Improved techniques for preparing eigenstates of fermionic Hamiltonians

Berry, Dominic W.; Kieferová, Mária; Scherer, Artur; Sanders, Yuval R.; Low, Guang Hao; Wiebe, Nathan; Gidney, Craig; Babbush, Ryan

doi:10.1038/s41534-018-0071-5

Cited by 114 publications

(88 citation statements)

References 64 publications

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“…This could potentially revolutionize research in chemistry and material science by allowing a new mechanism for designing new materials, drugs, and catalysts. Accordingly, there is now a significant body of literature dedicated to developing new algorithms [7][8][9][10][11][12][13][14][15][16][17][18][19][20], tighter bounds and better implementation strategies [21][22][23][24][25][26][27][28], more desirable Hamiltonian representations [29][30][31][32][33][34][35][36][37][38][39], and experimental demonstrations [40][41][42][43] for this problem.…”

Section: Introductionmentioning

confidence: 99%

Application of fermionic marginal constraints to hybrid quantum algorithms

2018

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Many quantum algorithms, including recently proposed hybrid classical/quantum algorithms, make use of restricted tomography of the quantum state that measures the reduced density matrices, or marginals, of the full state. The most straightforward approach to this algorithmic step estimates each component of the marginal independently without making use of the algebraic and geometric structure of the marginals. Within the field of quantum chemistry, this structure is termed the fermionic n-representability conditions, and is supported by a vast amount of literature on both theoretical and practical results related to their approximations. In this work, we introduce these conditions in the language of quantum computation, and utilize them to develop several techniques to accelerate and improve practical applications for quantum chemistry on quantum computers. As a general result, we demonstrate how these marginals concentrate to diagonal quantities when measured on random quantum states. We also show that one can use fermionic n-representability conditions to reduce the total number of measurements required by more than an order of magnitude for medium sized systems in chemistry. As a practical demonstration, we simulate an efficient restoration of the physicality of energy curves for the dilation of a four qubit diatomic hydrogen system in the presence of three distinct one qubit error channels, providing evidence these techniques are useful for pre-fault tolerant quantum chemistry experiments. semidefinite-ness, constrained spin-, and particle-numbers are expected to increase the observed energy of the 2-RDM with respect to the uncorrected noisy 2-RDM.

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Section: Introductionmentioning

confidence: 99%

Application of fermionic marginal constraints to hybrid quantum algorithms

2018

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“…VQE is advantageous for NISQ computers because of the short coherence times required compared to phase estimation [13]. Theoretical improvements of VQE to date have proposed methods to reduce the number of qubits and measurements required [24][25][26][27][28][29][30][31][32][33][34][35][36], and to improve the ansatz states [31,37,38], computation of gradients [39][40][41], and classical optimization techniques [42]. In the present paper we consider a separate issue: how quantum mechanical is this hybrid quantum-classical algorithm, for a given Hamiltonian?…”

Section: Introductionmentioning

confidence: 99%

Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers

Love

2019

Phys. Rev. Lett.

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Contextuality is an indicator of non-classicality, and a resource for various quantum procedures. In this paper, 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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“…Much work has been devoted to determining the most efficient implementation of the (controlled)-exp i  t -( )operation, using exact or approximate methods [19][20][21][22]. Alternatively, one may simulate  via a quantum walk, mapping the problem to phase estimating the unitary exp iarcsin  l -( ( ) ) for some λ, which may be implemented exactly [23][24][25][26]. In this work we do not consider such variations, but rather focus on the error in estimating the eigenvalue phases of the unitary U that is actually implemented on the quantum computer.…”

Section: Quantum Phase Estimationmentioning

confidence: 99%

“…calculation of g(k) from these probabilities via equation (23) or equation (24), and (3) estimation of the phases f from g(k). Clearly (2) and (3) only need to be done once for the entire set of experiments.…”

Section: Classical Computation Costmentioning

confidence: 99%

“…Both the Bayesian and time-series estimator can be adapted rather easily to compensate for this depolarizing channel. To adapt the time-series analysis, we note that the effect of depolarizing noise is to send g k g k p k  ( ) ( ) ( ) when k>0, via equation (23) and equation (41). Our time-series analysis was previously performed over the range k K K , , = -¼ (getting g k g k * -= ( ) ( )for free), and over this range…”

Section: Depolarizing Noisementioning

confidence: 99%

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Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments

2019

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Quantum phase estimation (QPE) is the workhorse behind any quantum algorithm and a promising method for determining ground state energies of strongly correlated quantum systems. Low-cost QPE techniques make use of circuits which only use a single ancilla qubit, requiring classical post-processing to extract eigenvalue details of the system. We investigate choices for phase estimation for a unitary matrix with low-depth noise-free or noisy circuits, varying both the phase estimation circuits themselves as well as the classical post-processing to determine the eigenvalue phases. We work in the scenario when the input state is not an eigenstate of the unitary matrix. We develop a new post-processing technique to extract eigenvalues from phase estimation data based on a classical time-series (or frequency) analysis and contrast this to an analysis via Bayesian methods. We calculate the variance in estimating single eigenvalues via the time-series analysis analytically, finding that it scales to first order in the number of experiments performed, and to first or second order (depending on the experiment design) in the circuit depth. Numerical simulations confirm this scaling for both estimators. We attempt to compensate for the noise with both classical post-processing techniques, finding good results in the presence of depolarizing noise, but smaller improvements in 9-qubit circuit-level simulations of superconducting qubits aimed at resolving the electronic ground state of a H 4 -molecule.

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Improved techniques for preparing eigenstates of fermionic Hamiltonians

Cited by 114 publications

References 64 publications

Application of fermionic marginal constraints to hybrid quantum algorithms

Application of fermionic marginal constraints to hybrid quantum algorithms

Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers

Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments

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