2021/05/26 by Alireza Seif, Mohammad Hafezi, Seif, Alireza +3 · 1 citation
Engineering · #Analog and Mixed-Signal Circuit Design #Electrical and Bioimpedance Tomography #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Information Theory (cs.IT) #Quantum Physics (quant-ph) #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2105.12589
openalex publication_date 2021/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 log4(n)), our method is highly robust to noise, and has sample complexity O(max(n,s)2 log4(n)), which can be compared to conventional methods that have sample complexity O(n3). Thus, our method is advantageous when the correlations are sufficiently sparse, that is, when s < O(n^(3/2) / log2(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.