Quantum state estimation is a fundamental task in quantum information processing, crucial for applications such as quantum metrology, quantum sensing, and quantum process tomography. However, conventional methods for estimating the state of a quantum system often suffer from significant computational complexity, particularly for large systems or when high precision is required. This work introduces a novel approach to quantum state estimation that leverages Randomized Benchmarking (RB) techniques. By adapting RB protocols specifically designed for quantum systems, we achieve efficient and accurate state estimation with a reduced number of measurements compared to traditional methods. The core idea is to use a series of carefully designed, randomized measurements to extract information about the unknown quantum state. The resulting estimation process avoids the need for exhaustive state tomography, dramatically reducing the computational burden. We detail the mathematical framework underlying this approach, including the formulation of the RB protocol, the estimation algorithm, and an analysis of the estimation error. The results demonstrate the effectiveness and potential of this method for various quantum state estimation scenarios.Quantum state estimation is a fundamental task in quantum information processing, crucial for applications such as quantum metrology, quantum sensing, and quantum process tomography. However, conventional methods for estimating the state of a quantum system often suffer from significant computational complexity, particularly for large systems or when high precision is required. This work introduces a novel approach to quantum state estimation that leverages Randomized Benchmarking (RB) techniques. By adapting RB protocols specifically designed for quantum systems, we achieve efficient and accurate state estimation with a reduced number of measurements compared to traditional methods. The core idea is to use a series of carefully designed, randomized measurements to extract information about the unknown quantum state. The resulting estimation process avoids the need for exhaustive state tomography, dramatically reducing the computational burden. We detail the mathematical framework underlying this approach, including the formulation of the RB protocol, the estimation algorithm, and an analysis of the estimation error. The results demonstrate the effectiveness and potential of this method for various quantum state estimation scenarios.

Sep 3, 20260 citations

Adaptive Quantum Process Tomography via Linear Regression Estimation

Qi Yu, Daoyi Dong, Yuanlong Wang +1 more

This paper proposes a recursively adaptive tomography protocol to improve the precision of quantum process estimation for finite dimensional systems. The problem of quantum process tomography is firstly formulated as a parameter estimation problem which can then be solved by the linear regression estimation method. An adaptive algorithm is proposed for the selection of subsequent input states given the previous estimation results. Numerical results show that the proposed adaptive process tomography protocol can achieve an improved level of estimation performance.This paper proposes a recursively adaptive tomography protocol to improve the precision of quantum process estimation for finite dimensional systems. The problem of quantum process tomography is firstly formulated as a parameter estimation problem which can then be solved by the linear regression estimation method. An adaptive algorithm is proposed for the selection of subsequent input states given the previous estimation results. Numerical results show that the proposed adaptive process tomography protocol can achieve an improved level of estimation performance.

Conference proceedings/Conference proceedings - IEEE International Conference on Systems, Man, and CyberneticsOct 11, 20204 citations

Quantum Estimation

François Chapeau‐Blondeau

Springer eBooksJan 1, 20260 citations

Efficient Learning of Arbitrary Single-Copy Quantum States

Shibdas Roy, Filippo Caruso, Srushti Patil +1 more

Quantum state tomography is the problem of estimating a given quantum state. Usually, it is required to run the quantum experiment - state preparation, state evolution, measurement - several times to be able to estimate the output quantum state of the experiment, because an exponentially high number of copies of the state is required. In this work, we present an efficient algorithm to estimate with a small but nonzero probability of error the output state of the experiment using a single copy of the state, without knowing the evolution dynamics of the state. It also does not destroy the original state, which can be recovered easily for any further quantum processing. As an example, it is usually required to repeat a quantum image processing experiment many times, since many copies of the state of the output image are needed to extract the information from all its pixels. The information from $\mathcal{N}$ pixels of the image can be inferred from a single run of the image processing experiment in our algorithm, to efficiently estimate the density matrix of the image state.Quantum state tomography is the problem of estimating a given quantum state. Usually, it is required to run the quantum experiment - state preparation, state evolution, measurement - several times to be able to estimate the output quantum state of the experiment, because an exponentially high number of copies of the state is required. In this work, we present an efficient algorithm to estimate with a small but nonzero probability of error the output state of the experiment using a single copy of the state, without knowing the evolution dynamics of the state. It also does not destroy the original state, which can be recovered easily for any further quantum processing. As an example, it is usually required to repeat a quantum image processing experiment many times, since many copies of the state of the output image are needed to extract the information from all its pixels. The information from$\mathcal{N}$pixels of the image can be inferred from a single run of the image processing experiment in our algorithm, to efficiently estimate the density matrix of the image state.

arXiv:2310.19748IEEE International Conference on Quantum Control, Computing and Learning (qCCL)Jun 25, 20250 citations

\mathcal{N}

pixels of the image can be inferred from a single run of the image processing experiment in our algorithm, to efficiently estimate the density matrix of the image state.