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Mao Y, Chaudhary M, Kondappan M, Shi J, Ilo-Okeke EO, Ivannikov V, Byrnes T. Measurement-Based Deterministic Imaginary Time Evolution. PHYSICAL REVIEW LETTERS 2023; 131:110602. [PMID: 37774296 DOI: 10.1103/physrevlett.131.110602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2022] [Revised: 07/30/2023] [Accepted: 08/17/2023] [Indexed: 10/01/2023]
Abstract
We introduce a method to perform imaginary time evolution in a controllable quantum system using measurements and conditional unitary operations. By performing a sequence of weak measurements based on the desired Hamiltonian constructed by a Suzuki-Trotter decomposition, an evolution approximating imaginary time evolution can be realized. The randomness due to measurement is corrected using conditional unitary operations, making the evolution deterministic. Both the measurements required for the algorithm and the conditional unitary operations can be constructed efficiently. We show that the algorithm converges only below a specified energy threshold and the complexity is estimated for some specific problem instances.
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Affiliation(s)
- Yuping Mao
- State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, China
- New York University Shanghai, 567 West Yangsi Road, Shanghai 200126, China
| | - Manish Chaudhary
- State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, China
- New York University Shanghai, 567 West Yangsi Road, Shanghai 200126, China
| | - Manikandan Kondappan
- State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, China
- New York University Shanghai, 567 West Yangsi Road, Shanghai 200126, China
| | - Junheng Shi
- New York University Shanghai, 567 West Yangsi Road, Shanghai 200126, China
- CAS Key Laboratory of Theoretical Physics and Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Ebubechukwu O Ilo-Okeke
- New York University Shanghai, 567 West Yangsi Road, Shanghai 200126, China
- NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
| | - Valentin Ivannikov
- New York University Shanghai, 567 West Yangsi Road, Shanghai 200126, China
- NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
| | - Tim Byrnes
- State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, China
- New York University Shanghai, 567 West Yangsi Road, Shanghai 200126, China
- NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- Shanghai Frontiers Science Center of Artificial Intelligence and Deep Learning, 567 West Yangsi Road, Shanghai 200126, China
- Center for Quantum and Topological Systems (CQTS), NYUAD Research Institute, New York University, Abu Dhabi, United Arab Emirates
- Department of Physics, New York University, New York, New York 10003, USA
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Manikandan SK, Elouard C, Murch KW, Auffèves A, Jordan AN. Efficiently fueling a quantum engine with incompatible measurements. Phys Rev E 2022; 105:044137. [PMID: 35590558 DOI: 10.1103/physreve.105.044137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2021] [Accepted: 03/25/2022] [Indexed: 06/15/2023]
Abstract
We propose a quantum harmonic oscillator measurement engine fueled by simultaneous quantum measurements of the noncommuting position and momentum quadratures of the quantum oscillator. The engine extracts work by moving the harmonic trap suddenly, conditioned on the measurement outcomes. We present two protocols for work extraction, respectively based on single-shot and time-continuous quantum measurements. In the single-shot limit, the oscillator is measured in a coherent state basis; the measurement adds an average of one quantum of energy to the oscillator, which is then extracted in the feedback step. In the time-continuous limit, continuous weak quantum measurements of both position and momentum of the quantum oscillator result in a coherent state, whose coordinates diffuse in time. We relate the extractable work to the noise added by quadrature measurements, and present exact results for the work distribution at arbitrary finite time. Both protocols can achieve unit work conversion efficiency in principle.
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Affiliation(s)
- Sreenath K Manikandan
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
- Center for Coherence and Quantum Optics, University of Rochester, Rochester, New York 14627, USA
- Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, SE-106 91 Stockholm, Sweden
| | - Cyril Elouard
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
- QUANTIC laboratory, INRIA Paris, 2 Rue Simone Iff, 75012 Paris, France
| | - Kater W Murch
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
| | - Alexia Auffèves
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | - Andrew N Jordan
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
- Center for Coherence and Quantum Optics, University of Rochester, Rochester, New York 14627, USA
- Institute for Quantum Studies, Chapman University, Orange, California, 92866, USA
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