Preparing quantum states by measurement-feedback control with Bayesian optimization

doi:10.1007/s11467-023-1311-5

Front. Phys.

2023, Vol. 18

Issue (6) : 61301 https://doi.org/10.1007/s11467-023-1311-5

RESEARCH ARTICLE

Preparing quantum states by measurement-feedback control with Bayesian optimization

Yadong Wu^1,^2,^3,⁴, Juan Yao^5,^6,⁷, Pengfei Zhang^1,⁸(

)

¹. Department of Physics, Fudan University, Shanghai 200438, China
². State Key Laboratory of Surface Physics, Key Laboratory of Micro and Nano Photonic Structures (MOE), Fudan University, Shanghai 200438, China
³. Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Shanghai 200433, China
⁴. Shanghai Qi Zhi Institute, AI Tower, Xuhui District, Shanghai 200232, China
⁵. Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
⁶. International Quantum Academy, Shenzhen 518048, China
⁷. Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
⁸. Walter Burke Institute for Theoretical Physics & Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125, USA

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Abstract

The preparation of quantum states is crucial for enabling quantum computations and simulations. In this work, we present a general framework for preparing ground states of many-body systems by combining the measurement-feedback control process (MFCP) with machine learning techniques. Specifically, we employ Bayesian optimization (BO) to enhance the efficiency of determining the measurement and feedback operators within the MFCP. As an illustration, we study the ground state preparation of the one-dimensional Bose−Hubbard model. Through BO, we are able to identify optimal parameters that can effectively drive the system towards low-energy states with a high probability across various quantum trajectories. Our results open up new directions for further exploration and development of advanced control strategies for quantum computations and simulations.

Keywords state preparation feedback control Bayesian optimization

Corresponding Author(s): Pengfei Zhang

About author:

^* These authors contributed equally to this work.

Issue Date: 30 June 2023

Cite this article:

Yadong Wu,Juan Yao,Pengfei Zhang. Preparing quantum states by measurement-feedback control with Bayesian optimization[J]. Front. Phys. , 2023, 18(6): 61301.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1311-5
https://academic.hep.com.cn/fop/EN/Y2023/V18/I6/61301

Fig.1 (a) MFCP for a quantum system.

A^(c m)

is the measurement step and

U^(F^)

is the feedback control step. At each time interval, the feedback control step evolves the system with the measurement signal

c m

. After

T

times the system is detected. (b) The general procedure of the BO method to obtain the global extremum of a “black-box” function

f (θ)

Fig.2 (a, b) Energy expectation of non-interacting Hamiltonian. Red curves are the mean value of

y (θ BO ∗)

for each epoch. Blue curves are the mean value of the minimal energy expectation

y min

during training. The shades are the minimal energy expectation standard variance of 10 different training processes. (c, d) Energy expectation during MFCP with 20 different initial states. Red curves are the mean value of energy expectation driven by analytical optimal operators with parameters

θ L

. Red shades are the energy standard variance. Blue curves are the mean value of energy expectation driven by operators after BO training

θ BO

. Gray dashed lines are the ground state energies without interaction. The true ground state energy is calculated as

E 0 / J = ? 4.854

for

N = 3, M = 4

and

E 0 / J = ? 6.472

for

N = 4, M = 4

respectively.

Fig.3 (a, b) Energy expectation of strong interaction system. Red curves are the mean value of

E B O = y (θ B O ∗)

for each epoch. Blue curves are the mean value of the minimal energy expectation

E m i n

during training. The shades are the minimal energy expectation standard variance of 10 different training processes. With strong interactions, true ground state energy is calculated as

E 0 / J = ? 2.771

for

N = 3, M = 4

and

E 0 / J = ? 2.204

for

N = 4, M = 4

. (c, d) Histogram of the first 100 small state energy among 200 dynamic trajectories. The light-red bar denotes the MFCP driven by

θ L

and the light-blue bar denotes the MFCP driven by

θ B O

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