ﻻ يوجد ملخص باللغة العربية
Long-range correlated errors can severely impact the performance of NISQ (noisy intermediate-scale quantum) devices, and fault-tolerant quantum computation. Characterizing these errors is important for improving the performance of these devices, via calibration and error correction, and to ensure correct interpretation of the results. We propose a compressed sensing method for detecting two-qubit correlated dephasing errors, assuming only that the correlations are sparse (i.e., at most s pairs of qubits have correlated errors, where s << n(n-1)/2, and n is the total number of qubits). In particular, our method can detect long-range correlations between any two qubits in the system (i.e., the correlations are not restricted to be geometrically local). Our method is highly scalable: it requires as few as m = O(s log n) measurement settings, and efficient classical postprocessing based on convex optimization. In addition, when m = O(s log^4(n)), our method is highly robust to noise, and has sample complexity O(max(n,s)^2 log^4(n)), which can be compared to conventional methods that have sample complexity O(n^3). Thus, our method is advantageous when the correlations are sufficiently sparse, that is, when s < O(n^(3/2) / log^2(n)). Our method also performs well in numerical simulations on small system sizes, and has some resistance to state-preparation-and-measurement (SPAM) errors. The key ingredient in our method is a new type of compressed sensing measurement, which works by preparing entangled Greenberger-Horne-Zeilinger states (GHZ states) on random subsets of qubits, and measuring their decay rates with high precision.
We introduce a recursive algorithm for performing compressed sensing on streaming data. The approach consists of a) recursive encoding, where we sample the input stream via overlapping windowing and make use of the previous measurement in obtaining t
In the problem of adaptive compressed sensing, one wants to estimate an approximately $k$-sparse vector $xinmathbb{R}^n$ from $m$ linear measurements $A_1 x, A_2 x,ldots, A_m x$, where $A_i$ can be chosen based on the outcomes $A_1 x,ldots, A_{i-1} x
We consider the problem of recovering a set of correlated signals (e.g., images from different viewpoints) from a few linear measurements per signal. We assume that each sensor in a network acquires a compressed signal in the form of linear measureme
We characterize the measurement complexity of compressed sensing of signals drawn from a known prior distribution, even when the support of the prior is the entire space (rather than, say, sparse vectors). We show for Gaussian measurements and emph{a
The 1-bit compressed sensing framework enables the recovery of a sparse vector x from the sign information of each entry of its linear transformation. Discarding the amplitude information can significantly reduce the amount of data, which is highly b