[Paper Review] Experimental demonstration of Pauli-frame randomization on a superconducting qubit

Matthew Ware, Guilhem Ribeill+4 more|arXiv (Cornell University)|Mar 5, 2018

Quantum Computing Algorithms and ArchitectureComputer Science73 references46 citations

TL;DR

This paper demonstrates Pauli-frame randomization (PFR) on a superconducting qubit to convert coherent, non-Markovian errors into stochastic Pauli errors, significantly improving the accuracy of quantum error models. Using gate set tomography, the authors show that PFR suppresses non-Markovian signatures from 43σ to 1987σ down to 0.3σ–2.7σ and improves Pauli error model fidelity, with no loss in gate fidelity and even reduced diamond norm error rates.

ABSTRACT

The promise of quantum computing with imperfect qubits relies on the ability of a quantum computing system to scale cheaply through error correction and fault-tolerance. While fault-tolerance requires relatively mild assumptions about the nature of qubit errors, the overhead associated with coherent and non-Markovian errors can be orders of magnitude larger than the overhead associated with purely stochastic Markovian errors. One proposal to address this challenge is to randomize the circuits of interest, shaping the errors to be stochastic Pauli errors but leaving the aggregate computation unaffected. The randomization technique can also suppress couplings to slow degrees of freedom associated with non-Markovian evolution. Here we demonstrate the implementation of Pauli-frame randomization in a superconducting circuit system, exploiting a flexible programming and control infrastructure to achieve this with low effort. We use high-accuracy gate-set tomography to characterize in detail the properties of the circuit error, with and without the randomization procedure, which allows us to make rigorous statements about Markovianity as well as the nature of the observed errors. We demonstrate that randomization suppresses signatures of non-Markovian evolution to statistically insignificant levels, from a Markovian model violation ranging from $43\sigma$ to $1987\sigma$, down to violations between $0.3\sigma$ and $2.7\sigma$ under randomization. Moreover, we demonstrate that, under randomization, the experimental errors are well described by a Pauli error model, with model violations that are similarly insignificant (between $0.8\sigma$ and $2.7\sigma$). Importantly, all these improvements in the model accuracy were obtained without degradation to fidelity, and with some improvements to error rates as quantified by the diamond norm.

Motivation & Objective

• To demonstrate that Pauli-frame randomization (PFR) can effectively convert coherent, non-Markovian errors into stochastic Pauli errors in a superconducting qubit system.
• To rigorously test whether PFR suppresses non-Markovian error signatures using high-accuracy gate set tomography (GST).
• To validate that the randomized error model is well described by a Pauli error model, with minimal model violations.
• To assess whether PFR improves the accuracy of error models without degrading gate fidelity or increasing error rates.

Proposed method

• PFR is implemented by inserting uniformly random Pauli operations between Clifford gates in a quantum circuit sequence.
• The final measurement basis is corrected via a Pauli frame correction (PL+1) to preserve the computational outcome without post-processing.
• High-accuracy gate set tomography (GST) is used to characterize gate errors, with insensitivity to state preparation and measurement (SPAM) errors.
• The diamond norm and average infidelity are computed to quantify error rates pre- and post-randomization.
• Statistical hypothesis testing is applied to assess the degree of Markovianity and Pauli model fidelity, using p-values derived from likelihood ratio tests.
• The experimental setup uses a flexible control and programming infrastructure to generate and execute 3.5 million unique randomized sequences with one shot per sequence to avoid correlation effects.

Experimental results

Research questions

• RQ1 Can Pauli-frame randomization effectively suppress non-Markovian error signatures in a superconducting qubit system?
• RQ2 To what extent does PFR improve the accuracy of a Pauli error model in the presence of experimental imperfections?
• RQ3 Does PFR preserve or enhance gate fidelity while reshaping noise into a more benign form?
• RQ4 Can gate set tomography reliably quantify the reduction in model violations due to randomization?
• RQ5 Is the improvement in error model accuracy statistically significant, and does it correlate with reduced diamond norm error?

Key findings

• PFR suppresses non-Markovian error signatures from a violation range of 43σ to 1987σ down to 0.3σ to 2.7σ, indicating statistically insignificant deviations from Markovianity.
• The Pauli error model fidelity is improved such that model violations are reduced to 0.8σ to 2.7σ under randomization, indicating a highly accurate Pauli description.
• The diamond norm error rate is reduced after randomization, demonstrating that PFR improves the overall error rate without degrading gate fidelity.
• All improvements in model accuracy and error suppression were achieved without any degradation in gate fidelity, and with some improvements in error rates.
• The experimental implementation achieved these results using a flexible control infrastructure and one-shot randomized sequences, minimizing correlation effects and ensuring statistical robustness.
• The study confirms that PFR is effective in shaping noise into a form compatible with fault-tolerant quantum computation, even under realistic experimental imperfections.