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Register a new userAmplitude estimation via maximum likelihood on noisy quantum computer
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Recently we find several candidates of quantum algorithms that may be implementable in near-term devices for estimating the amplitude of a given quantum state, which is a core subroutine in various computing tasks such as the Monte Carlo methods. One of those algorithms is based on the maximum likelihood estimate with parallelized quantum circuits; in this paper, we extend this method so that it can deal with the realistic noise effect. The validity of the proposed noise model is supported by an experimental demonstration on an IBM Q device, which accordingly enables us to predict the basic requirement on the hardware components (particularly the gate error) in quantum computers to realize the quantum speedup in the amplitude estimation task.
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Quantum Monte Carlo and quantum simulation are both important tools for understanding quantum many-body systems. As a classical algorithm, quantum Monte Carlo suffers from the sign problem, preventing its applications to most fermion systems and real time dynamics. In this paper, we introduce a novel non-variational algorithm using quantum simulation as a subroutine to accelerate quantum Monte Carlo by easing the sign problem. The quantum subroutine can be implemented with shallow circuits and, by incorporating error mitigation, reduce the Monte Carlo variance by orders of magnitude even when the circuit noise is significant. As such, the proposed quantum algorithm is applicable to near-term noisy quantum hardware.
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In this paper we derive from simple and reasonable assumptions a Gaussian noise model for NISQ Quantum Amplitude Estimation (QAE). We provide results from QAE run on various IBM superconducting quantum computers and Honeywells H1 trapped-ion quantum computer to show that the proposed model is a good fit for real-world experimental data. We then give an example of how to embed this noise model into any NISQ QAE algorithm, such that the amplitude estimation is noise-aware.
Maximum likelihood quantum state tomography yields estimators that are consistent, provided that the likelihood model is correct, but the maximum likelihood estimators may have bias for any finite data set. The bias of an estimator is the difference between the expected value of the estimate and the true value of the parameter being estimated. This paper investigates bias in the widely used maximum likelihood quantum state tomography. Our goal is to understand how the amount of bias depends on factors such as the purity of the true state, the number of measurements performed, and the number of different bases in which the system is measured. For that, we perform numerical experiments that simulate optical homodyne tomography under various conditions, perform tomography, and estimate bias in the purity of the estimated state. We find that estimates of higher purity states exhibit considerable bias, such that the estimates have lower purity than the true states.
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