Quantum process tomography via completely positive and trace-preserving projection

We present an algorithm for projecting superoperators onto the set of completely positive, trace-preserving maps. When combined with gradient descent of a cost function, the procedure results in an algorithm for quantum process tomography: finding the quantum process that best fits a set of sufficient observations. We compare the performance of our algorithm to the diluted iterative algorithm as well as second-order solvers interfaced with the popular CVX package for MATLAB, and find it to be significantly faster and more accurate while guaranteeing a physical estimate.Comment: 13pp, 8 fig

A quasi-current representation for information needs inspired by Two-State Vector Formalism

Recently, a number of quantum theory (QT)-based information retrieval (IR) models have been proposed for modeling session search task that users issue queries continuously in order to describe their evolving information needs (IN). However, the standard formalism of QT cannot provide a complete description for users’ current IN in a sense that it does not take the ‘future’ information into consideration. Therefore, to seek a more proper and complete representation for users’ IN, we construct a representation of quasi-current IN inspired by an emerging Two-State Vector Formalism (TSVF). With the enlightenment of the completeness of TSVF, a “two-state vector” derived from the ‘future’ (the current query) and the ‘history’ (the previous query) is employed to describe users’ quasi-current IN in a more complete way. Extensive experiments are conducted on the session tracks of TREC 2013 & 2014, and show that our model outperforms a series of compared IR models

Ultrafast quantum state tomography with feed-forward neural networks

Reconstructing the state of many-body quantum systems is of fundamental importance in quantum information tasks, but extremely challenging due to the curse of dimensionality. In this work, we present a quantum tomography approach based on neural networks to achieve the ultrafast reconstruction of multi-qubit states. Particularly, we propose a simple 3-layer feed-forward network to process the experimental data generated from measuring each qubit with a positive operator-valued measure, which is able to reduce the storage cost and computational complexity. Moreover, the techniques of state decomposition and $P$-order absolute projection are jointly introduced to ensure the positivity of state matrices learned in the maximum likelihood function and to improve the convergence speed and robustness of the above network. Finally, it is tested on a large number of states with a wide range of purity to show that we can faithfully tomography 11-qubit states on a laptop within 2 minutes under noise. Our numerical results also demonstrate that more state samples are required to achieve the given tomography fidelity for the low-purity states, and the increased depolarizing noise induces a linear decrease in the tomography fidelity

Fast quantum state reconstruction via accelerated non-convex programming

We propose a new quantum state reconstruction method that combines ideas from compressed sensing, non-convex optimization, and acceleration methods. The algorithm, called Momentum-Inspired Factored Gradient Descent (\texttt{MiFGD}), extends the applicability of quantum tomography for larger systems. Despite being a non-convex method, \texttt{MiFGD} converges \emph{provably} to the true density matrix at a linear rate, in the absence of experimental and statistical noise, and under common assumptions. With this manuscript, we present the method, prove its convergence property and provide Frobenius norm bound guarantees with respect to the true density matrix. From a practical point of view, we benchmark the algorithm performance with respect to other existing methods, in both synthetic and real experiments performed on an IBM's quantum processing unit. We find that the proposed algorithm performs orders of magnitude faster than state of the art approaches, with the same or better accuracy. In both synthetic and real experiments, we observed accurate and robust reconstruction, despite experimental and statistical noise in the tomographic data. Finally, we provide a ready-to-use code for state tomography of multi-qubit systems.Comment: 46 page

Supervised Hamiltonian learning via efficient and robust quantum descent

Given the recent developments in quantum techniques, modeling the physical Hamiltonian of a target quantum many-body system is becoming an increasingly practical and vital research direction. Here, we propose an efficient quantum strategy that mingles maximum-likelihood-estimate state and supervised machine learning. Given the measurement outcomes, we optimize the target model Hamiltonian and density operator via a series of quantum descent, which we prove is negative semi-definite with respect to the negative-log-likelihood function. In addition to such optimization efficiency, supervised Hamiltonian learning respects the locality of a given quantum system, therefore, extends readily to larger systems. Compared with previous approaches, it also exhibits better accuracy and overall stability toward noises, fluctuations, and temperature ranges, which we demonstrate with various examples.Comment: 12 pages, 8figure