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Zhang ZY, Hu JR, Fang YY, Li JF, Liu JM, Huang X, Sun Z. Quantum gate control of polar molecules with machine learning. J Chem Phys 2024; 161:034102. [PMID: 39007369 DOI: 10.1063/5.0216013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2024] [Accepted: 06/26/2024] [Indexed: 07/16/2024] Open
Abstract
We propose a scheme for achieving basic quantum gates using ultracold polar molecules in pendular states. The qubits are encoded in the YbF molecules trapped in an electric field with a certain gradient and coupled by the dipole-dipole interaction. The time-dependent control sequences consisting of multiple pulses are considered to interact with the pendular qubits. To achieve high-fidelity quantum gates, we map the control problem for the coupled molecular system into a Markov decision process and deal with it using the techniques of deep reinforcement learning (DRL). By training the agents over multiple episodes, the optimal control pulse sequences for the two-qubit gates of NOT, controlled NOT, and Hadamard are discovered with high fidelities. Moreover, the population dynamics of YbF molecules driven by the discovered gate sequences are analyzed in detail. Furthermore, by combining the optimal gate sequences, we successfully simulate the quantum circuit for entanglement. Our findings could offer new insights into efficiently controlling molecular systems for practical molecule-based quantum computing using DRL.
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Affiliation(s)
- Zuo-Yuan Zhang
- College of Physical Science and Technology, Yangzhou University, Yangzhou 225009, China
| | - Jie-Ru Hu
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Yu-Yan Fang
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Jin-Fang Li
- Department of Physics and Electronic Engineering, Xianyang Normal University, Shaanxi 712000, China
| | - Jin-Ming Liu
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
- Chongqing Key Laboratory of Precision Optics, Chongqing Institute of East China Normal University, Chongqing 401120, China
| | - Xinning Huang
- College of Physical Science and Technology, Yangzhou University, Yangzhou 225009, China
| | - Zhaoxi Sun
- Changping Laboratory, Beijing 102206, China
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Jahanpanah J, Esmaeilzadeh M. The stability conditions of diatomic molecules via analogy with the stability theory of lasers. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1155778] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- J. Jahanpanah
- Physics Department, Physics Faculty, Kharazmi University, Tehran, Iran
| | - M. Esmaeilzadeh
- Physics Department, Physics Faculty, Kharazmi University, Tehran, Iran
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Santos L, Justum Y, Vaeck N, Desouter-Lecomte M. Simulation of the elementary evolution operator with the motional states of an ion in an anharmonic trap. J Chem Phys 2015; 142:134304. [DOI: 10.1063/1.4916355] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ludovic Santos
- Laboratoire de Chimie Quantique et Photophysique, CP 160/09 Université Libre de Bruxelles, B-1050 Brussels, Belgium
| | - Yves Justum
- Laboratoire de Chimie Physique, UMR 8000 and CNRS, Université Paris-Sud, F-91405 Orsay, France
| | - Nathalie Vaeck
- Laboratoire de Chimie Quantique et Photophysique, CP 160/09 Université Libre de Bruxelles, B-1050 Brussels, Belgium
| | - M. Desouter-Lecomte
- Laboratoire de Chimie Physique, UMR 8000 and CNRS, Université Paris-Sud, F-91405 Orsay, France
- Département de Chimie, Université de Liège, Bât B6c, Sart Tilman B-4000, Liège, Belgium
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Shyshlov D, Berrios E, Gruebele M, Babikov D. On readout of vibrational qubits using quantum beats. J Chem Phys 2014; 141:224306. [PMID: 25494748 DOI: 10.1063/1.4903055] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Dmytro Shyshlov
- Chemistry Department, Marquette University, Milwaukee, Wisconsin 53201, USA
| | - Eduardo Berrios
- Department of Chemistry, Department of Physics and Center for Biophysics and Computational Biology, University of Illinois, Urbana, Illinois 61801, USA
| | - Martin Gruebele
- Department of Chemistry, Department of Physics and Center for Biophysics and Computational Biology, University of Illinois, Urbana, Illinois 61801, USA
| | - Dmitri Babikov
- Chemistry Department, Marquette University, Milwaukee, Wisconsin 53201, USA
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Jaouadi A, Barrez E, Justum Y, Desouter-Lecomte M. Quantum gates in hyperfine levels of ultracold alkali dimers by revisiting constrained-phase optimal control design. J Chem Phys 2013; 139:014310. [PMID: 23822306 DOI: 10.1063/1.4812317] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We simulate the implementation of a 3-qubit quantum Fourier transform gate in the hyperfine levels of ultracold polar alkali dimers in their first two lowest rotational levels. The chosen dimer is (41)K(87)Rb supposed to be trapped in an optical lattice. The hyperfine levels are split by a static magnetic field. The pulses operating in the microwave domain are obtained by optimal control theory. We revisit the problem of phase control in information processing. We compare the efficiency of two optimal fields. The first one is obtained from a functional based on the average of the transition probabilities for each computational basis state but constrained by a supplementary transformation to enforce phase alignment. The second is obtained from a functional constructed on the phase sensitive fidelity involving the sum of the transition amplitudes without any supplementary constrain.
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Affiliation(s)
- A Jaouadi
- Laboratoire de Chimie Physique, UMR 8000 and CNRS, Université Paris-Sud, Orsay, France
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Zhu J, Kais S, Wei Q, Herschbach D, Friedrich B. Implementation of quantum logic gates using polar molecules in pendular states. J Chem Phys 2013; 138:024104. [DOI: 10.1063/1.4774058] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Shyshlov D, Babikov D. Complexity and simplicity of optimal control theory pulses shaped for controlling vibrational qubits. J Chem Phys 2012. [PMID: 23181317 DOI: 10.1063/1.4765344] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In the context of molecular quantum computation the optimal control theory (OCT) is used to obtain shaped laser pulses for high-fidelity control of vibrational qubits. Optimization is done in time domain and the OCT algorithm varies values of electric field in each time step independently, tuning hundreds of thousands of parameters to find one optimal solution. Such flexibility is not available in experiments, where pulse shaping is done in frequency domain and the number of "tuning knobs" is much smaller. The question of possible experimental interpretations of theoretically found OCT solutions arises. In this work we analyze very accurate optimal pulse that we obtained for implementing quantum gate CNOT for the two-qubit system encoded into the exited vibrational states of thiophosgene molecule. Next, we try to alter this pulse by reducing the number of available frequency channels and intentionally introducing systematic and random errors (in frequency domain, by modifying the values of amplitudes and phases of different frequency components). We conclude that a very limited number of frequency components (only 32 in the model of thiophosgene) are really necessary for accurate control of the vibrational two-qubit system, and such pulses can be readily constructed using OCT. If the amplitude and phase errors of different frequency components do not exceed ±3% of the optimal values, one can still achieve accurate transformations of the vibrational two-qubit system, with gate fidelity of CNOT exceeding 0.99.
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Affiliation(s)
- Dmytro Shyshlov
- Department of Chemistry, Marquette University, PO Box 1881, Milwaukee, Wisconsin 53201, USA
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Zaari RR, Brown A. Effect of laser pulse shaping parameters on the fidelity of quantum logic gates. J Chem Phys 2012; 137:104306. [PMID: 22979858 DOI: 10.1063/1.4747703] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The effect of varying parameters specific to laser pulse shaping instruments on resulting fidelities for the ACNOT(1), NOT(2), and Hadamard(2) quantum logic gates are studied for the diatomic molecule (12)C(16)O. These parameters include varying the frequency resolution, adjusting the number of frequency components and also varying the amplitude and phase at each frequency component. A time domain analytic form of the original discretized frequency domain laser pulse function is derived, providing a useful means to infer the resulting pulse shape through variations to the aforementioned parameters. We show that amplitude variation at each frequency component is a crucial requirement for optimal laser pulse shaping, whereas phase variation provides minimal contribution. We also show that high fidelity laser pulses are dependent upon the frequency resolution and increasing the number of frequency components provides only a small incremental improvement to quantum gate fidelity. Analysis through use of the pulse area theorem confirms the resulting population dynamics for one or two frequency high fidelity laser pulses and implies similar dynamics for more complex laser pulse shapes. The ability to produce high fidelity laser pulses that provide both population control and global phase alignment is attributed greatly to the natural evolution phase alignment of the qubits involved within the quantum logic gate operation.
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Affiliation(s)
- Ryan R Zaari
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
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Wang L, Babikov D. Feasibility of encoding Shor's algorithm into the motional states of an ion in the anharmonic trap. J Chem Phys 2012; 137:064301. [PMID: 22897267 DOI: 10.1063/1.4742309] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We demonstrate theoretically that it may be possible to encode states of a multi-qubit system into the progression of quantized motional∕vibrational levels of an ion trapped in a weakly anharmonic potential. Control over such register of quantum information is achieved by applying oscillatory radio-frequency fields shaped optimally for excitation of the desired state-to-state transitions. Anharmonicity of the vibrational spectrum plays a key role in this approach to the control and quantum computation, since it allows resolving different state-to-state transitions and addressing them selectively. Optimal control theory is used to derive pulses for implementing the four-qubit version of Shor's algorithm in a single step. Accuracy of the qubit-state transformations, reached in the numerical simulations, is around 0.999. Very detailed insight is obtained by analysis of the time-evolution of state populations and by spectral analysis of the optimized pulse.
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Affiliation(s)
- Lei Wang
- Chemistry Department, Marquette University, PO Box 1881, Milwaukee, Wisconsin 53201, USA
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Shu CC, Rozgonyi T, González L, Henriksen NE. A theoretical investigation of the feasibility of Tannor-Rice type control: Application to selective bond breakage in gas-phase dihalomethanes. J Chem Phys 2012; 136:174303. [DOI: 10.1063/1.4706603] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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