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Imaginary-time evolution with quantum nondemolition measurements: Multiqubit interactions via measurement nonlinearities

Manikandan Kondappan1,2, Manish Chaudhary1,2, Ebubechukwu O. Ilo-Okeke2, Valentin Ivannikov2,3, and Tim Byrnes1,2,3,4,5,6,*

  • 1State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, China
  • 2New York University Shanghai, 1555 Century Ave, Pudong, Shanghai 200122, China
  • 3NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
  • 4Center for Quantum and Topological Systems (CQTS), NYUAD Research Institute, New York University Abu Dhabi, United Arab Emirates
  • 5National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
  • 6Department of Physics, New York University, New York, New York 10003, USA

  • *tim.byrnes@nyu.edu
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Phys. Rev. A 107, 042616 – Published 20 April, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.042616

Abstract

We show that quantum nondemolition (QND) measurements can be used to realize measurement-based imaginary-time evolution. In our proposed scheme, repeated weak QND measurements are used to estimate the energy of a given Hamiltonian. Based on this estimated energy, adaptive unitary operations are applied such that only the targeted energy eigenstates are fixed points of the evolution. In this way, the system is deterministically driven towards the desired state. The nonlinear nature of the QND measurement, which allows for producing interactions between systems, is explicitly derived in terms of measurement operators. We show that for suitable interaction times, single-qubit QND Hamiltonians can be converted to effective multiqubit imaginary time operations. We illustrate our techniques with the example of preparing a four-qubit cluster state, which is prepared using only collective single-qubit QND measurements and single-qubit adaptive operations.

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Outline

Information

Phys. Rev. A 107, 042616– Published 20 April, 2023
  • Received 13 October 2022
  • Accepted 6 March 2023
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