True experimental reconstruction of quantum states and processes via convex optimization (original) (raw)
Related papers
2021
We employ the compressed sensing (CS) algorithm and a heavily reduced data set to experimentally perform true quantum process tomography (QPT) on an NMR quantum processor. We obtain the estimate of the process matrix χ corresponding to various two-and three-qubit quantum gates with a high fidelity. The CS algorithm is implemented using two different operator bases, namely, the standard Pauli basis and the Pauli-error basis. We experimentally demonstrate that the performance of the CS algorithm is significantly better in the Pauli-error basis, where the constructed χ matrix is maximally sparse. We compare the standard least square (LS) optimization QPT method with the CS-QPT method and observe that, provided an appropriate basis is chosen, the CS-QPT method performs significantly better as compared to the LS-QPT method. In all the cases considered, we obtained experimental fidelities greater than 0.9 from a reduced data set, which was approximately five to six times smaller in size than a full data set. We also experimentally characterized the reduced dynamics of a two-qubit subsystem embedded in a three-qubit system, and used the CS-QPT method to characterize processes corresponding to the evolution of two-qubit states under various J-coupling interactions.
Parameter estimation of quantum processes using convex optimization
2010
A convex optimization based method is proposed for quantum process tomography, in the case of known channel model structure, but unknown channel parameters. The main idea is to select an affine parametrization of the Choi matrix as a set of optimization variables, and formulate a semidefinite programming problem with a least squares objective function. Possible convex relations between the optimization variables are also taken into account to improve the estimation. Simulation case studies show, that the proposed method can significantly increase the accuracy of the parameter estimation, if the channel model structure is known. Beside the convex part, the determination of the channel parameters from the optimization variables is a nonconvex step in general. In the case of Pauli channels however, the method reduces to a purely convex optimization problem, allowing to obtain a globally optimal solution.
Efficient Measurement of Quantum Dynamics via Compressive Sensing
Physical Review Letters, 2011
The characterization of a decoherence process is among the central challenges in quantum physics. A major difficulty with current quantum process tomography methods is the enormous number of experiments needed to accomplish a tomography task. Here we present a highly efficient method for tomography of a quantum process that has a small number of significant elements. Our method is based on the compressed sensing techniques being used in information theory. In this new method, for a system with Hilbert space dimension n and a process matrix of dimension n 2 × n 2 with sparsity s, the required number of experimental configurations is O(s log n 4 ). This heralds a logarithmic advantage in contrast to other methods of quantum process tomography. More specifically, for q-qubits with n = 2 q , the scaling of resources is O(sq) -linear in the product of sparsity and number of qubits.
Realization of quantum process tomography in NMR
Physical Review A, 2001
Quantum process tomography is a procedure by which the unknown dynamical evolution of an open quantum system can be fully experimentally characterized. We demonstrate explicitly how this procedure can be implemented with a nuclear magnetic resonance quantum computer. This allows us to measure the fidelity of a controlled-not logic gate and to experimentally investigate the error model for our computer. Based on the latter analysis, we test an important assumption underlying nearly all models of quantum error correction, the independence of errors on different qubits.
Efficient and Fast Optimization Algorithms for Quantum State Filtering and Estimation
2019 Tenth International Conference on Intelligent Control and Information Processing (ICICIP), 2019
In this paper, based on Alternating Direction Multiplier Method (ADMM) and Compressed Sensing (CS), we develop three types of novel convex optimization algorithms for the quantum state estimation and filtering. Considering sparse state disturbance and measurement noise simultaneously, we propose a quantum state filtering algorithm. At the same time, the quantum state estimation algorithms for either sparse state disturbance or measurement noise are proposed, respectively. Contrast with other algorithms in literature, simulation experiments verify that all three algorithms have low computational complexity, fast convergence speed and high estimation accuracy at lower measurement rates.
Physical Review A, 2018
We present the first NMR implementation of a scheme for selective and efficient quantum process tomography without ancilla. We generalize this scheme such that it can be implemented efficiently using only a set of measurements involving product operators. The method allows us to estimate any element of the quantum process matrix to a desired precision, provided a set of quantum states can be prepared efficiently. Our modified technique requires fewer experimental resources as compared to the standard implementation of selective and efficient quantum process tomography, as it exploits the special nature of NMR measurements to allow us to compute specific elements of the process matrix by a restrictive set of subsystem measurements. To demonstrate the efficacy of our scheme, we experimentally tomograph the processes corresponding to 'no operation', a controlled-NOT (CNOT), and a controlled-Hadamard gate on a two-qubit NMR quantum information processor, with high fidelities.
Variational Quantum Tomography with Incomplete Information by Means of Semidefinite Programs
International Journal of Modern Physics C, 2011
We introduce a new method to reconstruct unknown quantum states out of incomplete and noisy information. The method is a linear convex optimization problem, therefore with a unique minimum, which can be efficiently solved with Semidefinite Programs. Numerical simulations indicate that the estimated state does not overestimate purity, and neither the expectation value of optimal entanglement witnesses. The convergence properties of the method are similar to compressed sensing approaches, in the sense that, in order to reconstruct low rank states, it needs just a fraction of the effort corresponding to an informationally complete measurement.
Quantum process reconstruction based on mutually unbiased basis
We study a quantum process reconstruction based on the use of mutually unbiased projectors (MUB-projectors) as input states for a D-dimensional quantum system, with D being a power of a prime number. This approach connects the results of quantum-state tomography using mutually unbiased bases (MUB) with the coefficients of a quantum process, expanded in terms of MUBprojectors. We also study the performance of the reconstruction scheme against random errors when measuring probabilities at the MUB-projectors.
Quantum process estimation via generic two-body correlations
Physical Review A, 2010
Performance of quantum process estimation is naturally limited by fundamental, random, and systematic imperfections of preparations and measurements. These imperfections may lead to considerable errors in the process reconstruction because standard data-analysis techniques usually presume ideal devices. Here, by utilizing generic auxiliary quantum or classical correlations, we provide a framework for the estimation of quantum dynamics via a single measurement apparatus. By construction, this approach can be applied to quantum tomography schemes with calibrated faulty-state generators and analyzers. Specifically, we present a generalization of the work begun by M. Mohseni and D. A. Lidar [Phys. Rev. Lett. 97, 170501 (2006)] with an imperfect Bell-state analyzer. We demonstrate that for several physically relevant noisy preparations and measurements, classical correlations and a small data-processing overhead suffice to accomplish the full system identification. Furthermore, we provide the optimal input states whereby the error amplification due to inversion of the measurement data is minimal.