Hybrid Quantum-Classical Approach to Correlated Materials

Bauer, Bela; Wecker, Dave; Millis, Andrew J.; Hastings, Matthew B.; Troyer, Matthias

doi:10.1103/physrevx.6.031045

Cited by 267 publications

(257 citation statements)

References 60 publications

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“…Although there is no Trotter error at self-consistency for this case, noise from the quantum computer gives a small but finite value for the amplitude α 2 of the second cosine in Eq. (12), even though the exact solution has α 2 = 0. Nevertheless, our results demonstrate that the DMFT loop for the two-site problem can be iterated to convergence for parameters in the Mott insulating regime.…”

Section: Mott Insulating Phasementioning

confidence: 98%

“…3 are superimposed with the fits to the data [Eq. (12)] and the exact solution for those parameters. In both cases, there are only seven data points for G imp (t) because the Trotter step is so expensive in terms of CNOT gates that the noise generated for more time steps and a nonzero V would overwhelm the simulation.…”

Section: B Impurity Green's Functionmentioning

confidence: 99%

“…It has also been shown that DMFT's limitations, e.g. a small set of correlated orbitals and no momentum dependence of the self-energy can be overcome on quantum computers [12]. Here, we report on an implementation and benchmark of the two-site DMFT scheme described in Ref.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantum-classical simulation of two-site dynamical mean-field theory on noisy quantum hardware

Keen

Maier

Johnston

et al. 2020

Quantum Sci. Technol.

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We report on a quantum-classical simulation of the single-band Hubbard model using two-site dynamical mean-field theory (DMFT). Our approach uses IBM's superconducting qubit chip to compute the zero-temperature impurity Green's function in the time domain and a classical computer to fit the measured Green's functions and extract their frequency domain parameters. We find that the quantum circuit synthesis (Trotter) and hardware errors lead to incorrect frequency estimates, and subsequently to an inaccurate quasiparticle weight when calculated from the frequency derivative of the self-energy. These errors produce incorrect hybridization parameters that prevent the DMFT algorithm from converging to the correct self-consistent solution. To avoid this pitfall, we compute the quasiparticle weight by integrating the quasiparticle peaks in the spectral function. This method is much less sensitive to Trotter errors and allows the algorithm to converge to self-consistency for a half-filled Mott insulating system after applying quantum error mitigation techniques to the quantum simulation data. arXiv:1910.09512v1 [quant-ph]

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Section: Mott Insulating Phasementioning

confidence: 98%

Section: B Impurity Green's Functionmentioning

confidence: 99%

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Quantum-classical simulation of two-site dynamical mean-field theory on noisy quantum hardware

Keen

Maier

Johnston

et al. 2020

Quantum Sci. Technol.

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show abstract

“…Furthermore, certain problems in material simulation may be tackled by hybrid quantum-classical algorithms [14]. In most such applications, the task can be abstracted to applying a short-depth quantum circuits to some simple initial state and then estimating the expectation value of some observable after the circuit has been applied.…”

mentioning

confidence: 99%

Error Mitigation for Short-Depth Quantum Circuits

Temme¹,

Bravyi²,

Gambetta³

2017

Phys. Rev. Lett.

1,073

987

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Two schemes are presented that mitigate the effect of errors and decoherence in short-depth quantum circuits. The size of the circuits for which these techniques can be applied is limited by the rate at which the errors in the computation are introduced. Near-term applications of early quantum devices, such as quantum simulations, rely on accurate estimates of expectation values to become relevant. Decoherence and gate errors lead to wrong estimates of the expectation values of observables used to evaluate the noisy circuit. The two schemes we discuss are deliberately simple and don't require additional qubit resources, so to be as practically relevant in current experiments as possible. The first method, extrapolation to the zero noise limit, subsequently cancels powers of the noise perturbations by an application of Richardson's deferred approach to the limit. The second method cancels errors by resampling randomized circuits according to a quasi-probability distribution.From the time quantum computation generated wide spread interest, the strongest objection to its viability was the sensitivity to errors and noise. In an early paper, William Unruh [1] found that the coupling to the environment sets an ultimate time and size limit for any quantum computation. This initially curbed the hopes that the full advantage of quantum computing could be harnessed, since it set limits on the scalability of any algorithm. This problem was, at least in theory, remedied with the advent of quantum error correction [2][3][4]. It was proven that if both the decoherence and the imprecision of gates could be reduced below a finite threshold value, then quantum computation could be performed indefinitely [5,6]. Although it is the ultimate goal to reach this threshold in an experiment that is scalable to larger sizes, the overhead that is needed to implement a fully fault-tolerant gate set with current codes [7] seems prohibitively large [8,9]. In turn, it is expected that in the near term the progress in quantum experiments will lead to devices with dynamics, which are beyond what can be simulated with a conventional computer. This leads to the question: what computational tasks could be accomplished with only limited, or no error correction?The suggestions of near-term applications in such quantum devices mostly center around quantum simulations with short-depth circuit [10][11][12] and approximate optimization algorithms [13]. Furthermore, certain problems in material simulation may be tackled by hybrid quantum-classical algorithms [14]. In most such applications, the task can be abstracted to applying a short-depth quantum circuits to some simple initial state and then estimating the expectation value of some observable after the circuit has been applied. This estimation must be accurate enough to achieve a simulation precision comparable or exceeding that of classical algorithms. Yet, although the quantum system evolves coherently for the most part of the short-depth circuit, the effects of decoherence already become apparent...

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“…A number of approaches are currently being studied, using both classical and quantum methods. While classical methods are limited to specific conditions for efficient simulation of quantum systems [10,11], quantum methods have a much larger scope, and a range of techniques have been developed so far, such as analogue [1,2], digital [12,13], digital-analogue [14,15], algorithmic [16][17][18] and embedded [19,20], each with its own advantages and disadvantages. Most methods consider ideal quantum systems, where the constituent elements are isolated from the outside world.…”

Section: Introductionmentioning

confidence: 99%

Experimental demonstration of a measurement-based realisation of a quantum channel

et al. 2018

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We introduce and experimentally demonstrate a method for realising a quantum channel using the measurement-based model. Using a photonic setup and modifying the bases of single-qubit measurements on a four-qubit entangled cluster state, representative channels are realised for the case of a single qubit in the form of amplitude and phase damping channels. The experimental results match the theoretical model well, demonstrating the successful performance of the channels. We also show how other types of quantum channels can be realised using our approach. This work highlights the potential of the measurement-based model for realising quantum channels which may serve as building blocks for simulations of realistic open quantum systems.

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Hybrid Quantum-Classical Approach to Correlated Materials

Cited by 267 publications

References 60 publications

Quantum-classical simulation of two-site dynamical mean-field theory on noisy quantum hardware

Quantum-classical simulation of two-site dynamical mean-field theory on noisy quantum hardware

Error Mitigation for Short-Depth Quantum Circuits

Experimental demonstration of a measurement-based realisation of a quantum channel

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