A Survey of Quantum Lyapunov Control Methods

Cong, Shuang; Meng, Fanqing

doi:10.1155/2013/967529

Cited by 28 publications

(17 citation statements)

References 45 publications

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“…3, in which 11 ρ is probability of the qubit in state L . The maximum transfer probability ( 11 ρ in Fig.…”

Section: Numerical Simulation and Results Analysismentioning

confidence: 99%

“…This theorem was originally used to judge if a system was stable, and later it was widely used to design at least a stable control system. Now the Lyapunov control method becomes a very popular control law design method in systems control community like the optimal control method, and it has the advantages of easy to design, and the control law has analytical form [11]. For the design of the control law based on Lyapunov control method, one should select a Lyapunov function ( ) V x which is semi-definite positive and differentiable in the phase space ( )…”

Section: Design Of Control Field For the Two-level Dqdmentioning

confidence: 99%

“…Quantum Lyapunov control method has been studied for ten years, and obtained series of research achievements [11,12]. We expect to use quantum Lyapunov control method [13] to design a Lyapunov control field specially for the state transfer of two-level DQD system in order to obtain higher state transfer performances.…”

Section: Introductionmentioning

confidence: 99%

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Ultrafast Manipulation of a Double Quantum-Dot Charge Qubit Using Lyapunov-Based Control Method

Cong

Gao

Cao

et al. 2015

IEEE J. Quantum Electron.

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Abstract-For a double quantum dot (DQD) system, here we propose alternative ultrafast manipulate approach: Lyapunov control method, to transfer the state from R to L on the picosecond scale, orders of magnitude faster and transfer probability higher than the previously measured electrically controlled charge-or spin-based quits. The control laws are composed of two-direction components, one is used to eliminate the dissipation in the system, another is used to transfer the state. The control theory's stability ensures the system can be transferred to the target state in high probability, and the coefficients in control laws leads very fast convergence. The role of eliminating the dissipation plays the suppression of decoherence effect. Numerical simulation results show that under the realistic implementation conditions, the transfer probability and fidelity can be increased up to 98.79% and 98.97%, respectively. This is the first result directly applicable to a DQD system's state transferring using the Lyapunov control method. We also give specific experimental realization scheme.Index terms-double quantum dot (DQD), LZS interference, quantum Lyapunov control method, numerical simulations I. INTRODUCTIONEMICONDUCTOR quantum dot is an artificial solid-state quantum system, its shape and size are manageable, easy to manipulate and measure, moreover, it can make use of the mature semiconductor integrated circuit technology in classical computer, all of these advantages make the quantum dots be highly scalable and become one of the powerful candidates for quantum compute. The decoherence time of the free electrons in semiconductor quantum dots is usually within a few nanoseconds ( manipulation need to accomplish the manipulation process of the quantum system before the decoherence. In recent years, people have worked intensively on the experimental apparatus for realizing this goal. LZS interference was first proposed by Landau, Zener and Stücklberg which occurs when the control field sweeps through the anti-crossing of a two-level system. There will generate a significant tunneling from the ground state to the excited state, in this way, the interference caused by the evolutionary trajectory of ground state and exited state will lead to the LZS interference. As the target state is defined by the constructive interference of LZS interference, and research results show that the LZS interference method is robust to certain types of noise and might enable the implementation of manipulating qubits with high fidelity [4][5][6][7], therefore the coherent dynamics of LZS interference process aroused a great deal of interest for quantum control [8]. Cao et. al. carried out the qubits state transfer in a double quantum dot (DQD) system by utilizing the LZS interference [9]. In their experiments, the system could transfer from the initial state to target state with a probability of ~ 68%, and the fidelity of the system could reach ~ 80%.Can other control methods be used for further improving the state transfer performances of...

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“…3, in which 11 ρ is probability of the qubit in state L . The maximum transfer probability ( 11 ρ in Fig.…”

Section: Numerical Simulation and Results Analysismentioning

confidence: 99%

Section: Design Of Control Field For the Two-level Dqdmentioning

confidence: 99%

See 1 more Smart Citation

Ultrafast Manipulation of a Double Quantum-Dot Charge Qubit Using Lyapunov-Based Control Method

Cong

Gao

Cao

et al. 2015

IEEE J. Quantum Electron.

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show abstract

“…Most studies of quantum control are concerned with transferring the state of the system to a desired final state [9,10]. Quantum Lyapunov control (QLC) has been widely studied to control quantum systems for state preparation [11,12], trajectory tracking [13,14] and state transfer [15][16][17] with different Lyapunov functions [18,19]. In QLC, the control laws are designed by keeping the first-order time derivative of a selected Lyapunov function less than zero.…”

Section: Introductionmentioning

confidence: 99%

“…, Hamiltonians H 0 , H 1 , H 2 and Lyapunov control parameter K j in Equation(19). : for t = 1, 2, .…”

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confidence: 99%

State Transfer via On-Line State Estimation and Lyapunov-Based Feedback Control for a N-Qubit System

Harraz

Cong

2019

Entropy

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In this paper, we propose a Lyapunov-based state feedback control for state transfer based on the on-line quantum state estimation (OQSE). The OQSE is designed based on continuous weak measurements and compressed sensing. The controlled system is described by quantum master equation for open quantum systems, and the continuous measurement operators are derived according to the dynamic equation of system. The feedback control law is designed based on the Lyapunov stability theorem, and a strict proof of proposed control laws are given. At each sampling time, the state is estimated on-line, which is used to design the control law. The simulation experimental results show the effectiveness of the proposed feedback control strategy.

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Quantum optimization algorithms: Energetic implications

Hong Enriquez,

Badia,

Chapman

et al. 2024

Concurrency and Computation

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SummarySince the dawn of quantum computing (QC), theoretical developments like Shor's algorithm proved the conceptual superiority of QC over traditional computing. However, such quantum supremacy claims are difficult to achieve in practice because of the technical challenges of realizing noiseless qubits. In the near future, QC applications will need to rely on noisy quantum devices that offload part of their work to classical devices. One way to achieve this is by using parameterized quantum circuits in optimization or even in machine learning tasks. The energy requirements of quantum algorithms have not yet been studied extensively. In this article, we explore several optimization algorithms using both theoretical insights and numerical experiments to understand their impact on energy consumption. Specifically, we highlight why and how algorithms like quantum natural gradient descent, simultaneous perturbation stochastic approximations or circuit learning methods, are at least to more energy efficient than their classical counterparts; why feedback‐based quantum optimization is energy‐inefficient; and how techniques like Rosalin can improve the energy efficiency of other algorithms by a factor of 20. Finally, we use the NchooseK high‐level programming model to run optimization problems on both gate‐based quantum computers and quantum annealers. Empirical data indicate that these optimization problems run faster, have better success rates, and consume less energy on quantum annealers than on their gate‐based counterparts.

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A Survey of Quantum Lyapunov Control Methods

Cited by 28 publications

References 45 publications

Ultrafast Manipulation of a Double Quantum-Dot Charge Qubit Using Lyapunov-Based Control Method

Ultrafast Manipulation of a Double Quantum-Dot Charge Qubit Using Lyapunov-Based Control Method

State Transfer via On-Line State Estimation and Lyapunov-Based Feedback Control for a N-Qubit System

Quantum optimization algorithms: Energetic implications

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