The basis pursuit problem seeks a minimum one-norm solution of an underdetermined least-squares problem. Basis denoise (BPDN) fits the only approximately, and single parameter determines curve that traces optimal trade-off between fit solution. We prove this is convex continuously differentiable over all points interest, show it gives explicit relationship to two other optimization problems closely related BPDN. describe root-finding algorithm for finding arbitrary on curve; suitable are...

Quantum computing promises to offer substantial speed-ups over its classical counterpart for certain problems. However, the greatest impediment realizing full potential is noise that inherent these systems. The widely accepted solution this challenge implementation of fault-tolerant quantum circuits, which out reach current processors. Here we report experiments on a noisy 127-qubit processor and demonstrate measurement accurate expectation values circuit volumes at scale beyond brute-force...

Journal Article 1-Bit matrix completion Get access Mark A. Davenport, Davenport † School of Electrical and Computer Engineering, Georgia Institute Technology, Atlanta, GA, USA †Corresponding author. Email: mdav@gatech.edu Search for other works by this author on: Oxford Academic Google Scholar Yaniv Plan, Plan Department Mathematics, University British Columbia, Vancouver, BC, Canada, yaniv@math.ubc.ca Ewout van den Berg, Berg IBM T.J. Watson Research Center, Yorktown Heights, NY, USA,...

We introduce a new estimator for the vector of coefficients $\beta$ in linear model $y=X\beta+z$, where $X$ has dimensions $n\times p$ with $p$ possibly larger than $n$. SLOPE, short Sorted L-One Penalized Estimation, is solution to \[\min_{b\in\mathbb{R}^p}\frac{1}{2}\Vert y-Xb\Vert _{\ell_2}^2+\lambda_1\vert b\vert _{(1)}+\lambda_2\vert b\vert_{(2)}+\cdots+\lambda_p\vert b\vert_{(p)},\] $\lambda_1\ge\lambda_2\ge\cdots\ge\lambda_p\ge0$ and $\vert b\vert_{(1)}\ge\vert...

The joint-sparse recovery problem aims to recover, from sets of compressed measurements, unknown sparse matrices with nonzero entries restricted a subset rows. This is an extension the single-measurement-vector (SMV) widely studied in sensing. We analyze properties for two types algorithms. First, we show that using sum-of-norm minimization cannot exceed uniform rate sequential SMV $\ell_1$ minimization, and there are problems can be solved one approach but not other. Second, performance...

The use of convex optimization for the recovery sparse signals from incomplete or compressed data is now common practice. Motivated by success basis pursuit in recovering vectors, new formulations have been proposed that take advantage different types sparsity. In this paper we propose an efficient algorithm solving a general class sparsifying formulations. For several sparsity provide applications, along with details on how to apply algorithm, and experimental results.

Measurements on current quantum processors are subject to hardware imperfections that lead readout errors. These errors manifest themselves as a bias in expectation values. Here, we consider very simple method forces the value appear multiplicative factor can be measured directly and removed at cost of an increase sampling complexity for observable. This was previously discussed by Karalekas et al. [Quantum Sci. Technol. 5, 024003 (2020)] product single-qubit readout-error models. formally...

Secondary school level quantum physics (QP) courses have recently been implemented in the national curricula of many countries. QP gives opportunities to acquaint students with more recent and its applications discuss aspects nature science. Research has shown that is a challenging area for students. Because inclusion rather new most countries, it interesting compare from these countries make choices by curriculum designers visible. In this study, we provide detailed overview fifteen We...

We study the flow of information and evolution internal representations during deep neural network (DNN) training, aiming to demystify compression aspect bottleneck theory. The theory suggests that DNN training comprises a rapid fitting phase followed by slower phase, in which mutual $I(X;T)$ between input $X$ $T$ decreases. Several papers observe estimated on different models, but true over these networks is provably either constant (discrete $X$) or infinite (continuous $X$). This work...

Noise in pre-fault-tolerant quantum computers can result biased estimates of physical observables. Accurate bias-free be obtained using probabilistic error cancellation (PEC), which is an error-mitigation technique that effectively inverts well-characterized noise channels. Learning correlated channels large circuits, however, has been a major challenge and severely hampered experimental realizations. Our work presents practical protocol for learning inverting sparse model able to capture...

Probabilistic error cancellation (PEC) is a technique that generates error-mitigated estimates of expectation values from ensembles quantum circuits. In this work we extend the application PEC unitary-only circuits to dynamic with midcircuit measurements and classically controlled (feedforward) Clifford operations. Our approach extends sparse Pauli-Lindblad noise model characterizing gates target channels containing feedforward while accounting for nonlocal measurement crosstalk in...

We introduce a novel method for sparse regression and variable selection, which is inspired by modern ideas in multiple testing. Imagine we have observations from the linear model y = X beta + z, then suggest estimating coefficients means of new estimator called SLOPE, solution to minimize 0.5 ||y - Xb\|_2^2 lambda_1 |b|_(1) lambda_2 |b|_(2) ... lambda_p |b|_(p); here, >= λ_2 λ_p 0 |b|_(p) order statistic magnitudes b. The regularizer sorted L1 norm penalizes according their rank: higher...

Geophysical inverse problems typically involve a trade-off between data misfit and some prior model. Pareto curves trace the optimal these two competing aims. These are used commonly in with two-norm priors which they plotted on log-log scale known as L-curves. For other priors, such sparsity-promoting one-norm prior, remain relatively unexplored. We show how lead to new insights into regularization. First, we confirm theoretical properties of smoothness convexity from stylized geophysical...

Many applications of practical interest rely on time evolution Hamiltonians that are given by a sum Pauli operators. Quantum circuits for exact single operators well known, and can be extended trivially to sums commuting Paulis concatenating the individual terms. In this paper we reduce circuit complexity Hamiltonian simulation partitioning into mutually clusters exponentiating elements within each cluster after applying simultaneous diagonalization. We provide algorithm sets subsets, show...

Effective noise models are essential for analyzing and understanding the dynamics of quantum systems, particularly in applications like error mitigation correction. However, even when processes well-characterized isolation, effective channels impacting target operations can differ significantly, as different gates experience distinct ways. Here, we present a model construction method that builds an from Lindbladian description physical acting simultaneously to desired gate operation. It...

Sparco is a framework for testing and benchmarking algorithms sparse reconstruction. It includes large collection of reconstruction problems drawn from the imaging, compressed sensing, geophysics literature. also implementing new test can be used as tool reproducible research. implemented entirely in Matlab, released open-source software under GNU Public License.

Advances in solid-state technology have enabled the development of silicon photomultiplier sensor arrays capable sensing individual photons. Combined with high-frequency time-to-digital converters (TDCs), this opens up prospect sensors recording high accuracy both time and location each detected photon. Such a capability could lead to significant improvements imaging accuracy, especially for applications operating low photon fluxes such as light detection ranging positron-emission...

We describe a simple algorithm for sampling n-qubit Clifford operators uniformly at random. The outputs the in form of quantum circuits with most 5n + 2n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> elementary gates and maximum depth ${\mathcal{O}}\left({n\,{\text{log}}\,n}\right)$ on fully connected topologies. circuit can be output streaming fashion as proceeds, different parts generated parallel. has an...

Generating samples from the output distribution of a quantum circuit is ubiquitous task used as building block many algorithms. Here we show how to accomplish this on noisy processor lacking full-blown error correction for special class circuits dominated by Clifford gates. Our approach based coherent Pauli checks (CPCs) that detect errors in verifying commutation rules between random Pauli-type check operators and considered circuit. main contributions are follows. First, derive simple...

Pre-fault tolerant quantum computers have already demonstrated the ability to estimate observable values accurately, at a scale beyond brute-force classical computation. This has been enabled by error mitigation techniques that often rely on representative model device noise. However, learning and maintaining these models is complicated fluctuations in noise over unpredictable time scales, for instance, arising from resonant interactions between superconducting qubits defect two-level...