Session F72: Benchmarking Gates and Quantum Processes

Wigner State and Process Tomography on Near-Term Quantum Devices

With the growing interest and rapid development in near-term quantum devices, the migration of theoretical and experimental approaches from existing devices to near-term quantum devices are imperative. We present an experimental scanning-based tomography approach in the context of finite-dimensional Wigner representations. These representations provide a rich visualization of quantum operators using shapes assembled from a linear combination of spherical harmonics. These shapes, i.e., spherical droplets, can be recreated experimentally by measuring the expectation values of rotated axial tensor operators. This study provides a reformulation of the theory of Wigner state and process tomography for the case of a general-purpose pure-state quantum computer. We present an experimental framework for implementing the scanning-based tomography technique for circuit-based quantum computers and showcase results from IBM quantum experience. We also present a method for estimating the density and process matrices from experimentally tomographed

spherical droplets. This tomography approach can be directly accessed using python packages.   

Markovianization through Dynamical Decoupling in Randomized Benchmarking

While a myriad of techniques for the characterization of quantum noise in the so-called Markovian, i.e., memoryless, regime have been developed to date, it is expected for temporal correlations and memory effects to become one of the major contributors to errors as quantum systems scale up in size and depth. We demonstrate the effectiveness of incorporating Dynamical Decoupling (DD) [1,2] and Randomized Benchmarking (RB) [3,4], two of the most user-friendly protocols known hitherto, to simultaneously consume temporal correlations, i.e., non-Markovianity, and predict average gate fidelities of effectively Markovianized noise.

We analytically predict a non-Markovian Average Sequence Fidelity (ASF) decay reducing to its Markovian counterpart, plus perturbative non-Markovian corrections, upon the application of suitable ideal DD pulses on a broad class of non-Markovian noise models. Furthermore, under finite-width DD pulses, we simulate and analyze the ASF for realistic noise sources, still obtaining an effective Markovianization of RB data in the fast and small-width DD sequence limit. Our results show a convenient and effective way of consuming non-Markovianity while benchmarking the error rates of the resulting Markovianized noise.

[1] G. D. Berk et. al., arXiv:2110.02613 [quant-ph] (2021).

[2] N. Ezzel et. al., arXiv:2207.03670 [quant-ph] (2022).

[3] J. Helsen et. al., PRX Quantum, 3, 020357 (2022).

[4] P. Figueroa-Romero, K. Modi & M.-H. Hsieh, arXiv:2202.11338 [quant-ph] (2022).   

Author not Attending

The dynamics of noninteracting bosons has attracted interest due to the BosonSampling problem and its computational difficulty. A challenge in experimental systems implementing these dynamics is verifying that the output distributions are close to the desired ones. Motivated by a cold atom optical lattice experiment, we formalize the notion of genuine multiparticle indistinguishability, making use of tools from representation theory. We then construct novel witnesses of it, aiming for small variance and robustness to small miscalibrations of the unitary that governs the dynamics. We also discuss the possibility of using the representation theoretic framework to infer the linear optical unitary, by preparing many initial states.   

A randomized benchmarking suite for mid-circuit measurements

Mid-circuit measurements are a key component in many quantum information computing protocols, including quantum error correction, fault-tolerant logical operations, and measurement based quantum computing. As such, techniques to quickly and efficiently characterize or benchmark their performance are of great interest. Beyond the measured qubit, it is also relevant to determine what, if any, impact mid-circuit measurement has on adjacent, unmeasured, spectator qubits. Here, we present a mid-circuit measurement benchmarking suite developed from the ubiquitous paradigm of randomized benchmarking. We show how our benchmarking suite can be used to both detect as well as quantify errors on both measured and spectator qubits. We demonstrate the scalability of our suite by simultaneously characterizing mid-circuit measurement on multiple qubits from an IBM Quantum Falcon device, and support our experimental results with numerical simulations.   

Good models for noisy mid-circuit measurements

Quantum measurement, or readout, is traditionally the last step in a quantum circuit (program) that gets run on a quantum computer. But qubits can also be measured — sometimes repeatedly — in the middle of a quantum circuit. These mid-circuit measurements are critical for quantum error correction, and are now being implemented in a growing range of testbed quantum processors. Like all quantum logic operations, they're not perfect. And when they fail, they can fail in novel ways that don't afflict circuit-terminating measurements (e.g., failing to fully collapse the quantum state). Mid-circuit measurements can be modeled by quantum instruments — a particular kind of quantum channel — but like process matrices, instruments don't lend themselves to intuition. Here, we construct new models and metrics for errors in mid-circuit measurements, inspired by the error generator representation of errors in logic gates, and show how to use these models for better characterization and simulation of realistic errors in mid-circuit measurements.   

Tomographic characterization of quantum gates with error amplification

Characterization of gate error is a fundamental step toward improvement of gate accuracy. Quantum tomography is an attractive class of characterization protocols along with the direction because it provides several information of errors, but its standard protocol suffers from low reliability originated from state-and-measurement (SPAM) error. Advanced tomographic protocols such as gate-set tomography, idle tomography, and Hamiltonian error-amplifying tomography use an error-amplification process to overcome the low reliability. One disadvantage of the use of error-amplification is an increase in computational cost and instability of data-fitting because of its high nonlinearity with respect to fitting parameters. Here we propose a new data-processing method (estimator) for quantum tomographic protocols with error-amplification, which enables us to reduce computational cost and instability of data-fitting. We theoretically and numerically show that the method proposed has sufficiently high reliability in practical situation for development of quantum computer.   

Quantifying the imperfection for non-trace-preserving quantum operations

In quantum information and quantum computing theory, quantum operations are usually assumed to be completely positive trace-preserving linear maps, but this is not the case for realistic quantum systems. Given the measurements and post-selection, non-preserving trace operations occur. We propose a generic metric to compare two non-trace-preserving quantum operations. This metric provides a worst-case error bound for the operation and can be efficiently computed. In addition, we discuss the occurrences of non-trace-preserving operations, classifying them into three main categories: leakage, feed-forward control, and intrinsically probabilistic gates. We also discuss how the metric can be used to study error propagation and estimate thresholds in fault-tolerant quantum computing.   

Efficient online quantum gate set diagnosis by Fast-Bayesian Tomography

To push the error rate closer to the threshold for fault-tolerate quantum computing, it is critical to characterise the gate error and fix them actively. Harnessed the power of Bayesian approach, Fast Bayesian Tomography (FBT) is a self-consistent process tomography technique, which is experimentally flexible and computationally efficient. In this work, we demonstrate the experimental approach of running the FBT online, which allows the model to be updated as experiment data obtained. Various improvements have been achieved to make the protocol even more efficient and experimentally low-cost. We are also showing the practical diagnosis applications of the FBT protocol on our 2 qubit system based on silicon quantum dots.   

Randomized benchmarking into the quantum advantage regime

Randomized benchmarking (RB) methods are widely used for quantifying the performance of quantum processors. However, most existing protocols are limited in scalability, e.g., because they require classical computations that scale exponentially in the number of qubits. In this talk I will present scalable RB protocols that can benchmark universal gate sets, mid-circuit measurements, and compiler performance. These techniques are practical even in the many-qubit regime, where classical simulations of general circuits are infeasible. I will show how random circuits with a reflection structure, known as randomized mirror circuits, can be used to efficiently and reliably estimate the average error rate of universal gate sets. I will then show how these methods can be adapted to construct scalable and efficient full-stack quantum computing benchmarks, including a scalable version of the quantum volume benchmark. RB with mirror circuits uses a streamlined, gate-efficient fidelity estimation technique. A similar technique can be used to simplify RB of Clifford gates by removing its inversion step. I will show how this idea enables RB of mid-circuit measurements, which are a critical quantum computing primitive that cannot be benchmarked using conventional RB methods. Using theory, simulations, and experiments on contemporary quantum processors, I will show that our RB methods are scalable, reliable, and powerful tools for understanding quantum computer performance. Our experimental results demonstrate the importance of scalable benchmarks for fully capturing the error present in medium- and large-scale quantum processors.   

Benchmarking quantum logic operations for achieving fault tolerance

Contemporary methods for benchmarking noisy quantum processors typically measure average error rates or process infidelities. However, thresholds for fault-tolerant quantum error correction are given in terms of worst-case error rates — defined via the diamond norm — which can differ from average error rates by orders of magnitude. One method for resolving this discrepancy is to randomize the physical implementation of quantum gates, using techniques like randomized compiling (RC). Here, we use gate set tomography to perform precision characterization of a set of two-qubit logic gates to study RC on a superconducting quantum processor. We find that, under RC, gate errors are accurately described by a stochastic Pauli noise model without coherent errors, and that spatially-correlated coherent errors and non-Markovian errors are strongly suppressed. We further show that the average and worst-case error rates are equal for randomly compiled gates, and measure a maximum worst-case error of 0.0197(3) for our gate set. Our results show that randomized benchmarks are a viable route to both verifying that a quantum processor's error rates are below a fault-tolerance threshold, and to bounding the failure rates of near-term algorithms, if — and only if — gates are implemented via randomization methods which tailor noise.   

Learning quantum dynamics: Lindblad operators from classical shadows

Learning dynamics from repeated observation of time evolution of an open quantum system, namely, the problem of quantum process tomography, is an important but, in general, difficult task. The exploration of additional constraints that make the problem tractable motivates us to consider the problem of Lindblad operator discovery from observations. We point out that for moderate-size Hilbert spaces, low Kraus rank of the channel, and short time steps, the eigenvalues of the Choi matrix corresponding to the channel have a special structure. We use the least square method for the estimation of a channel where, for fixed inputs, we estimate the outputs by classical shadows. We then denoise the resultant noisy estimate of the channel by diagonalizing the nominal Choi matrix, truncating some eigenvalues, and altering it to a genuine Choi matrix. We use tools from random matrix theory to understand the effect of estimation noise in the eigenspectrum of the estimated Choi matrix. We, further, verify that our method of channel reconstruction gets more accurate as the sample size increases.    

Efficient gate set tomography using compressed sensing

Gate set tomography (GST) is a widely used technique for characterizing a set of noisy quantum gates. GST is accurate and robust, but it is expensive: conventional GST requires running many circuits, and it uses intensive classical computation to analyze the data. GST fits an error model to data, and the model’s parameters correspond to the rates of different kinds of errors. Some of these parameters model commonly observed physical effects (e.g., gate over- or under-rotation errors, depolarization, amplitude damping), but many of the parameters model esoteric effects that are typically not present in real-world systems (e.g., high-weight Hamiltonian errors). We therefore expect many, or even most, of the true parameter values to be negligible or zero. When this is true, GST is estimating a sparse vector of parameters, and such vectors can be estimated with high efficiency using compressed sensing methods. In this talk, I explore the possibility of applying compressed sensing methods to GST. Our aim is to create a super-efficient version of GST that uses fast analysis on data from a practical number of circuits, and which is practical well beyond the 1-3 qubit regime in which conventional GST is feasible.

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

    

Randomized Benchmarking Beyond Groups

Randomized benchmarking (RB) is the gold standard for experimentally evaluating the quality of quantum operations. The current framework for RB is centered on groups and their representations, but this can be problematic. For example, Clifford circuits need up to O(n^2) gates, and thus Clifford RB cannot scale to larger devices. Attempts to remedy this include new schemes such as linear cross-entropy benchmarking (XEB), cycle benchmarking, and non-uniform RB, but they do not fall within the group-based RB framework. In this work, we formulate the universal randomized benchmarking (URB) framework which does away with the group structure and also replaces the recovery gate plus measurement component with a general "post-processing" POVM. Not only does this framework cover most of the existing benchmarking schemes, but it also gives the language for and helps inspire the formulation of new schemes. We specifically consider a class of URB schemes called twirling schemes. For twirling schemes, the post-processing POVM approximately factorizes into an intermediate channel, inverting maps, and a final measurement. This leads us to study the twirling map corresponding to the gate ensemble specified by the scheme. We prove that if this twirling map is strictly within unit distance of the Haar twirling map in induced diamond norm, the probability of measurement as a function of gate length is a single exponential decay up to small error terms. The core technical tool we use is the matrix perturbation theory of linear operators on quantum channels.