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Scalable randomized benchmarking of quantum computers using mirror circuits
Timothy Proctor, Stefan Seritan, Kenneth Rudinger, Erik Nielsen, Robin Blume-Kohout, Kevin Young
TL;DR
Existing randomized benchmarks have scaling limitations that constrain their use for many-qubit processors. This paper introduces mirror RB to estimate average many-qubit layer infidelity, demonstrating it in simulations up to 225 qubits and on a cloud processor to reveal and quantify crosstalk.
Problem
Existing benchmarks either require exponentially expensive classical computations or benchmark composite n-qubit Clifford gates whose implementation overhead grows with system size.
Source: p. 1Method
Mirror RB uses randomized mirror circuits to approximately estimate the infidelity of an average Pauli-dressed n-qubit layer.
Source: pp. 1–2Results
Mirror RB revealed and quantified crosstalk errors on up to 16 physical qubits, while simulations showed rΩ≈ϵΩ for models with and without crosstalk.
Source: pp. 3–4Takeaways & Limitations
MRB enables holistic randomized benchmarking of hundreds or thousands of qubits when typical n-qubit layers have significantly non-zero fidelity.
Source: pp. 1, 4For physically relevant error distributions, rΩ is conjectured to slightly underestimate ϵΩ; its possible underestimation is bounded by about a factor of two.
Source: p. 3
Abstract
from arXiv · showhide
The performance of quantum gates is often assessed using some form of randomized benchmarking. However, the existing methods become infeasible for more than approximately five qubits. Here we show how to use a simple and customizable class of circuits -- randomized mirror circuits -- to perform scalable, robust, and flexible randomized benchmarking of Clifford gates. We show that this technique approximately estimates the infidelity of an average many-qubit logic layer, and we use simulations of up to 225 qubits with physically realistic error rates in the range 0.1-1% to demonstrate its scalability. We then use up to 16 physical qubits of a cloud quantum computing platform to demonstrate that our technique can reveal and quantify crosstalk errors in many-qubit circuits.
Simulations
The simulations test mirror RB across processor sizes up to 225 qubits, using both independently sampled error models and models with or without long-range crosstalk. They compare the estimated layer error rate with the error rate extracted from each model.
Simulations
- Simulations covered 18 processor sizes from 1 to 225 qubits on subsets of a 15 × 15 lattice, with 50 experiment designs and 30 circuits per benchmark depth.The layer set used parallel nearest-neighbor CNOTs and single-qubit Clifford gates, with the edge grab sampling distribution.Source: Simulations · p. 7
- In 900 simulations, independently sampled error models varied readout and gate errors, including errors on neighboring qubits.The simulations extracted ϵΩ from each error model and estimated rΩ from its data.Source: Simulations · p. 7
- The two illustrative models used 0.5% readout error and 0.1% and 1% one- and two-qubit gate errors, with the second model adding distance-dependent crosstalk from each CNOT.The simulations compared rΩ with ϵΩ under both models; the crosstalk error decreased with lattice distance from a CNOT.Source: Simulations · p. 7
IBM Q Quito demonstrations
The Quito demonstrations compared mirror, direct, and standard randomized benchmarking on one to five qubits. Standard RB measured average Clifford infidelity, while direct and mirror RB approximately measured average layer error.
IBM Q Quito demonstrations
- Direct RB used the same layer set and sampling distribution as the concurrent mirror RB demonstration to compare estimates of ϵΩ.Its circuits compiled random stabilizer-state preparation and return subcircuits, which makes direct RB unscalable for n ≫ 1.Source: IBM Q Quito demonstrations · p. 8
- Standard RB compiled n-qubit Clifford subroutines, which require at least O(n^2/log(n)) two-qubit gates for a typical Clifford.The compilers might not have been optimal, but the stated scaling cannot be improved upon in these results.Source: IBM Q Quito demonstrations · p. 8
- Standard RB error rates rose from 0.041(1)% at one qubit to 95(7)% at five qubits, and are not directly comparable to direct and mirror RB rates.Standard RB measures average n-qubit Clifford infidelity; direct and mirror RB approximately measure ϵΩ, the error rate of an average layer.Source: IBM Q Quito demonstrations · p. 8
IBM Q Rueschlikon demonstrations
Mirror RB was run on multiple subsets of IBM Q Rueschlikon, spanning one to 16 qubits. The sampling scheme used at most one CNOT per layer and is not suitable for much larger processors.
IBM Q Rueschlikon demonstrations
- On the 16-qubit Rueschlikon processor, mirror RB tested subsets of 1, 2, 4, 8, and 16 qubits, dividing the processor into 16/n regions for each size.One-qubit circuits ran simultaneously to match IBM’s calibration experiments.Source: IBM Q Rueschlikon demonstrations · p. 8
- Each sampled layer had a 50% chance of one CNOT between a uniformly selected connected pair; otherwise it contained only single-qubit Clifford gates.The sampling distribution is not suitable for much larger processors because CNOT density tends to zero as n grows, and layers with very few two-qubit gates cannot be scrambling.Source: IBM Q Rueschlikon demonstrations · p. 8
- The Rueschlikon sampling distribution is unsuitable for much larger processors because its CNOT density tends to zero as n increases.The passage notes that circuits with very few two-qubit gates cannot be scrambling.Source: IBM Q Rueschlikon demonstrations · p. 8