IEEE Conference on Decision and Control (CDC)

Experimental design and identifiability of model parameters for quantum systems

Ming Zhang, S. G. Schirmer, Hong‐Yi Dai, Weiwei Zhou, Min Lin

Published Dec 1, 2009• 5 citations

Abstract

This paper explores the experimental design and identifiability problems for both closed and open quantum systems. In general, the identifiability of quantum systems depends on both the choice of model sets and experimental design. The limits of identifiability in certain experimental settings and ways to improve the identifiability of model parameters by changing experimental conditions are investigated. Furthermore, it is exemplified that the experiment design in the domain of quantum system identification at least include the three following aspects: (1) initialization procedures, (2) measurement methods, and (3) the choice of coherent control.

DOI: 10.1109/cdc.2009.5400380

Related papers

Experimentally Determining Bloch Parameters of Hamiltonian for Single-Qubit Systems

Ming Zhang, Zhou Wei-Wei, Hong‐Yi Dai +3 more

By considering the identification problem of unknown but fixed Hamiltonian H = S 0 σ 0 + Σ i = x, y, z S i σ i where σ i (i = x, y, z) are pauli matrices and σ 0 = I, we explore the feasibility and limitation of empirically determining the Hamiltonian parameters for quantum systems under experimental conditions imposed by projective measurements and initialization procedures. It may be unsurprising to physicists that one can not obtain the knowledge of So no matter what kind of projective measurements and initialization are permitted, but the observation draws our attention to the importance of the parameter identifiability under different experimental condition. It has also been revealed that one can obtain the knowledge of |S z | and S x 2 + S y 2 at most when only the projective measurement {|0⟩⟨0|, |1⟩⟨1|} is permitted to perform on and initialize the qubit. Further more, we demonstrated that it is feasible to distinguish |S x |, |S y |, and |S Z | even without any a priori information about Hamiltonian if at least two kinds of projective measurement or initialization procedures are permitted. It should be emphasized that both projective measurements and initialization procedures play an important role in quantum system identification.

Communications in Theoretical PhysicsJun 1, 20104 citations

Quantum system identification: Hamiltonian estimation using spectral and Bayesian analysis

Sophie G Schirmer, Frank C Langbein

Identifying the Hamiltonian of a quantum system from experimental data is considered. General limits on the identifiability of model parameters with limited experimental resources are investigated, and a specific Bayesian estimation procedure is proposed and evaluated for a model system where a-priori information about the Hamiltonian's structure is available.

arXiv:0911.5429International Symposium on Communications, Control and Signal ProcessingMar 1, 20106 citations

Experimental graybox quantum system identification and control

Akram Youssry, Yang Yang, Robert J. Chapman +4 more

Understanding and controlling engineered quantum systems is key to developing practical quantum technology. However, given the current technological limitations, such as fabrication imperfections and environmental noise, this is not always possible. To address these issues, a great deal of theoretical and numerical methods for quantum system identification and control have been developed. These methods range from traditional curve fittings, which are limited by the accuracy of the model that describes the system, to machine learning methods, which provide efficient control solutions but no control beyond the output of the model, nor insights into the underlying physical process. Here we experimentally demonstrate a "graybox" approach to construct a physical model of a quantum system and use it to design optimal control. We report superior performance over model fitting, while generating unitaries and Hamiltonians, which are quantities not available from the structure of standard supervised machine learning models. Our approach combines physics principles with high-accuracy machine learning and is effective with any problem where the required controlled quantities cannot be directly measured in experiments. This method naturally extends to time-dependent and open quantum systems, with applications in quantum noise spectroscopy and cancellation.

arXiv:2206.12201Jun 24, 20223 citations

Identifiability and characterization of transmon qutrits through Bayesian experimental design

Sohail R. Reddy

Robust control of a quantum system is essential to utilize the current noisy quantum hardware to its full potential, such as quantum algorithms. To achieve such a goal, a systematic search for an optimal control for any given experiment is essential. The design of optimal control pulses requires accurate numerical models and, therefore, accurate characterization of the system parameters. We present an online Bayesian approach for quantum characterization of qutrit systems, which automatically and systematically identifies optimal experiments that provide maximum information on the system parameters, thereby greatly reducing the number of experiments that need to be performed on the quantum testbed. Unlike most characterization protocols that provide point-estimates of the parameters, the proposed approach is able to estimate their probability distribution. The applicability of the Bayesian experimental design technique was demonstrated on test problems, where each experiment was defined by a parameterized control pulse. In addition to this, we also present an approach for iterative pulse extension, which is robust under uncertainties in transition frequencies and coherence times, and shot noise, despite being initialized with wide uninformative priors. Furthermore, we provide a mathematical proof of the theoretical identifiability of the model parameters and present conditions on the quantum state under which the parameters are identifiable. The proof and conditions for identifiability are presented for both closed and open quantum systems using the Schrödinger equation and the Lindblad master equation, respectively.

arXiv:2312.10233Journal of Applied PhysicsJun 14, 20240 citations

Effective model parameters identification for open quantum systems

Erling Gong, Weiwei Zhou, Ming Zhang +1 more

The identifiability of model parameters for open quantum systems is a crucial prerequisite for quantum control. By investigating two-level dephasing open quantum systems, we discuss under which conditions the information about Hamiltonian and dephasing parameters can be obtained. Using simulated experiments Time-series analysis and Bayesian strategy for extracting model parameters from limited and noisy data are both adopted and compared.

arXiv:1012.4593International Conference on Electrical and Control EngineeringSep 1, 20112 citations

Experimental graybox quantum system identification and control

Akram Youssry, Yang Yang, Robert J. Chapman +4 more

Abstract Understanding and controlling engineered quantum systems is key to developing practical quantum technology. However, given the current technological limitations, such as fabrication imperfections and environmental noise, this is not always possible. To address these issues, a great deal of theoretical and numerical methods for quantum system identification and control have been developed. These methods range from traditional curve fittings, which are limited by the accuracy of the model that describes the system, to machine learning (ML) methods, which provide efficient control solutions but no control beyond the output of the model, nor insights into the underlying physical process. Here we experimentally demonstrate a ‘graybox’ approach to construct a physical model of a quantum system and use it to design optimal control. We report superior performance over model fitting, while generating unitaries and Hamiltonians, which are quantities not available from the structure of standard supervised ML models. Our approach combines physics principles with high-accuracy ML and is effective with any problem where the required controlled quantities cannot be directly measured in experiments. This method naturally extends to time-dependent and open quantum systems, with applications in quantum noise spectroscopy and cancellation.

npj Quantum InformationJan 13, 202414 citations