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Learning faithful representations of quantum states is crucial to fully characterizing the variety of many-body states created on quantum processors. While various tomographic methods such as classical shadow and MPS tomography have shown…
To simulate bosons on a qubit- or qudit-based quantum computer, one has to regularize the theory by truncating infinite-dimensional local Hilbert spaces to finite dimensions. In the search for practical quantum applications, it is important…
Existing quantum state tomography methods are limited in scalability due to their high computation and memory demands, making them impractical for recovery of large quantum states. In this work, we address these limitations by reformulating…
Quantum state tomography (QST) is typically performed from a frequentist viewpoint using maximum likelihood estimation (MLE) which seeks to find the best plausible state consistent with the data by maximizing a likelihood function /…
The Barrett-Cavalcanti-Lal-Maroney (BCLM) argument stands as the most effective means of demonstrating the reality of the quantum state. Its advantages include being derived from very few assumptions, and a robustness to experimental error.…
We present a novel method to perform quantum state tomography for many-particle systems which are particularly suitable for estimating states in lattice systems such as of ultra-cold atoms in optical lattices. We show that the need for…
Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the…
Quantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum systems. In this paper, we study estimation of…
We apply a recently developed framework for analyzing the convergence of stochastic algorithms to the general problem of large-scale nonconvex composite optimization more generally, and nonconvex likelihood maximization in particular. Our…
Quantum metrology offers the potential to surpass its classical counterpart, pushing the boundaries of measurement precision toward the ultimate Heisenberg limit. This enhanced precision is normally attained by utilizing large squeezed…
We use a constrained convex optimization (CCO) method to experimentally characterize arbitrary quantum states and unknown quantum processes on a two-qubit NMR quantum information processor. Standard protocols for quantum state and quantum…
Tomography of a quantum state is usually based on positive operator-valued measure (POVM) and on their experimental statistics. Among the available reconstructions, the maximum-likelihood (MaxLike) technique is an efficient one. We propose…
To control a dynamical system it is essential to obtain an accurate estimate of the current system state based on uncertain sensor measurements and existing system knowledge. An optimization-based moving horizon estimation (MHE) approach…
Quantum state tomography is an essential component of modern quantum technology. In application to continuous-variable harmonic-oscilator systems, such as the electromagnetic field, existing tomography methods typically reconstruct the…
While quantum state tomography (QST) remains the gold standard for benchmarking and verifying quantum devices, it requires an exponentially large number of measurements and classical computational resources for generic quantum many-body…
In this paper, we present a novel optimization algorithm designed specifically for estimating state-space models to deal with heavy-tailed measurement noise and constraints. Our algorithm addresses two significant limitations found in…
Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article…
It is a well-known fact that the optimal POVM for quantum state tomography is the symmetric, informationally complete, positive operator valued measure (SIC-POVM). We investigate the same problem only in the case when there are some a…
Optimization problems involving sequential decisions in a stochastic environment were studied in Stochastic Programming (SP), Stochastic Optimal Control (SOC) and Markov Decision Processes (MDP). In this paper we mainly concentrate on SP…
We present a method for quantum state tomography that enables the efficient estimation, with fixed precision, of any of the matrix elements of the density matrix of a state, provided that the states from the basis in which the matrix is…