Abstract
We present a method for mitigating measurement errors on quantum computing platforms that does not form the full assignment matrix, or its inverse, and works in a subspace defined by the noisy input bit-strings. This method accommodates both uncorrelated and correlated errors, and allows for computing accurate error bounds. Additionally, we detail a matrix-free preconditioned iterative solution method that converges in $\mathcal{O}(1)$ steps that is performant and uses orders of magnitude less memory than direct factorization. We demonstrate the validity of our method, and mitigate errors in a few seconds on numbers of qubits that would otherwise be intractable.
Highlights
Rapid developments in the fabrication, control, and deployment of quantum computing systems have brought qubit counts to approximately 100, where it might be possible to show advantage over classical computation methods in one or more limited cases [1,2,3]
For short-depth quantum circuits that can be executed on current-generation hardware, measurement errors play an outsized role and their correction is critical to many near-term experiments [21,22,23,24,25,26,27,28]
Where pnoisy is a vector of noisy probabilities returned by the quantum system, pideal is the probabilities in the absence of measurement errors, and A is the 2N × 2N complete assignment matrix (A-matrix), where element Arow,col is the probability of bit string col being converted to bit string
Summary
Rapid developments in the fabrication, control, and deployment of quantum computing systems have brought qubit counts to approximately 100, where it might be possible to show advantage over classical computation methods in one or more limited cases [1,2,3] Such breakthroughs are hampered by noise and errors that conspire to limit the effectiveness of quantum computers at tackling problems of appreciable scale. For situations where explicitly forming Ais still prohibitive due to large numbers of unique samples, it is possible to use preconditioned matrix-free iterative linear-solution methods. Such methods have been explored in numerical solutions of large-scale steady-state density matrices [37]. II, which motives the subspace reduction procedure and describes how it is performed
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
