Real Randomized Benchmarking

Abstract

Randomized benchmarking provides a tool for obtaining precise quantitative estimates of the average error rate of a physical quantum channel. Here we define real randomized benchmarking, which enables a separate determination of the average error rate in the real and complex parts of the channel. This provides more fine-grained information about average error rates with approximately the same cost as the standard protocol. The protocol requires only averaging over the real Clifford group, a subgroup of the full complex Clifford group, and makes use of the fact that it forms an orthogonal 2-design. It therefore allows benchmarking of fault-tolerant gates for an encoding which does not contain the full Clifford group transversally. Furthermore, our results are especially useful when considering quantum computations on rebits (or real encodings of complex computations), in which case the real Clifford group now plays the role of the complex Clifford group when studying stabilizer circuits.

25 pages, v3: accepted in Quantum 2018-08-09

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• Improved spectral gaps for random quantum circuits: large local dimensions and all-to-all interactions
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• Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits
• A Practical Introduction to Benchmarking and Characterization of Quantum Computers
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• Techniques for learning sparse Pauli-Lindblad noise models
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• Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks
• Coherent randomized benchmarking
• A Theory of Direct Randomized Benchmarking
• Wigner's Theorem for stabilizer states and quantum designs
• Measurement-based interleaved randomised benchmarking using IBM processors
• Real randomized measurements for analyzing properties of quantum states
• Highly-entangled, highly-doped states that are efficiently cross-device verifiable
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• Generalized group designs: constructing novel unitary 2-, 3- and 4-designs
• A graph-theoretic approach to chaos and complexity in quantum systems