Session D72: Techniques for Learning Noise in Quantum Systems

Random Pulse Sequences for Noise Spectroscopy

Qubit noise spectroscopy is an important tool for experimental investigations of open quantum systems. However, conventional noise spectroscopy techniques are time-consuming, because they require repeated measurements of the noise spectral density S(ω) at different frequencies ω. Here we describe an alternative method for quickly and approximately characterizing S(ω). This method uses random pulse sequences, with carefully-controlled correlations among the pulses, to measure arbitrary linear functions of S(ω). This method has many applications. We can do parametric estimation of noise spectra and learning an effective description of the environment, such as the 1-D chain representation. We also develop several compressed sensing protocals to characterizing noise spectra that consist of a few isolated peaks. We illustrate these applications by simulations on quantum dots and superconducting qubits.   

Estimating quantum gate fidelities in context

It is often desireable to characterize quantum gates in the context in which they are being used, both in space (by applying simultaneous operations on surrounding qubits), and in time (e.g. preceding operations on the same qubits). In this talk we will present a flexible framework for estimating the average gate fidelity of a quantum operation in any particular context of interest. We will discuss two extensions to this simple idea, one that allows us to budget the coherent and incoherent errors, and one that allows us to efficiently characterize the individual operations in a larger Clifford circuit, such as a surface-code stabilizer circuit.   

Precision gate characterization in the presence of low-frequency noise on a superconducting processor

Coherent amplification, the primary tool for precision quantum estimation, remains elusive for many tasks because the necessary coherence is scrambled by noise processes. One such noise process in superconducting-qubit platforms is flux noise, which causes slow fluctuations of the qubit frequency. In addition to making the qubit frequency itself ill defined for estimation purposes, these fluctuations mask deviations in other well-defined parameters in the system. We present a characterization technique that allows us to precisely target select unitary parameters for controlled-Z gates in the presence of such low-frequency noise, obtaining up to 20 times precision improvement in these parameters. The simplicity and directness of this method makes it a robust and reliable tool for precision characterization of noisy quantum devices.   

Resource-efficient frame-based non-Gaussian quantum noise spectroscopy and optimized control

Many state-of-the art qubit devices are exposed to noise that is temporally correlated (“non-Markovian”) and non-Gaussian. Characterizing such noise in a way that is accurate and useful for predicting arbitrary controlled dynamics is challenging given finite control resources. A recently proposed formalism [1] leverages the notion of a “frame” to generalize transfer filter-function techniques beyond the frequency domain and overcome important limitations of existing approaches. Notably, by tying the choice of frame to the available control, a model-reduced representation of the open-system dynamics is obtained, allowing efficient noise characterization under experimental constraints. Within this general framework, we show how to achieve digital noise spectroscopy of non-Gaussian classical dephasing using a window frame. Focusing on random telegraph noise as a concrete example, we demonstrate how non-Gaussian noise spectroscopy can provide high-order control-adapted noise spectra for qubit dynamics prediction and noise-tailored decoupling design. We find that, depending on the operating parameter regime, control that is optimized based on non-Gaussian noise spectroscopy can substantially outperform standard Walsh decoupling sequences as well as control that is optimized based only on Gaussian noise spectroscopy.

 

[1] T. Chalermpusitarak, B. Tonekaboni, Y. Wang, L. M. Norris, L. Viola, and G. A. Paz-Silva, Phys. Rev. X Quantum 2, 030315 (2021).

    

Two Qubit Correlated Noise and Crosstalk Characterization

Spatiotemporally correlated noise and crosstalk have a negative impact on error correcting schemes. We propose and validate a nonparametric quantum noise spectroscopy protocol to measure the spectra associated with spatiotemporally correlated dephasing noise and fluctuating crosstalk on two qubits. This method is also used to estimate the static components of the crosstalk and the dephasing noise processes acting on each qubit. Our scheme reconstructs the real and imaginary components of the two-qubit cross-spectrum by using two fixed total time pulse sequences and performing single qubit and joint two-qubit measurements to separately resolve spatially correlated noise processes from the individual noise spectra of the participating qubits. We benchmark our protocol by reconstructing the spectra of engineered spatiotemporally correlated noise processes produced by Schrodinger Wave Autoregressive Moving Average, a technique developed by our group [1] to generate phase error on qubit control lines. Our results demonstrate the utility of our protocol in characterizing spatiotemporally correlated noise and crosstalk in a multiqubit device for potential use in noise-adapted control or error mitigation schemes.

[1] Murphy, Andrew, et al. "Universal-dephasing-noise injection via Schrödinger-wave autoregressive moving-average models." Physical Review Research 4.1 (2022): 013081.   

Modeling Low-Frequency Hamiltonian Noise

The ability to precisely and completely characterize the behavior of as-built quantum computing hardware is essential to the development of next-generation quantum computers. Tomographic protocols, such as gate set tomography (GST), produce incredibly detailed descriptions of the noise in a system, but do so under the assumption that the noise is markovian. Non-markovian noise sources (e.g. leakage, crosstalk and temporal correlations) are common in real systems, and are pernicious in that we not only do not capture them with most existing characterization protocols, but they can in fact corrupt our estimates for the markovian noise in a device.

In this work we introduce a method for modeling and characterizing non-markovianity due to temporally correlated fluctuating hamiltonians in the quasi-static DC/low-frequency limit and demonstrate its performance in simulation. While not fully general,

this limit captures many important forms of non-markovianity, such as non-markovian dephasing. Moreover, this demonstrates an essential first step in the development of models for non-markovianity arising from hamiltonians fluctating according to arbitrary noise spectra.   

Full characterisation of quantum non-Markovian processes: from tomography to noise detection.

Every experimental realisation of a quantum process faces the possibility of noise coming from the environment. Although in small quantum devices, the noise is assumed to be uncorrelated (Markovian) this assumption fails as the size and complexity increase, and the various system-environment interactions become correlated (non-Markovian).

We present a method of full quantum process tomography that captures non-Markovian noise and a method to detect quantum memory in a non-Markovian process [1]. We call a process Markovian when the environment does not provide a memory that retains correlations across different system-environment interactions. We define two types of non-Markovian processes, depending on the required memory being classical or quantum. We formalise this distinction using the process matrix formalism, through which a process is represented as a multipartite state. Within this formalism, a test for entanglement in the state can be mapped to a test for quantum memory in the process.

We demonstrate the method in a simple toy model, but our methods have been applied experimentally, too, in photonics [2] and superconducting qubits [3].

[1] C. Giarmatzi and F. Costa Quantum 5, 440 (2021)

[2] K. Goswami, C. Giarmatzi, et al. Phys. Rev. A 104, 022432 (2021)

[3] Upcoming paper   

Identifying Off-Resonant Errors on Fixed Frequency Transmons

Quantum gate error rates have dropped steadily on IBM processors over the last years, making more sophisticated computations possible, but also increasing the challenge of characterizing the remaining errors. In particular, non-Markovian errors have been thought likely to limit gates on IBM systems, but directly detecting these errors has been elusive, limiting our ability to mitigate them efficiently. We probe our system for off-resonant excitations, a specific form of non-Markovian coherent error, using continuous phase amplification. Since errors due to excitations of an off-resonant transition are non-stationary they are hard to amplify and detect without using this technique. These errors exist in all microwave driven one- and two-qubit gates on IBM devices and can bottleneck performance near collisions (e.g. driving the cross-resonance interaction during single qubit gates or vice versa). Furthermore we can use this same methodology to access to the errors caused by TLS, showing evidence of coherent, off-resonant interactions with subsystems that are not qubits. We explore these results and their impact on gate error for IBM deployed devices.   

Noise Modeling of the IBM Quantum Experience

The influence of noise in quantum dynamics is one of the main factors preventing Noisy Intermediate-Scale Quantum (NISQ) devices from performing useful quantum computations. Errors must be suppressed in order to achieve the desired levels of accuracy, which requires a thorough understanding of the nature and interplay of the different sources of noise. In this work, we propose an effective error model of single-qubit operations on the IBM Quantum Experience, that possesses considerable predictive power and takes into account spatio-temporally correlated noise. Additionally, we showcase how Quantum Noise Spectroscopy (QNS) can be used alongside other error characterization techniques, such as T1 experiments, to obtain a more complete error model of the system. We focus on a Hamiltonian description of the noise, with parameters obtained from a small set of characterization experiments. We show that simulations using this error model are capable of recovering the characterization experiments' results to a high degree of accuracy. We also successfully compare the simulations against test data consisting of experimental results of varying circuit lengths and types of implemented operations. Lastly, we characterize the fluctuation of the noise model parameters as functions of time, observing large variations in some devices.   

Self-consistent learning and control of arbitrary quantum correlated noise, and beyond

The demands of fault tolerance mean that a wide variety of simple and exotic noise types must be tamed for quantum devices to progress. Real-world hurdles range from imperfect gates and decoherence, to spatiotemporal non-Markovianity, crosstalk, correlated control errors, and undesirable driving of bath transitions. These effects must be treated, but how can we combine everything into a feasible and useful framework, and how can this then be learned? Fortunately, as devices improve, the presence of noise gets sparser and permits more sophisticated models for efficient and general characterisation. Combining recent advances in tensor network learning with non-Markovian process characterisation, we develop efficient techniques to capture a near-universal model for quantum noise. The three fundamental categories we consider are: correlated background dynamics, correlated control imperfections, and control-environment interactions. Our approach to characterise these components employs no assumptions about prior calibrations, and can accommodate large numbers of time-steps and qubits from relatively few experiments. The result is a practical, scalable, and consistent procedure capable of describing arbitrary open dynamics and experimental controls. We stress that the framework is hardware agnostic, but the models are readily modular and can be adapted based on the expected physics of the device or intended purpose of the characterisation. The resulting estimate not only spells out errors, but also serves as a reliable mapping from all experimenter-chosen parameters to circuit outcomes. Hence, this has ready accessibility and applicability to all applied quantum information processing. We bolster these claims with an extensive set of numerical and experimental results. In particular, we demonstrate powerful applications of our method, including bespoke dynamical decoupling sequences, pulse shaping, and optimal logical control choices for any two-qubit gate decomposition. We anticipate this approach to be useful at informing all levels of the quantum control stack: in error suppression, error mitigation, and error correction.   

Model-Based Qubit Noise Spectroscopy

Qubit noise spectroscopy (QNS) is a valuable tool for both the characterization of a qubit's environment and as a precursor to more effective qubit control to improve qubit fidelities. Existing approaches to QNS are what the classical spectrum estimation literature would call "non-parametric" approaches, in that a series of probe sequences are used to estimate noise power at a set of points or bands. In contrast, model-based approaches to spectrum estimation assume additional structure of the spectrum and leverage this for improved statistical accuracy or other capabilities, such as superresolution. Here, we derive model-based QNS approaches using inspiration from classical signal processing, primarily though the recently developed Schrodinger wave autoregressive moving-average (SchWARMA) approach for correlated noise models. We show, using simulation and experimental data, how these model-based QNS approaches maintain the statistical and computational benefits of their classical counterparts, resulting in powerful new estimation approaches. Beyond the direct application of these approaches to QNS, we anticipate that the underlying models will find utility in adaptive feedback control for quantum systems, in analogy with their role in classical adaptive estimation and control.   

Experimental Multi-Time Process Tomography on Superconducting Qubits

The maturation of quantum technologies in the past decade has been enabled, in no small part, by the ongoing advancement of noise characterisation techniques. For Markovian noise sources, quantum process tomography or QPT (a natural extension of quantum state tomography) is one such technique which has become ubiquitous in the experimental toolbox. However, techniques like QPT have no capacity to characterise sources of non-Markovian noise (e.g. memory effects, system drifts and crosstalk), which we know exist nontrivially in the vast majority of experimental hardware. In this talk, we introduce a methodology to perform multi-time quantum process tomography, which uses a process matrix formalism to allow for full characterisation of non-Markovian dynamics. We discuss the experimental procedure required to perform multi-time process tomography on a superconducting quantum device, and present results where we successfully detect quantum memory effects on an in-house superconducting device and a publicly available IBM processor.