Related papers: Minimax Isometry Method: A compressive sensing app…
We present a method to considerably improve the numerical performance for solving Eliashberg-type coupled equations on the imaginary axis. Instead of the standard practice of introducing a hard numerical cutoff for treating the infinite…
We consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional. The…
Measuring the vibronic spectrum probes dynamical processes in molecular systems. When interpreted via suitable theoretical tools, the experimental data provides comprehensive information about the system in question. For complex many-body…
A statistical method is derived for the calculation of thermodynamic properties of many-body systems at low temperatures. This method is based on the self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo J. Chem.…
Recently, significant connections between compressed sensing problems and optimization of a particular class of functions relating to solutions of Hamilton-Jacobi equation was discovered. In this paper we introduce a fast approximate…
We introduce sparse-ir, a collection of libraries to efficiently handle imaginary-time propagators, a central object in finite-temperature quantum many-body calculations. We leverage two concepts: firstly, the intermediate representation…
The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…
Several powerful machines, such as the D-Wave 2000Q, dedicated to solving combinatorial optimization problems through the Ising-model formulation have been developed. To input problems into the machines, the unknown parameters on the Ising…
We present a systematic study of quantum system compression for the evolution of generic many-body problems. The necessary numerical simulations of such systems are seriously hindered by the exponential growth of the Hilbert space dimension…
In this paper, we present the Monte-Carlo Compressive Optimization algorithm, a new method to solve a combinatorial optimization problem that is assumed compressible. The method relies on random queries to the objective function in order to…
In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to…
Simulation of quantum systems promises to deliver physical and chemical predictions for the frontiers of technology. Unfortunately, the exact representation of these systems is plagued by the exponential growth of dimension with the number…
A compressed sensing method consists of a rectangular measurement matrix, $M \in \mathbbm{R}^{m \times N}$ with $m \ll N$, together with an associated recovery algorithm, $\mathcal{A}: \mathbbm{R}^m \rightarrow \mathbbm{R}^N$. Compressed…
Modern scientific instruments produce vast amounts of data, which can overwhelm the processing ability of computer systems. Lossy compression of data is an intriguing solution, but comes with its own drawbacks, such as potential signal…
Compressed sensing is a signal processing technique that allows for the reconstruction of a signal from a small set of measurements. The key idea behind compressed sensing is that many real-world signals are inherently sparse, meaning that…
We investigate the compression of quantum information with respect to a given set $\mathcal{M}$ of high-dimensional measurements. This leads to a notion of simulability, where we demand that the statistics obtained from $\mathcal{M}$ and an…
Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…
Compressed sensing is a method that allows a significant reduction in the number of samples required for accurate measurements in many applications in experimental sciences and engineering. In this work, we show that compressed sensing can…
Compressive sensing (CS) combines data acquisition with compression coding to reduce the number of measurements required to reconstruct a sparse signal. In optics, this usually takes the form of projecting the field onto sequences of random…