Shadow estimation of gate-set properties from random sequences

Abstract

With quantum computing devices increasing in scale and complexity, there is a growing need for tools that obtain precise diagnostic information about quantum operations. However, current quantum devices are only capable of short unstructured gate sequences followed by native measurements. We accept this limitation and turn it into a new paradigm for characterizing quantum gate-sets. A single experiment—random sequence estimation—solves a wealth of estimation problems, with all complexity moved to classical post-processing. We derive robust channel variants of shadow estimation with close-to-optimal performance guarantees and use these as a primitive for partial, compressive and full process tomography as well as the learning of Pauli noise. We discuss applications to the quantum gate engineering cycle, and propose novel methods for the optimization of quantum gates and diagnosing cross-talk.

Operational Markovianization in randomized benchmarking

“…As a perspective, we expect these ideas to be useful, easily adapted, and enhanced, to other scalable and holistic benchmarking and characterization techniques, e.g. [9][10][11][12][13], most of which are the intellectual progeny of RB.…”

“…Despite not Markovianizing the average sequence fidelity, equation (11) establishes that Pauli-twirling will, in general, reduce the variance of sequence fidelities [58]. The importance of this is twofold, if non-exponential deviations are present, it allows for confidence as to whether these are due to non-Markovianity or e.g.…”

“…Due to the simplicity of RB-based protocols, they have become ubiquitous both for small systems [3][4][5][6][7][8], as well as a steppingstone for scalable techniques for more ambitious learning of quantum noise [9][10][11][12][13]. However, the manageable analytical behavior of the RB data-namely, an exponential decay capturing average gate-fidelities, with state preparation and measurement (SPAM) errors isolated as multiplicative and offset constants-is guaranteed only with highly-simplified and unrealistic assumptions about the noise.…”

Classical shadows with Pauli-invariant unitary ensembles

“…The classical shadow paradigm, with the sample efficiency it touts, has attracted considerable attention over the last couple of years 7 . Several applications have been proposed 1,[8][9][10][11][12][13][14][15][16][17][18][19][20][21] , ranging from the estimation of properties of quantum states and gates to quantum chaos in quantum evolution. Moreover, several improved versions of this protocol have been developed 1,8,[22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] , such as noise-resilient versions 20,37 .…”

Randomised benchmarking for universal qudit gates

“…A recent scheme that is more general than randomised benchmarking is shadow estimation [68]. For this scheme, real irreducible representations (of a group) are fundamental.…”