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Stevens J, Szombati D, Maffei M, Elouard C, Assouly R, Cottet N, Dassonneville R, Ficheux Q, Zeppetzauer S, Bienfait A, Jordan AN, Auffèves A, Huard B. Energetics of a Single Qubit Gate. PHYSICAL REVIEW LETTERS 2022; 129:110601. [PMID: 36154409 DOI: 10.1103/physrevlett.129.110601] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2021] [Revised: 08/19/2022] [Accepted: 08/24/2022] [Indexed: 06/16/2023]
Abstract
Qubits are physical, a quantum gate thus not only acts on the information carried by the qubit but also on its energy. What is then the corresponding flow of energy between the qubit and the controller that implements the gate? Here we exploit a superconducting platform to answer this question in the case of a quantum gate realized by a resonant drive field. During the gate, the superconducting qubit becomes entangled with the microwave drive pulse so that there is a quantum superposition between energy flows. We measure the energy change in the drive field conditioned on the outcome of a projective qubit measurement. We demonstrate that the drive's energy change associated with the measurement backaction can exceed by far the energy that can be extracted by the qubit. This can be understood by considering the qubit as a weak measurement apparatus of the driving field.
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Affiliation(s)
- J Stevens
- Ecole Normale Supérieure de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - D Szombati
- Ecole Normale Supérieure de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - M Maffei
- CNRS and Université Grenoble Alpes, Institut Néel, F-38042 Grenoble, France
| | - C Elouard
- QUANTIC team, INRIA de Paris, 2 Rue Simone Iff, 75012 Paris, France
| | - R Assouly
- Ecole Normale Supérieure de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - N Cottet
- Ecole Normale Supérieure de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - R Dassonneville
- Ecole Normale Supérieure de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Q Ficheux
- Ecole Normale Supérieure de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - S Zeppetzauer
- Ecole Normale Supérieure de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - A Bienfait
- Ecole Normale Supérieure de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - A N Jordan
- Institute for Quantum Studies, Chapman University, 1 University Drive, Orange, California 92866, USA
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
| | - A Auffèves
- CNRS and Université Grenoble Alpes, Institut Néel, F-38042 Grenoble, France
| | - B Huard
- Ecole Normale Supérieure de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France
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2
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Schäfer F, Sekatski P, Koppenhöfer M, Bruder C, Kloc M. Control of stochastic quantum dynamics by differentiable programming. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2021. [DOI: 10.1088/2632-2153/abec22] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
Abstract
Control of the stochastic dynamics of a quantum system is indispensable in fields such as quantum information processing and metrology. However, there is no general ready-made approach to the design of efficient control strategies. Here, we propose a framework for the automated design of control schemes based on differentiable programming. We apply this approach to the state preparation and stabilization of a qubit subjected to homodyne detection. To this end, we formulate the control task as an optimization problem where the loss function quantifies the distance from the target state, and we employ neural networks (NNs) as controllers. The system’s time evolution is governed by a stochastic differential equation (SDE). To implement efficient training, we backpropagate the gradient information from the loss function through the SDE solver using adjoint sensitivity methods. As a first example, we feed the quantum state to the controller and focus on different methods of obtaining gradients. As a second example, we directly feed the homodyne detection signal to the controller. The instantaneous value of the homodyne current contains only very limited information on the actual state of the system, masked by unavoidable photon-number fluctuations. Despite the resulting poor signal-to-noise ratio, we can train our controller to prepare and stabilize the qubit to a target state with a mean fidelity of around 85%. We also compare the solutions found by the NN to a hand-crafted control strategy.
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3
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Monroe JT, Yunger Halpern N, Lee T, Murch KW. Weak Measurement of a Superconducting Qubit Reconciles Incompatible Operators. PHYSICAL REVIEW LETTERS 2021; 126:100403. [PMID: 33784149 DOI: 10.1103/physrevlett.126.100403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2020] [Revised: 11/19/2020] [Accepted: 01/29/2021] [Indexed: 06/12/2023]
Abstract
Traditional uncertainty relations dictate a minimal amount of noise in incompatible projective quantum measurements. However, not all measurements are projective. Weak measurements are minimally invasive methods for obtaining partial state information without projection. Recently, weak measurements were shown to obey an uncertainty relation cast in terms of entropies. We experimentally test this entropic uncertainty relation with strong and weak measurements of a superconducting transmon qubit. A weak measurement, we find, can reconcile two strong measurements' incompatibility, via backaction on the state. Mathematically, a weak value-a preselected and postselected expectation value-lowers the uncertainty bound. Hence we provide experimental support for the physical interpretation of the weak value as a determinant of a weak measurement's ability to reconcile incompatible operations.
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Affiliation(s)
- Jonathan T Monroe
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
| | - Nicole Yunger Halpern
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, Maryland 20742, USA
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - Taeho Lee
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
| | - Kater W Murch
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
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4
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Naghiloo M, Tan D, Harrington PM, Alonso JJ, Lutz E, Romito A, Murch KW. Heat and Work Along Individual Trajectories of a Quantum Bit. PHYSICAL REVIEW LETTERS 2020; 124:110604. [PMID: 32242716 DOI: 10.1103/physrevlett.124.110604] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2019] [Accepted: 02/07/2020] [Indexed: 06/11/2023]
Abstract
We use a near quantum limited detector to experimentally track individual quantum state trajectories of a driven qubit formed by the hybridization of a waveguide cavity and a transmon circuit. For each measured quantum coherent trajectory, we separately identify energy changes of the qubit as heat and work, and verify the first law of thermodynamics for an open quantum system. We further establish the consistency of these results by comparison with the master equation approach and the two-projective-measurement scheme, both for open and closed dynamics, with the help of a quantum feedback loop that compensates for the exchanged heat and effectively isolates the qubit.
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Affiliation(s)
- M Naghiloo
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
| | - D Tan
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, People's Republic of China
| | - P M Harrington
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
| | - J J Alonso
- Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany
| | - E Lutz
- Institute for Theoretical Physics I, University of Stuttgart, D-70550 Stuttgart, Germany
| | - A Romito
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - K W Murch
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
- Institute for Materials Science and Engineering, St. Louis, Missouri 63130, USA
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5
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Harrington PM, Tan D, Naghiloo M, Murch KW. Characterizing a Statistical Arrow of Time in Quantum Measurement Dynamics. PHYSICAL REVIEW LETTERS 2019; 123:020502. [PMID: 31386500 DOI: 10.1103/physrevlett.123.020502] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2018] [Revised: 04/02/2019] [Indexed: 06/10/2023]
Abstract
In both thermodynamics and quantum mechanics, the arrow of time is characterized by the statistical likelihood of physical processes. We characterize this arrow of time for the continuous quantum measurement dynamics of a superconducting qubit. By experimentally tracking individual weak measurement trajectories, we compare the path probabilities of forward and backward-in-time evolution to develop an arrow of time statistic associated with measurement dynamics. We compare the statistics of individual trajectories to ensemble properties showing that the measurement dynamics obeys both detailed and integral fluctuation theorems, thus establishing the consistency between microscopic and macroscopic measurement dynamics.
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Affiliation(s)
- P M Harrington
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
| | - D Tan
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, People's Republic of China
| | - M Naghiloo
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
| | - K W Murch
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
- Institute for Materials Science and Engineering, St. Louis, Missouri 63130, USA
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6
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Dynamics of a qubit while simultaneously monitoring its relaxation and dephasing. Nat Commun 2018; 9:1926. [PMID: 29765040 PMCID: PMC5954145 DOI: 10.1038/s41467-018-04372-9] [Citation(s) in RCA: 38] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2017] [Accepted: 04/25/2018] [Indexed: 11/16/2022] Open
Abstract
Decoherence originates from the leakage of quantum information into external degrees of freedom. For a qubit, the two main decoherence channels are relaxation and dephasing. Here, we report an experiment on a superconducting qubit where we retrieve part of the lost information in both of these channels. We demonstrate that raw averaging the corresponding measurement records provides a full quantum tomography of the qubit state where all three components of the effective spin-1/2 are simultaneously measured. From single realizations of the experiment, it is possible to infer the quantum trajectories followed by the qubit state conditioned on relaxation and/or dephasing channels. The incompatibility between these quantum measurements of the qubit leads to observable consequences in the statistics of quantum states. The high level of controllability of superconducting circuits enables us to explore many regimes from the Zeno effect to underdamped Rabi oscillations depending on the relative strengths of driving, dephasing, and relaxation. Information leaked by a quantum system into its environment causes decoherence but if it is recorded then it can be used to infer the quantum state. Ficheux et al. monitor the relaxation and dephasing of a qubit and show that this allows all three components of the qubit to be probed simultaneously.
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7
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Kittipute K, Saratayon P, Srisook S, Wardkein P. Homodyne detection of short-range Doppler radar using a forced oscillator model. Sci Rep 2017; 7:43680. [PMID: 28252000 PMCID: PMC5333100 DOI: 10.1038/srep43680] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2016] [Accepted: 01/26/2017] [Indexed: 11/09/2022] Open
Abstract
This article presents the homodyne detection in a self-oscillation system, which represented by a short-range radar (SRR) circuit, that is analysed using a multi-time forced oscillator (MTFO) model. The MTFO model is based on a forced oscillation perspective with the signal and system theory, a second-order differential equation, and the multiple time variable technique. This model can also apply to analyse the homodyne phenomenon in a difference kind of the oscillation system under same method such as the self-oscillation system, and the natural oscillation system with external forced. In a free oscillation system, which forced by the external source is represented by a pendulum with an oscillating support experiment, and a modified Colpitts oscillator circuit in the UHF band with input as a Doppler signal is a representative of self-oscillation system. The MTFO model is verified with the experimental result, which well in line with the theoretical analysis.
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8
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Campagne-Ibarcq P, Jezouin S, Cottet N, Six P, Bretheau L, Mallet F, Sarlette A, Rouchon P, Huard B. Using Spontaneous Emission of a Qubit as a Resource for Feedback Control. PHYSICAL REVIEW LETTERS 2016; 117:060502. [PMID: 27541448 DOI: 10.1103/physrevlett.117.060502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2016] [Indexed: 06/06/2023]
Abstract
Persistent control of a transmon qubit is performed by a feedback protocol based on continuous heterodyne measurement of its fluorescence. By driving the qubit and cavity with microwave signals whose amplitudes depend linearly on the instantaneous values of the quadratures of the measured fluorescence field, we show that it is possible to stabilize permanently the qubit in any targeted state. Using a Josephson mixer as a phase-preserving amplifier, it was possible to reach a total measurement efficiency η=35%, leading to a maximum of 59% of excitation and 44% of coherence for the stabilized states. The experiment demonstrates multiple-input multiple-output analog Markovian feedback in the quantum regime.
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Affiliation(s)
- P Campagne-Ibarcq
- Laboratoire Pierre Aigrain, Ecole Normale Supérieure-PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, 24 rue Lhomond, 75231 Paris Cedex 05, France
- Quantic Team, INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France
| | - S Jezouin
- Laboratoire Pierre Aigrain, Ecole Normale Supérieure-PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, 24 rue Lhomond, 75231 Paris Cedex 05, France
- Quantic Team, INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France
| | - N Cottet
- Laboratoire Pierre Aigrain, Ecole Normale Supérieure-PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, 24 rue Lhomond, 75231 Paris Cedex 05, France
- Quantic Team, INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France
| | - P Six
- Quantic Team, INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France
- Centre Automatique et Systèmes, Mines ParisTech, PSL Research University, 60 Boulevard Saint-Michel, 75272 Paris Cedex 6, France
| | - L Bretheau
- Laboratoire Pierre Aigrain, Ecole Normale Supérieure-PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, 24 rue Lhomond, 75231 Paris Cedex 05, France
- Quantic Team, INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France
| | - F Mallet
- Laboratoire Pierre Aigrain, Ecole Normale Supérieure-PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, 24 rue Lhomond, 75231 Paris Cedex 05, France
- Quantic Team, INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France
| | - A Sarlette
- Quantic Team, INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France
| | - P Rouchon
- Quantic Team, INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France
- Centre Automatique et Systèmes, Mines ParisTech, PSL Research University, 60 Boulevard Saint-Michel, 75272 Paris Cedex 6, France
| | - B Huard
- Laboratoire Pierre Aigrain, Ecole Normale Supérieure-PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, 24 rue Lhomond, 75231 Paris Cedex 05, France
- Quantic Team, INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France
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