Session B50: Characterizing Noise with QCVV Techniques

Detecting Non-Markovian Errors in Superconducting Qubit Operations Using Partial Tomography

With recent progress in materials and qubit design, the coherence times of superconducting qubits have been improved to 0.1 - 1 ms [1,2]. Since the gate fidelity of superconducting qubits is typically limited by decoherence, these advancements have resulted in single-qubit error rates below 10^-4 and two-qubit gates below 10^-3 [2-5]. With further improvements in coherence times, the fidelity of qubit operations could enter a regime no longer limited by qubit coherence and the dominant operational errors may be non-Markovian. To anticipate this progress, we introduce a novel characterization scheme based on partial tomography that can reconstruct error channels without assuming Markovian noise. We leverage this method to measure quasi-static noise, crosstalk and context-dependent coherent errors, which are considered to be among the most common non-Markovian errors in superconducting qubits [6,7]. With numerical simulations and experiments we show how this novel protocol can help to understand and mitigate correlated errors in superconducting qubits.

 

[1] A.P.M. Place et al., Nat. Commun 12., 1779 (2021).

[2] A. Somoroff et al., Phys. Rev. Lett. 130, 267001 (2023).

[3] Z. Li et al., arXiv 2302.08690 (2023).

[4] L. Ding et al., arXiv 2304.06087 (2023).

[5] H. Zhang et al., arXiv 2309.05720 (2023).

[6] D.M. Debroy et al., arXiv 2303.17565 (2023).

[7] M. Papič et al., arXiv 2305.08916 (2023).   

Scalable, Accurate, and Honest Approximation of Correlated-Qubit Noise

Accurate modeling of noise in realistic quantum processors is critical for constructing fault-tolerant quantum computations. While a full simulation of actual noisy quantum circuits provides information about correlated noise among all qubits and is therefore accurate, it is, however, computationally expensive as it requires resources that grow exponentially with the qubit number. In this talk, I will present an efficient systematic construction of approximate noise channels, where their accuracy can be enhanced by incorporating noise components with higher qubit-qubit correlation degree. To formulate such approximate channels, I will first present a method, dubbed the cluster expansion approach, to decompose the Lindbladian generator of an actual Markovian noise channel into components based on interqubit correlation degree. I then demonstrate how to generate a k-th order approximate noise channel by truncating the cluster expansion and incorporate noise components with correlations only up to the k-th degree. The constructed approximate noise channels are required to be accurate and also "honest", i.e., the actual errors are not underestimated in our physical models. As an example application, I will apply this method to model noise in a three-qubit quantum processor that stabilizes a [[2,0,0]] codeword, which is one of the four Bell states. I will show that for realistic noise strength typical of fixed-frequency superconducting qubits coupled via always-on static interactions, correlated noise beyond two-qubit correlation can significantly affect the code simulation accuracy. Since our approach provides a systematic noise characterization, it enables the potential for scalable, accurate, and honest approximation to simulate large numbers of qubits from full modeling or experimental characterizations of small enough quantum subsystems, which are efficient but still retain essential noise features of the entire device.   

Modeling the effects of 1/f noise on QCVV experiments

Real-world quantum processors are subjected to a wide variety of classical, colored noise sources with correlations that span the shortest to the longest experimentally relevant timescales. Examples include phase noise in lasers, 1/f noise in solid-state systems, and long-term drift. In this talk I discuss the impacts of these noise sources on quantum characterization, verification and validation (QCVV) experiments. I’ll then present a formalism based on cumulant expansions that can be used to efficiently simulate, predict, and analyze quantum circuit experiments subject to colored noise. Finally, I’ll discuss how we can generalize some of our usual metrics of quantum processor performance to capture colored noise.

Sandia National Laboratories is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.   

Learning the capabilities of quantum computers using physics-informed neural networks

The computational power of contemporary quantum processors is limited by hardware errors that cause computations to fail. In principle, each quantum processor's computational capabilities can be captured by a capability function. A capability function quantifies how well a processor can run each possible quantum circuit by mapping a circuit to the processor's success rate on that circuit, as quantified by, e.g., fidelity. However, capability functions are typically unknown and challenging to model. In this talk, I will present results on using purpose-built artificial neural networks to learn an approximation to a processor's capability function. These “physics-informed” neural networks efficiently encode how errors propagate through and interfere within circuits, enabling accurate capability predictions even in the presence of strongly coherent errors. 

 

SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.   

Unified Quantum State Tomography and Hamiltonian Learning: A Language-Translation-Like Approach for Quantum Systems

As quantum technology continues to make rapid strides, the quest for efficient, scalable tools for quantum system characterization assumes greater importance. Quantum State Tomography and Hamiltonian learning have become indispensable for deciphering and fine-tuning quantum systems. The amalgamation of these tools, however, is yet to be realized. Here, we introduce a novel method that facilitates this integration, drawing on the principles of machine translation from the Natural Language Processing (NLP) domain. We apply our methodology to an extensive spectrum of quantum systems, ranging from 2-qubit cases to 2D antiferromagnetic Heisenberg model, and demonstrate the versatility of our approach by employing various Quantum State Tomography methods. Additionally, the scalability of our method, along with its few-shot learning capabilities, promises a significant reduction in the resources needed for quantum system characterization and optimization.   

Measuring circuit errors in context for surface code circuits

Abstract: In the operation of a fault-tolerant quantum computer, the vast majority of time spent by individual qubits will be executing stabilizer extraction circuits. As such, it is important to maximize performance within this particular structured circuit. The spatial and temporal context of an operation can significantly impact the errors seen, and as such it is important to characterize the operations within stabilizer extraction circuits in the context they will most often see. We will discuss one such way to characterize these errors within the context of the surface code stabilizer extraction circuit.   

Enabling efficient characterization of measurement noise with measurement randomized compiling

Measurements are a vital part of any quantum computation, whether as a final step to retrieve results, as an intermediate step to inform subsequent operations, or as part of the computation itself (as in measurement-based quantum computing). However, measurements, like any aspect of a quantum system, are highly error-prone and difficult to characterize and model. In this talk, I will present a new noise tailoring method called measurement randomized compiling, which tailors the effective noise on measurements to a form which is simpler and easier to characterize accurately. The tailored noise is consistent with models of measurements used for many theoretical studies of quantum computing, including in the quantum error correction setting. In particular, our technique reduces generic errors in a measurement to act like a confusion matrix, i.e. to report the incorrect outcome with some probability, and as a stochastic channel that is independent of the measurement outcome on any unmeasured qudits in the system. footnote{The research presented in this talk was co-authored by Joel J. Wallman.}   

Modeling Logical Qubit Performance in the Presence of Physical Crosstalk Noise

Given the increasing number of experimental logical qubit demonstrations, it is increasingly important to study how physical noise impacts logical qubit performance, especially in the presence of correlated physical noise and at low logical code distance. We use the Logical Qubit Simulator (LoQS) package to numerically study the effects of physical crosstalk noise on logical qubit performance for several quantum error-correcting codes; in particular, we investigate how noise strength and type of crosstalk noise (e.g. gate spillover, always-on interactions) impact the logical qubit.   

Emergent Non-Markovian Dynamics in Logical Qubit Systems

Simulations of error-corrected logical qubits have demonstrated that logical qubit dynamics can exhibit non-Markovian behavior, even when the underlying physical noise is Markovian. Such non-Markovian errors present challenges to holistic logical qubit characterization and can also non-trivially degrade the performance of error-corrected hardware in unexpected ways. By examining the gate composability requirement for Markovian dynamics, we provide illustrative examples to explain the emergence of logical non-Markovianity. We use these results to comment on the utility of characterization protocols for logical qubits.   

Improving the fidelity of flux-based gates in superconducting processors through model learning of qubit and control stack parameters.

The flux-based controlled-phase (CZ) gate offers potential speed-ups for two-qubit entangling gates, by operating at the speed limit of the transverse coupling between the computational |1,1> and non-computational |0,2> states. The scheme entails flux control of transmon frequency using a unipolar or bipolar square pulse. While ideally, the population exchange between the |1,1> and |0,2> states near resonance should show symmetric chevron-like oscillation patterns around the target flux amplitude, experiments reveal asymmetries that impact fidelity of flux-based gates. Using a physics-informed machine learning model to minimize the Euclidean distance between experimental and simulated chevrons, we learnt pulse distortions occuring down the control line, besides learning some relevant system Hamiltonian parameters. Our framework complements the Cryoscope technique of measuring the step response of flux control lines, as we also model pulse distortions after digital-to-analog conversion in the control stack. The model achieves a 99.5% match with experimental chevron data for unipolar flux pulses, and was validated for chevrons obtained for bipolar pulses. We shed light on the physical implication of the learnt parameters, and lay out actionable insights about correcting the pulse distortions to improve fidelity of the flux-based gates.   

Deep Learning based adaptive characterisation of QPUs

Detailed device characterisation is necessary for both obtaining the optimised gate-sets on a given hardware as well as identifying device imperfections and error sources to improve the next design iteration. Typical textbook characterisation routines do not scale efficiently to large multi-qubit chips, requiring the development of techniques based on statistical and information theoretic foundations. We present the application of Deep Learning based characterisation techniques that adaptively recommends Bayesian Optimal Experiments at every step to maximise the expected information gain about the system, while taking into account the entire history of past experiments. The cost of calculating expensive Bayesian posteriors is amortised by the use of a Reinforcement Learning system which simultaneously learns both the design policy and lower bounds on the otherwise computationally intractable Expected Information Gain. A physics accurate fully-differentiable digital twin that models the open quantum dynamics of the QPU, the control electronics and the noise & transfer functions for the whole stack lies at the heart of this closed loop adaptive calibration and characterisation process. We demonstrate the application of these bayesian adaptive experiments on multi-qubit superconducting QPU systems.   

Estimating fidelity by propagating errors through quantum circuits

As quantum computers continue to develop and advance, the need to be able to predict their performance continues to be important.  Current attempts either assume overly simplified error models or aim to describe the error in a dense format, making modeling computationally infeasible.  Here, we propose a new method where each gate error can be approximated by the rates of a polynomial number of primitive error generators. These errors can be propagated through a Clifford circuit allowing for us to efficiently generate an error map for the entire circuit to high order.  This method captures the transformations individual errors undergo as they interact with gates and other error generators while being scalable to large quantum processors.  Additionally, time dependent error rates can be used to capture the behavior of non-Markovian noise.  We demonstrate the accuracy of this new method by comparing the predicted end of circuit error generator with the true end of circuit error generator created by propagating process matrices.  SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.   

Linear-quadratic regulation of drift in quantum processor

Rapid calibration and recalibration of a quantum processor in the presence of drift will be essential to achieve and maintain error rates below fault tolerance thresholds. Towards this goal, we are adapting the classical linear-quadratic regulator (LQR) within the context of quantum devices to support a streaming calibration approach that uses active feedback to rapidly tune device settings on-line. One starts by identifying an appropriate error model for a device and an observation function such as repeated sequences of gates, as in gate set tomography and robust phase estimation. Next, one defines a quadratic cost function to penalize deviations from the target performance. The LQR provides the optimal control law that minimizes this cost function. Experimental implementation of LQR policies require very little computational resources and can be embedded directly on classical control hardware for low-latency, real-time control of drift in current devices.