Witnessing eigenstates for quantum simulation of Hamiltonian spectra

Santagati, Raffaele; Wang, J.; Gentile, Antonio A.; Paesani, Stefano; Wiebe, Nathan; McClean, Jarrod R.; Morley-Short, Sam; Shadbolt, Peter; Bonneau, Damien; Silverstone, Joshua W.; Tew, David P.; Zhou, Xiaoqi; O’Brien, Jeremy L; Thompson, Mark G.

doi:10.1126/sciadv.aap9646

Cited by 211 publications

(247 citation statements)

References 62 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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“…One approach to dealing with this issue is to mimic wave function collapse by implicitly introducing biases against data that is more likely to come from other eigenvalues. This approach is taken by by Wiebe and Granade [37] and by Santagati et al [38], wherein a Bayesian form of phase estimation is used to introduce such biases through applying a unimodal approximation to the posterior.…”

Section: Application To Collapse-free Phase Estimationmentioning

confidence: 99%

Structured filtering

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Wiebe

2017

New J. Phys.

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A major challenge facing existing sequential Monte Carlo methods for parameter estimation in physics stems from the inability of existing approaches to robustly deal with experiments that have different mechanisms that yield the results with equivalent probability. We address this problem here by proposing a form of particle filtering that clusters the particles that comprise the sequential Monte Carlo approximation to the posterior before applying a resampler. Through a new graphical approach to thinking about such models, we are able to devise an artificial-intelligence based strategy that automatically learns the shape and number of the clusters in the support of the posterior. We demonstrate the power of our approach by applying it to randomized gap estimation and a form of low circuit-depth phase estimation where existing methods from the physics literature either exhibit much worse performance or even fail completely.

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“…In these settings the focus is on determining an optical phase-shift [13][14][15] through an interferometric setup. There is experimental work on (silicon) quantum photonic processors [16][17][18] on multiple-eigenvalue estimation for Hamiltonians which could also benefit from using the classical post-processing techniques that we develop in this paper. Figure 1.…”

Section: Introductionmentioning

confidence: 99%

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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Witnessing eigenstates for quantum simulation of Hamiltonian spectra

Abstract: We introduce the concept of an eigenstate witness and use it to find energies of quantum systems with quantum computers.

Cited by 211 publications

References 62 publications

Application of fermionic marginal constraints to hybrid quantum algorithms

Application of fermionic marginal constraints to hybrid quantum algorithms

Structured filtering

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

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