[Paper Review] Universal Dephasing Noise Injection via Schrodinger Wave Autoregressive Moving Average Models

Andrew Murphy, J. Epstein+11 more|arXiv (Cornell University)|Feb 5, 2021

Neural Networks and Reservoir Computing59 references8 citations

TL;DR

This paper introduces a platform-agnostic method for injecting arbitrary-spectrum dephasing noise into quantum circuits using Schrödinger Wave Autoregressive Moving Average (SchWARMA) models. By embedding SchWARMA-designed error gates into quantum circuits or injecting noise via Software Defined Radio (SDR), the method enables precise, reproducible noise injection on cloud-based and lab-based quantum processors, validated through quantum noise spectroscopy and signal analysis with strong agreement between injected and reconstructed spectra.

ABSTRACT

We present and validate a novel method for noise injection of arbitrary spectra in quantum circuits that can be applied to any system capable of executing arbitrary single qubit rotations, including cloud-based quantum processors. As the consequences of temporally-correlated noise on the performance of quantum algorithms are not well understood, the capability to engineer and inject such noise in quantum systems is paramount. To date, noise injection capabilities have been limited and highly platform specific, requiring low-level access to control hardware. We experimentally validate our universal method by comparing to a direct hardware-based noise-injection scheme, using a combination of quantum noise spectroscopy and classical signal analysis to show that the two approaches agree. These results showcase a highly versatile method for noise injection that can be utilized by theoretical and experimental researchers to verify, evaluate, and improve quantum characterization protocols and quantum algorithms for sensing and computing.

Motivation & Objective

• To develop a platform-agnostic method for injecting temporally correlated dephasing noise in quantum circuits.
• To enable controlled study of noise effects on quantum algorithms and characterization protocols.
• To overcome limitations of existing noise injection techniques that are hardware-specific and require low-level access.
• To validate the SchWARMA model as both a statistical and generative model for phase noise in quantum systems.
• To demonstrate compatibility with cloud-based quantum processors like IBM Quantum Experience.

Proposed method

• The SchWARMA model is used to generate time-correlated phase noise with arbitrary power spectral density.
• A gate-based noise injection approach inserts instantaneous phase rotations (error gates) between control pulses to simulate noise on the qubit's reference frame.
• An SDR-based hardware implementation directly modulates the master clock signal with SchWARMA-generated phase noise.
• The injected noise is reconstructed using quantum noise spectroscopy (QNS) to compare with the target spectrum.
• Forward simulations of SchWARMA models are used to validate agreement with experimental data.
• The method is tested on both IBM Quantum Experience (cloud-based) and an in-house transmon qubit system (lab-based), enabling cross-platform validation.

Experimental results

Research questions

• RQ1 Can SchWARMA-based noise injection be implemented on cloud-based quantum processors with restricted gate access?
• RQ2 How accurately can SchWARMA model and inject arbitrary dephasing noise spectra in real quantum hardware?
• RQ3 To what extent does the SDR-based hardware injection method reproduce the target noise spectrum?
• RQ4 How well do forward simulations of the SchWARMA model match experimental data from both gate-based and SDR-based injection?
• RQ5 Can the SchWARMA framework be extended to non-Gaussian, non-stationary, and spatiotemporally correlated noise?

Key findings

• The SchWARMA-based gate injection method successfully reproduces target dephasing noise spectra on IBM Quantum Experience with restricted gate access.
• Quantum noise spectroscopy results show strong agreement between injected and reconstructed noise spectra across both gate-based and SDR-based methods.
• The SDR-based method directly measures the injected noise spectrum, confirming agreement with the desired SchWARMA-generated spectrum.
• Forward simulations of the SchWARMA model show high correlation with experimental data, validating its predictive power for temporally correlated dephasing noise.
• The method is platform-agnostic and applicable to any system supporting arbitrary single-qubit rotations, including cloud-based quantum processors.
• The framework is extensible to non-Gaussian, non-stationary, and spatiotemporally correlated noise, demonstrating broad applicability.