Quantum computation of nonlinear maps

• URL: http://arxiv.org/abs/2105.07317v1
• Date: Sat, 15 May 2021 23:57:26 GMT
• Title: Quantum computation of nonlinear maps
• Authors: I. Y. Dodin and E. A. Startsev
• Abstract summary: We compute a general differentiable invertible nonlinear map on a quantum computer using only linear unitary operations. More iterations produce spurious echos, which are unavoidable in any finite unitary emulation of generic non-conservative dynamics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum algorithms for computing classical nonlinear maps are widely known for toy problems but might not suit potential applications to realistic physics simulations. Here, we propose how to compute a general differentiable invertible nonlinear map on a quantum computer using only linear unitary operations. The price of this universality is that the original map is represented adequately only on a finite number of iterations. More iterations produce spurious echos, which are unavoidable in any finite unitary emulation of generic non-conservative dynamics. Our work is intended as the first survey of these issues and possible ways to overcome them in the future. We propose how to monitor spurious echos via auxiliary measurements, and we illustrate our results with numerical simulations.

Related papers

• Single Qubit Error Mitigation by Simulating Non-Markovian Dynamics [0.0]
  We present a simulation scheme for open qubit dynamics described by a larger class of maps. We illustrate our scheme on an IBM quantum processor by showing that we can recover the initial state of a Lindblad evolution.
  arXiv  Detail & Related papers  (2023-03-06T16:35:44Z)
• Tensor Networks or Decision Diagrams? Guidelines for Classical Quantum Circuit Simulation [65.93830818469833]
  tensor networks and decision diagrams have independently been developed with differing perspectives, terminologies, and backgrounds in mind. We consider how these techniques approach classical quantum circuit simulation, and examine their (dis)similarities with regard to their most applicable abstraction level. We provide guidelines for when to better use tensor networks and when to better use decision diagrams in classical quantum circuit simulation.
  arXiv  Detail & Related papers  (2023-02-13T19:00:00Z)
• Dynamical chaos in nonlinear Schr\"odinger models with subquadratic power nonlinearity [137.6408511310322]
  We deal with a class of nonlinear Schr"odinger lattices with random potential and subquadratic power nonlinearity. We show that the spreading process is subdiffusive and has complex microscopic organization. The limit of quadratic power nonlinearity is also discussed and shown to result in a delocalization border.
  arXiv  Detail & Related papers  (2023-01-20T16:45:36Z)
• Virtual linear map algorithm for classical boost in near-term quantum computing [0.0]
  We introduce the Virtual Linear Map Algorithm (VILMA) VILMA estimates multiple operator averages using classical post-processing of informationally complete measurement outcomes. We show that VILMA allows for the variational optimisation of the virtual circuit through sequences of efficient linear programs.
  arXiv  Detail & Related papers  (2022-07-04T12:34:26Z)
• Challenges for quantum computation of nonlinear dynamical systems using linear representations [2.2000635322691378]
  We show that a necessary projection into a feasible finite-dimensional space will in practice induce numerical artifacts which can be hard to eliminate or even control. As a result, a practical, reliable and accurate way to use quantum computation for solving general nonlinear dynamical systems is still an open problem.
  arXiv  Detail & Related papers  (2022-02-04T15:29:53Z)
• Operational applications of the diamond norm and related measures in quantifying the non-physicality of quantum maps [0.0]
  We study the non-physicality of linear maps based on different ways to approximate a given linear map with quantum channels. We show that for any trace-preserving map, the quantities both reduce to a fundamental distance measure: the diamond norm.
  arXiv  Detail & Related papers  (2021-02-15T19:00:00Z)
• Physical Implementability of Linear Maps and Its Application in Error Mitigation [12.539795808097063]
  We decompose a target linear map into a linear combination of physically implementable operations. We show this measure is efficiently computable by semidefinite programs. We endow this measure with an operational meaning within the quantum error mitigation scenario.
  arXiv  Detail & Related papers  (2020-12-20T16:03:09Z)
• Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms [74.17312533172291]
  We describe a method for mapping any finite nonlinear dynamical system to an infinite linear dynamical system (embedding) We then explore an approach for approximating the resulting infinite linear system with finite linear systems (truncation)
  arXiv  Detail & Related papers  (2020-12-12T00:01:10Z)
• Quantum-Inspired Algorithms from Randomized Numerical Linear Algebra [53.46106569419296]
  We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression. We argue that the previous quantum-inspired algorithms for these problems are doing leverage or ridge-leverage score sampling in disguise.
  arXiv  Detail & Related papers  (2020-11-09T01:13:07Z)
• Simulating nonnative cubic interactions on noisy quantum machines [65.38483184536494]
  We show that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. On noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates.
  arXiv  Detail & Related papers  (2020-04-15T05:16:24Z)
• Efficient classical simulation of random shallow 2D quantum circuits [104.50546079040298]
  Random quantum circuits are commonly viewed as hard to simulate classically. We show that approximate simulation of typical instances is almost as hard as exact simulation. We also conjecture that sufficiently shallow random circuits are efficiently simulable more generally.
  arXiv  Detail & Related papers  (2019-12-31T19:00:00Z)

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.