Characterizing the Reproducibility of Noisy Quantum Circuits.

Samudra Dasgupta,Travis S Humble

doi:10.3390/e24020244

Samudra Dasgupta, Travis S Humble

Open Access

https://doi.org/10.3390/e24020244

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Abstract

The ability of a quantum computer to reproduce or replicate the results of a quantum circuit is a key concern for verifying and validating applications of quantum computing. Statistical variations in circuit outcomes that arise from ill-characterized fluctuations in device noise may lead to computational errors and irreproducible results. While device characterization offers a direct assessment of noise, an outstanding concern is how such metrics bound the reproducibility of a given quantum circuit. Here, we first directly assess the reproducibility of a noisy quantum circuit, in terms of the Hellinger distance between the computational results, and then we show that device characterization offers an analytic bound on the observed variability. We validate the method using an ensemble of single qubit test circuits, executed on a superconducting transmon processor with well-characterized readout and gate error rates. The resulting description for circuit reproducibility, in terms of a composite device parameter, is confirmed to define an upper bound on the observed Hellinger distance, across the variable test circuits. This predictive correlation between circuit outcomes and device characterization offers an efficient method for assessing the reproducibility of noisy quantum circuits.

Highlights

Reproducibility is important for validating the performance of applications in quantum computing and as a measure of consistency in computation
Current NISQ devices are strongly affected by intrinsic noise that lead to a variety of computational error mechanisms
We have characterized the ability to reproduce the output generated by noisy quantum circuit, using single qubit rotation gates and asymmetric noisy readout

Summary

Introduction

Quantum advantages may be found for solving a variety of problems, such as simulating quantum many-body systems [2], solving unstructured optimization problems [3], achieving complex linear algebra computations [4], efficiently sampling high-dimensional probability distributions [5], and enhancing the security of communication networks [6] These assessments are based on an idealized quantum computing model [7,8,9], comprising of an n qubit register that encodes a 2n -dimensional Hilbert space C2⊗n. A crude approximation to an actual device can be conceptualized as a stack of interacting layers [10,11,12] that includes physical qubits, a physical control layer, a hardware-aware compiler, a logical control layer (including fault tolerant quantum error correction protocols), and a logical compiler and circuit optimizer, as well as the quantum algorithms and applications Each of these intermediate processes introduce the possibility for noise and errors that make modeling the system more complicated. This is made more difficult by the inherent randomness that often manifests in the computed results, inability to pin-point exactly where in a circuit an error has occurred, curse of dimensionality, and the inability to step through program execution [14,15,16]

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