Related papers: Rigorous Maximum Likelihood Estimation for Quantum…
Quantum state tomography (QST) aims at reconstructing the state of a quantum system. However in conventional QST the number of measurements scales exponentially with the number of qubits. Here we propose a QST protocol, in which the…
We consider the system identification problem of estimating a dynamical parameter of a Markovian quantum open system (the atom maser), by performing continuous time measurements in the system's output (outgoing atoms). Two estimation…
The reconstruction of quantum states from experimental measurements, often achieved using quantum state tomography (QST), is crucial for the verification and benchmarking of quantum devices. However, performing QST for a generic…
The maximum likelihood amplitude estimation algorithm (MLAE) is a practical solution to the quantum amplitude estimation problem with Heisenberg limit error convergence. We improve MLAE by using random depths to avoid the so-called critical…
We study the problem of controlling how a limited communication bandwidth budget is allocated across heterogeneously quantized sensor measurements. The performance criterion is the trace of the error covariance matrix of the linear minimum…
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…
The linear regression model with a random variable (RV) measurement matrix, where the mean of the random measurement matrix has full column rank, has been extensively studied. In particular, the quasiconvexity of the maximum likelihood…
Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density…
A major bottleneck in the quest for scalable many-body quantum technologies is the difficulty in benchmarking their preparations, which suffer from an exponential `curse of dimensionality' inherent to their quantum states. We present an…
Transformer-based large language models (LLMs) have achieved remarkable success as model sizes continue to grow, yet their deployment remains challenging due to significant computational and memory demands. Quantization has emerged as a…
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…
We propose a manifold optimization approach to solve linear semidefinite programs (SDP) with low-rank solutions, with an emphasis on SDP relaxations for polynomial optimization problems. This approach incorporates the inexact augmented…
It has been recently shown that a state generated by a one-dimensional noisy quantum computer is well approximated by a matrix product operator with a finite bond dimension independent of the number of qubits. We show that full quantum…
Lagrangian particle tracking is essential for characterizing turbulent flows, but inferring particle acceleration from inherently noisy position data remains a significant challenge. Fluid particles in turbulence experience extreme,…
Quantum state tomography is a key technique for quantum information processing, but is challenging due to the exponential growth of its complexity with the system size. In this work, we propose an algorithm which iteratively finds the best…
Quantum error mitigation is an important technique to reduce the impact of noise in quantum computers. With more and more qubits being supported on quantum computers, there are two emerging fundamental challenges. First, the number of shots…
Recent machine learning methods use increasingly large deep neural networks to achieve state of the art results in various tasks. The gains in performance come at the cost of a substantial increase in computation and storage requirements.…
High-performance techniques to simulate quantum programs on classical hardware rely on exponentially large vectors to represent quantum states. When simulating quantum algorithms, the quantum states that occur are often sparse due to…
In this paper, a nonparametric maximum likelihood (ML) estimator for band-limited (BL) probability density functions (pdfs) is proposed. The BLML estimator is consistent and computationally efficient. To compute the BLML estimator, three…
Amplitude Estimation (AE) is a critical subroutine in many quantum algorithms, allowing for a quadratic speedup in various applications like those involving estimating statistics of various functions as in financial Monte Carlo simulations.…