighteen 16-qubit quantum circuits under environmental noise, each corresponding to a unitary coupled cluster state preparation of a different molecule or molecular configuration. Additionally, we analyze the nature of simple gate errors in noise-free circuits of up to 40 qubits. We find that, in most cases, the Jordan-Wigner (JW) encoding produces smaller errors under a noisy environment as compared to the Bravyi-Kitaev (BK) encoding. For the JW encoding, pure- * To whom correspondence should be addressed † Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA ‡ Parallel Computing Lab, Intel Corporation, Santa Clara, CA 95054, USA ¶ Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA dephasing noise is shown to produce substantially smaller errors than pure relaxation noise of the same magnitude. We report error trends in both molecular energy and electron particle number within a unitary coupled cluster state preparation scheme, against changes in nuclear charge, bond length, number of electrons, noise types, and noise magnitude. These trends may prove to be useful in making algorithmic and hardware-related choices for quantum simulation of molecular energies.

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“…The PEA always needs an initial guess of the wave function corresponding to the desired energy. This can be either the result of some approximate, polynomially scaling ab initio method [7,9], or as originally proposed by Aspuru-Guzik, et al[6] the exact state or its approximation prepared by the adiabatic state preparation (ASP) method. Figure 1.…”

mentioning

confidence: 99%

“…These cover: calculations of thermal rate constants of chemical reactions [5], non-relativistic energy calculations [6][7][8][9], quantum chemical dynamics [10], calculations of molecular properties [11], initial state preparation [12,13], and also first proof-of-principle experimental realizations [14][15][16][17]. An interested reader can find a comprehensive review in [18].…”

mentioning

confidence: 99%

Relativistic quantum chemistry on quantum computers

et al. 2012

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Last years witnessed a remarkable interest in application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, even first proof-of-principle experimental realizations have been reported. However, so far only the nonrelativistic regime (i.e. Schroedinger equation) has been explored, while it is well known that relativistic effects can be very important in chemistry. In this communication we present the first quantum algorithm for relativistic computations of molecular energies. We show how to efficiently solve the eigenproblem of the Dirac-Coulomb Hamiltonian on a quantum computer and demonstrate the functionality of the proposed procedure by numerical simulations of computations of the spinorbit splitting in the SbH molecule. Finally, we propose quantum circuits with 3 qubits and 9 or 10 CNOTs, which implement a proof-of-principle relativistic quantum chemical calculation for this molecule and might be suitable for an experimental realization.Quantum computing [1] is one of the fastest growing fields of computer science nowadays. Recent huge interest in this interdisciplinary field has been fostered by the prospects of solving certain types of problems more effectively than in the classical setting [2,3]. The prominent example is the integer factorization problem where quantum computing offers an exponential speedup over its classical counterpart [2]. But it is not only cryptography that can benefit from quantum computers. As was first proposed by R. Feynman [4], quantum computers could in principle be used for efficient simulation of another quantum system. This idea, which employs mapping of the Hilbert space of a studied system onto the Hilbert space of a register of quantum bits (qubits), both of them being exponentially large, can in fact be adopted also in quantum chemistry.Several papers using this idea and dealing with the interconnection of quantum chemistry and quantum computing have appeared in recent years. An efficient (polynomially scaling) algorithm for calculations of non-relativistic molecular energies, that employs the phase estimation algorithm (PEA) of Abrams and Lloyd [19], was proposed in the pioneering work by Aspuru-Guzik, et al. [6]. When the ideas of measurement based quantum computing are adopted [20], the phase estimation algorithm can be formulated in an iterative manner [iterative phase estimation (IPEA)] with only one read-out qubit [8,9]. If the phase φ (0 ≤ φ < 1), which is directly related to the desired energy [9], is expressed in the binary form: φ = 0.φ 1 φ 2 . . ., φ i = {0, 1}, one bit of φ is measured on the read-out qubit at each iteration step. The algorithm is iterated backwards from the least significant bits of φ to the most significant ones, where the k-th iteration is shown in Figure 1. Not to confuse the reader, H in the exponential denotes the Hamiltonian operator, whereas H (in a box) denotes the standard single-qubit Hadamard gate. |ψ system represents the part of a quantum register that e...

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Quantum algorithm for obtaining the energy spectrum of molecular systems

Cited by 119 publications

References 32 publications

Exploiting Locality in Quantum Computation for Quantum Chemistry

Exploiting Locality in Quantum Computation for Quantum Chemistry

Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation

Relativistic quantum chemistry on quantum computers

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