1
|
Magann AB, Rudinger KM, Grace MD, Sarovar M. Feedback-Based Quantum Optimization. PHYSICAL REVIEW LETTERS 2022; 129:250502. [PMID: 36608235 DOI: 10.1103/physrevlett.129.250502] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2021] [Revised: 08/08/2022] [Accepted: 09/23/2022] [Indexed: 06/17/2023]
Abstract
It is hoped that quantum computers will offer advantages over classical computers for combinatorial optimization. Here, we introduce a feedback-based strategy for quantum optimization, where the results of qubit measurements are used to constructively assign values to quantum circuit parameters. We show that this procedure results in an estimate of the combinatorial optimization problem solution that improves monotonically with the depth of the quantum circuit. Importantly, the measurement-based feedback enables approximate solutions to the combinatorial optimization problem without the need for any classical optimization effort, as would be required for the quantum approximate optimization algorithm. We demonstrate this feedback-based protocol on a superconducting quantum processor for the graph-partitioning problem MaxCut, and present a series of numerical analyses that further investigate the protocol's performance.
Collapse
Affiliation(s)
- Alicia B Magann
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Livermore, California 94550, USA
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Kenneth M Rudinger
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Matthew D Grace
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Livermore, California 94550, USA
| | - Mohan Sarovar
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Livermore, California 94550, USA
| |
Collapse
|
2
|
|
3
|
Ho TS, Rabitz H. Accelerated monotonic convergence of optimal control over quantum dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:026703. [PMID: 20866936 DOI: 10.1103/physreve.82.026703] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2009] [Revised: 05/21/2010] [Indexed: 05/29/2023]
Abstract
The control of quantum dynamics is often concerned with finding time-dependent optimal control fields that can take a system from an initial state to a final state to attain the desired value of an observable. This paper presents a general method for formulating monotonically convergent algorithms to iteratively improve control fields. The formulation is based on a two-point boundary-value quantum control paradigm (TBQCP) expressed as a nonlinear integral equation of the first kind arising from dynamical invariant tracking control. TBQCP is shown to be related to various existing techniques, including local control theory, the Krotov method, and optimal control theory. Several accelerated monotonic convergence schemes for iteratively computing control fields are derived based on TBQCP. Numerical simulations are compared with the Krotov method showing that the new TBQCP schemes are efficient and remain monotonically convergent over a wide range of the iteration step parameters and the control pulse lengths, which is attributable to the trap-free character of the transition probability quantum dynamics control landscape.
Collapse
Affiliation(s)
- Tak-San Ho
- Department of Chemistry, Princeton University, Princeton, NJ 08544, USA.
| | | |
Collapse
|
4
|
|
5
|
Local Control Theory: Recent Applications to Energy and Particle Transfer Processes in Molecules. ADVANCES IN CHEMICAL PHYSICS 2009. [DOI: 10.1002/9780470431917.ch2] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/04/2023]
|
6
|
Sugimori K, Ito T, Takata Y, Ichitani K, Nagao H, Nishikawa K. Theoretical Study of Above-Threshold Dissociation on Diatomic Molecules by Using Nonresonant Intense Laser Pulses. J Phys Chem A 2007; 111:9417-23. [PMID: 17784738 DOI: 10.1021/jp074071x] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The above-threshold dissociation of the ground state of a OH molecule under intense nonresonant laser pulses has been studied using the time-dependent Schrödinger equation with discrete variable representation. The applied field is assumed as a two-color mixed nonresonant laser pulses which has the nonresonant frequency omega and the overtone 2omega. After modulating the relative phase factor between the omega and 2omega pulse, we extracted a three-photon absorption peak or a five-photon absorption peak in the ATD spectrum.
Collapse
|
7
|
Sugawara M. Quantum dynamics driven by continuous laser fields under measurements: Towards measurement-assisted quantum dynamics control. J Chem Phys 2005; 123:204115. [PMID: 16351248 DOI: 10.1063/1.2132275] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study quantum system dynamics driven by continuous laser fields under the measurement process. In order to take into account the system transition due to the measurement, we define the superoperator which eliminates the coherence relevant to the measured quantum states. We clarify that the dynamics of the measured states is frozen in the frequent measurement limit, while the space spanned by unmeasured states is isolated from the original system. We also derive the effective Liouvillian which governs incoherent population dynamics under the condition, in which measurements are frequently applied. We apply the formulation to two-level and Lambda-type three-level systems and clarify how the quantum measurements hinder the coherent population dynamics driven by the continuous laser fields in practical examples. Analysis on the laser field amplitude dependency of the final distribution in the t-->infinity limit suggests the possibility of the measurement-assisted quantum control.
Collapse
Affiliation(s)
- M Sugawara
- Department of Fundamental Science and Technology, Graduate School of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan.
| |
Collapse
|
8
|
Xu R, Yan Y, Ohtsuki Y, Fujimura Y, Rabitz H. Optimal control of quantum non-Markovian dissipation: Reduced Liouville-space theory. J Chem Phys 2004; 120:6600-8. [PMID: 15267552 DOI: 10.1063/1.1665486] [Citation(s) in RCA: 52] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Abstract
An optimal control theory for open quantum systems is constructed containing non-Markovian dissipation manipulated by an external control field. The control theory is developed based on a novel quantum dissipation formulation that treats both the initial canonical ensemble and the subsequent reduced control dynamics. An associated scheme of backward propagation is presented, allowing the efficient evaluation of general optimal control problems. As an illustration, the control theory is applied to the vibration of the hydrogen fluoride molecule embedded in a non-Markovian dissipative medium. The importance of control-dissipation correlation is evident in the results.
Collapse
Affiliation(s)
- Ruixue Xu
- Open Laboratory of Bond-Selective Chemistry, University of Science and Technology of China, Hefei, China.
| | | | | | | | | |
Collapse
|
9
|
|
10
|
Sugawara M. General formulation of locally designed coherent control theory for quantum system. J Chem Phys 2003. [DOI: 10.1063/1.1559680] [Citation(s) in RCA: 65] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
11
|
|
12
|
Sugawara M, Yoshizawa S, Yabushita S. Coherent control of wavepacket dynamics by locally designed external field. Chem Phys Lett 2001. [DOI: 10.1016/s0009-2614(01)01259-3] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
13
|
|
14
|
Ohtsuki Y, Sugawara M, Kono H, Fujimura Y. Quantum Control of Molecular Reaction Dynamics by Laser Pulses: Development of Theory and Its Application. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 2001. [DOI: 10.1246/bcsj.74.1167] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
|
15
|
Umeda H, Fujimura Y. Quantum control of chemical reaction dynamics in a classical way. J Chem Phys 2000. [DOI: 10.1063/1.1287837] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
16
|
Hoki K, Ohtsuki Y, Kono H, Fujimura Y, Koseki S. Quantum Control of the Photodissociation of Sodium Iodide. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 1999. [DOI: 10.1246/bcsj.72.2665] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
17
|
|
18
|
Ohtsuki Y, Yahata Y, Kono H, Fujimura Y. Application of a locally optimized control theory to pump–dump laser-driven chemical reactions. Chem Phys Lett 1998. [DOI: 10.1016/s0009-2614(98)00224-3] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
19
|
Tanimura Y, Maruyama Y. Gaussian–Markovian quantum Fokker–Planck approach to nonlinear spectroscopy of a displaced Morse potentials system: Dissociation, predissociation, and optical Stark effects. J Chem Phys 1997. [DOI: 10.1063/1.474531] [Citation(s) in RCA: 66] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
|
20
|
Watanabe Y, Umeda H, Ohtsuki Y, Kono H, Fujimura Y. A theory of coherent control of reaction dynamics based on the optimization of a linear time-invariant system with complex variables. Chem Phys 1997. [DOI: 10.1016/s0301-0104(97)00057-8] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
21
|
A nuclear wavepacket study of unimolecular reactions in ultrashort pulsed lasers. J CHEM SCI 1995. [DOI: 10.1007/bf02869977] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
|