Evidence for the utility of quantum computing before fault tolerance.

Quantum computing promises to offer substantial speed-ups over its classical counterpart for certain problems. However, the greatest impediment to realizing its full potential is noise that is inherent to these systems. The widely accepted solution to this challenge is the implementation of fault-tolerant quantum circuits, which is out of reach for current processors. Here we report experiments on a noisy 127-qubit processor and demonstrate the measurement of accurate expectation values for circuit volumes at a scale beyond brute-force classical computation. We argue that this represents evidence for the utility of quantum computing in a pre-fault-tolerant era. These experimental results are enabled by advances in the coherence and calibration of a superconducting processor at this scale and the ability to characterize1 and controllably manipulate noise across such a large device. We establish the accuracy of the measured expectation values by comparing them with the output of exactly verifiable circuits. In the regime of strong entanglement, the quantum computer provides correct results for which leading classical approximations such as pure-state-based 1D (matrix product states, MPS) and 2D (isometric tensor network states, isoTNS) tensor network methods2,3 break down. These experiments demonstrate a foundational tool for the realization of near-term quantum applications4,5.

SLOPE-ADAPTIVE VARIABLE SELECTION VIA CONVEX OPTIMIZATION.

We introduce a new estimator for the vector of coefficients ß in the linear model y = Xß + z, where X has dimensions n × p with p possibly larger than n. SLOPE, short for Sorted L-One Penalized Estimation, is the solution to [Formula: see text]where λ1 ≥ λ2 ≥ … ≥ λ p ≥ 0 and [Formula: see text] are the decreasing absolute values of the entries of b. This is a convex program and we demonstrate a solution algorithm whose computational complexity is roughly comparable to that of classical ℓ1 procedures such as the Lasso. Here, the regularizer is a sorted ℓ1 norm, which penalizes the regression coefficients according to their rank: the higher the rank-that is, stronger the signal-the larger the penalty. This is similar to the Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B57 (1995) 289-300] procedure (BH) which compares more significant p-values with more stringent thresholds. One notable choice of the sequence {λ i } is given by the BH critical values [Formula: see text], where q ∈ (0, 1) and z(α) is the quantile of a standard normal distribution. SLOPE aims to provide finite sample guarantees on the selected model; of special interest is the false discovery rate (FDR), defined as the expected proportion of irrelevant regressors among all selected predictors. Under orthogonal designs, SLOPE with λBH provably controls FDR at level q. Moreover, it also appears to have appreciable inferential properties under more general designs X while having substantial power, as demonstrated in a series of experiments running on both simulated and real data.

Single-photon sampling architecture for solid-state imaging sensors.

Advances in solid-state technology have enabled the development of silicon photomultiplier sensor arrays capable of sensing individual photons. Combined with high-frequency time-to-digital converters (TDCs), this technology opens up the prospect of sensors capable of recording with high accuracy both the time and location of each detected photon. Such a capability could lead to significant improvements in imaging accuracy, especially for applications operating with low photon fluxes such as light detection and ranging and positron-emission tomography. The demands placed on on-chip readout circuitry impose stringent trade-offs between fill factor and spatiotemporal resolution, causing many contemporary designs to severely underuse the technology's full potential. Concentrating on the low photon flux setting, this paper leverages results from group testing and proposes an architecture for a highly efficient readout of pixels using only a small number of TDCs. We provide optimized design instances for various sensor parameters and compute explicit upper and lower bounds on the number of TDCs required to uniquely decode a given maximum number of simultaneous photon arrivals. To illustrate the strength of the proposed architecture, we note a typical digitization of a 60 × 60 photodiode sensor using only 142 TDCs. The design guarantees registration and unique recovery of up to four simultaneous photon arrivals using a fast decoding algorithm. By contrast, a cross-strip design requires 120 TDCs and cannot uniquely decode any simultaneous photon arrivals. Among other realistic simulations of scintillation events in clinical positron-emission tomography, the above design is shown to recover the spatiotemporal location of 99.98% of all detected photons.