Variational Quantum Algorithms for Trace Distance and Fidelity Estimation

• URL: http://arxiv.org/abs/2012.05768v3
• Date: Thu, 11 Nov 2021 09:41:45 GMT
• Title: Variational Quantum Algorithms for Trace Distance and Fidelity Estimation
• Authors: Ranyiliu Chen, Zhixin Song, Xuanqiang Zhao, Xin Wang
• Abstract summary: We introduce hybrid quantum-classical algorithms for two distance measures on near-term quantum devices. First, we introduce the Variational Trace Distance Estimation (VTDE) algorithm. Second, we introduce the Variational Fidelity Estimation (VFE) algorithm.
• Score: 7.247285982078057
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Estimating the difference between quantum data is crucial in quantum computing. However, as typical characterizations of quantum data similarity, the trace distance and quantum fidelity are believed to be exponentially-hard to evaluate in general. In this work, we introduce hybrid quantum-classical algorithms for these two distance measures on near-term quantum devices where no assumption of input state is required. First, we introduce the Variational Trace Distance Estimation (VTDE) algorithm. We in particular provide the technique to extract the desired spectrum information of any Hermitian matrix by local measurement. A novel variational algorithm for trace distance estimation is then derived from this technique, with the assistance of a single ancillary qubit. Notably, VTDE could avoid the barren plateau issue with logarithmic depth circuits due to a local cost function. Second, we introduce the Variational Fidelity Estimation (VFE) algorithm. We combine Uhlmann's theorem and the freedom in purification to translate the estimation task into an optimization problem over a unitary on an ancillary system with fixed purified inputs. We then provide a purification subroutine to complete the translation. Both algorithms are verified by numerical simulations and experimental implementations, exhibiting high accuracy for randomly generated mixed states.

Related papers

• Evaluation of phase shifts for non-relativistic elastic scattering using quantum computers [39.58317527488534]
  This work reports the development of an algorithm that makes it possible to obtain phase shifts for generic non-relativistic elastic scattering processes on a quantum computer.
  arXiv  Detail & Related papers  (2024-07-04T21:11:05Z)
• Heisenberg-limited adaptive gradient estimation for multiple observables [0.39102514525861415]
  In quantum mechanics, measuring the expectation value of a general observable has an inherent statistical uncertainty. We provide an adaptive quantum algorithm for estimating the expectation values of $M$ general observables within root mean squared error. Our method paves a new way to precisely understand and predict various physical properties in complicated quantum systems using quantum computers.
  arXiv  Detail & Related papers  (2024-06-05T14:16:47Z)
• Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications [80.04533958880862]
  Quantum computing sets the foundation for new ways of designing algorithms. New challenges arise concerning which field quantum speedup can be achieved. Looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms.
  arXiv  Detail & Related papers  (2024-02-26T09:32:07Z)
• Variational Benchmarks for Quantum Many-Body Problems [31.612670123381868]
  We introduce a metric of variational accuracy, the V-score, obtained from the variational energy and its variance. We provide an extensive curated dataset of variational calculations of many-body quantum systems. The V-score can be used as a metric to assess the progress of quantum variational methods toward a quantum advantage for ground-state problems.
  arXiv  Detail & Related papers  (2023-02-09T20:21:17Z)
• Importance sampling for stochastic quantum simulations [68.8204255655161]
  We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
  arXiv  Detail & Related papers  (2022-12-12T15:06:32Z)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• Mitigating algorithmic errors in quantum optimization through energy extrapolation [4.426846282723645]
  We present a scalable extrapolation approach to mitigating a non-negligible error in estimates of the ground state energy. We have verified the validity of these approaches through both numerical simulation and experiments on an IBM quantum computer.
  arXiv  Detail & Related papers  (2021-09-16T17:39:11Z)
• Distance-aware Quantization [30.06895253269116]
  Quantization methods use a rounding function to map full-precision values to the nearest quantized ones. We introduce a novel quantizer, dubbed a distance-aware quantizer (DAQ), that mainly consists of a distance-aware soft rounding (DASR) and a temperature controller.
  arXiv  Detail & Related papers  (2021-08-16T09:25:22Z)
• An efficient adaptive variational quantum solver of the Schrodinger equation based on reduced density matrices [8.24048506727803]
  We present an efficient adaptive variational quantum solver of the Schrodinger equation based on ADAPT-VQE. This new algorithm is quite suitable for quantum simulations of chemical systems on near-term noisy intermediate-scale hardware.
  arXiv  Detail & Related papers  (2020-12-13T12:22:41Z)
• Quantum state preparation with multiplicative amplitude transduction [0.0]
  Two variants of the algorithm with different emphases are introduced. One variant uses fewer qubits and no controlled gates, while the other variant potentially requires fewer gates overall. A general analysis is given to estimate the number of qubits necessary to achieve a desired precision in the amplitudes of the computational basis states.
  arXiv  Detail & Related papers  (2020-06-01T14:36:50Z)
• Variational Quantum Algorithms for Steady States of Open Quantum Systems [2.740982822457262]
  We propose a variational quantum algorithm to find the steady state of open quantum systems. The fidelity between the optimal mixed state and the true steady state is over 99%. This algorithm is derived from the natural idea of expressing mixed states with purification.
  arXiv  Detail & Related papers  (2020-01-08T14:47:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.