Simulation of electronic structure Hamiltonians using quantum computers

Whitfield, James D.; Biamonte, Jacob; Aspuru‐Guzik, Alán

doi:10.1080/00268976.2011.552441

Cited by 432 publications

(615 citation statements)

References 49 publications

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“…Finally, this sorted list of Pauli operators was translated into gate sequences of basis changes Hadamard and Yb (basis change to Y), CNOTs, and Z-rotations with the standard circuit synthesis for exponentials of tensor products of Pauli operators 2 . A useful introduction to these circuits for the JW mapping can be found in Whitfield et al 12 Figure 1: For pristine (noise-free) circuits, the bars show one standard deviation of the chemical energy estimator (square root of the variance of the estimator). A larger standard deviation implies that a larger number of measurements is required.…”

Section: Simulation Detailsmentioning

confidence: 99%

“…The approximation becomes exact as η approaches infinity. The effects of Trotterization order have been studied elsewhere 12,[25][26][27] . As the focus of the present study is the effects of decoherence, most of our quantum circuits estimate the molecular energy using a Trotter number of one.…”

Section: Molecular State Preparationmentioning

confidence: 99%

“…The first uses the quantum phase estimation (QPE) algorithm [9][10][11][12][13] to evolve an initial state toward the molecular ground state. The second approach is the variational quantum eigensolver (VQE) [14][15][16] .…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Simulation Detailsmentioning

confidence: 99%

Section: Molecular State Preparationmentioning

confidence: 99%

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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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“…They are clearly vitally important for the correct estimate of the asymptotic scaling of any method [7,8,14,15]. For that reason, we review the origin of that scaling here for the most common and readily available local basis, the Gaussian atomic orbital basis.…”

Section: Spatial Localitymentioning

confidence: 99%

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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“…1a). Reducing the number of qubits in quantum simulations and quantum chemistry has been achieved with recursive phase estimation [13][14][15][16] , while ground state projections have been demonstrated by exploiting similar techniques in NMR 17 .…”

mentioning

confidence: 99%

Experimental realization of Shor's quantum factoring algorithm using qubit recycling

et al. 2012

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Quantum computational algorithms exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms 1-3 . Shor's quantum algorithm 4 for fast number factoring is a key example and the prime motivator in the international effort to realise a quantum computer 5 . However, due to the substantial resource requirement, to date, there have been only four small-scale demonstrations 6-9 . Here we address this resource demand and demonstrate a scalable version of Shor's algorithm in which the n qubit control register is replaced by a single qubit that is recycled n times: the total number of qubits is one third of that required in the standard protocol [10][11][12] . Encoding the work register in higher-dimensional states, we implement a two-photon compiled algorithm to factor N = 21. The algorithmic output is distinguishable from noise, in contrast to previous demonstrations. These results point to larger-scale implementations of Shor's algorithm by harnessing scalable resource reductions applicable to all physical architectures.Shor's factoring algorithm consists of a quantum order finding algorithm, preceded and succeeded by various classical routines. While the classical tasks are known to be efficient on a classical computer, order finding is understood to be intractable classically. However, it is known that this part of the algorithm can be performed efficiently on a quantum computer. To determine the prime factors of an odd integer N , one chooses a coprime of N , x. The order r relates x to N according to x r mod N = 1, and can be used to obtain the factors, given by the greatest common divisor gcd(x r 2 ± 1, N ). The quantum order finding circuit involves two registers: a work register and a control register. In the standard protocol, the work register performs modular arithmetic with m = log 2 N qubits, enough to encode the number N , and the n qubit control register provides the algorithmic output, with n bits of precision.Measuring the control register in the computational basis will yield a result of k2 n /r where k is an integer between 0 and r − 1, with the value of k occurring probabilistically. Dividing the result by 2 n gives the first n bits of k/r and r may be found with classical processing, using the continued fraction algorithm. For large n, and a perfectly functioning circuit, the output probability distribution of the control register is a series of well defined peaks at values of k2 n /r (Fig. 1b). (See Appendix for details.)Here we implement an iterative version of the order finding algorithm 10,11 , in which the control register contains only a single qubit which is recycled n times, using a sequence of measurement and feed-forward operations, with each step providing an additional bit of precision (Fig. 1a). Reducing the number of qubits in quantum simulations and quantum chemistry has been achieved with recursive phase estimation 13-16 , while ground state projections have been demonstrated by exploiting similar techniques in NMR 17 .The iterative version of...

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Simulation of electronic structure Hamiltonians using quantum computers

Cited by 432 publications

References 49 publications

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

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

Exploiting Locality in Quantum Computation for Quantum Chemistry

Experimental realization of Shor's quantum factoring algorithm using qubit recycling

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