Session D50: Holistic QCVV Techniques and Shadow Tomography

Validating models of quantum computers in practice

Predictive models of quantum computing devices are essential for understanding quantum devices' behavior, quantifying the rates and kinds of errors, and enabling engineering improvements. But models for a processor's behavior—whether derived from theory or from experimental characterization protocols run on a device—are not always accurate. Models are useful only inasmuch as their predictions are accurate, and inconsistencies with experimental data suggest that a model should be adjusted or replaced. We present simple and easy-to-use techniques for testing the validity of models using experimental data from running quantum circuits, and we demonstrate them using data from cloud-access quantum computers. We begin by showing how to determine if a model is consistent with a data set. Most real world models are not fully consistent with data, so we then show how to probe the inconsistencies between the model and the data by quantifying and analyzing the deviations using operationally meaningful error metrics.   

Scalable Benchmarking of Quantum Chemistry Algorithms using Circuit Mirroring

Current benchmarking methods for measuring progress towards applications on quantum computers often lack scalability and specificity. This limits their ability to produce generalizable metrics of processor performance. We will describe a method for creating scalable application-specific benchmarks using mirrored subcircuits that quantify a device's ability to execute particular subroutines or entire algorithms. We will then apply this method to two quantum chemistry subroutines, performing noisy numerical simulations and interpreting their results within the paradigm of volumetric benchmarking. We will show how to extract effective error rates and predict full circuit fidelities from the subcircuit data and demonstrate that we can distinguish differences in performance resulting from structural properties of the circuits.   

Parity Measurement Gate Set Tomography

Parity measurements, used for detecting errors during the execution of a logical quantum circuit, are essential components of quantum error correction. We seek to fully characterize a parity measurement in order to understand its error mechanisms and how to mitigate them. However, parity measurements admit complex error modes, including those found neither in quantum gates nor terminating measurements. We experimentally characterize a two-qubit mid-circuit parity measurement using quantum instrument gate set tomography (arXiv:2103.03008) on IBM Quantum hardware, modeling the parity check as a two-qubit quantum instrument; this allows us to both fully reconstruct the parity measurement's corresponding process matrices as well as detect the presence of non-Markovian errors introduced by the measurement.   

Characterizing Hybrid Quantum Algorithms for Quantum Performance Benchmarks

Hybrid quantum algorithms have emerged as potential candidates to gain computational advantage on Noisy Intermediatory-Scale Quantum (NISQ) Computers. Here we discuss two such algorithms used in Quantum Chemistry and Machine Learning: Variational Quantum Eigensolver (VQE) and Quantum Convolution Neural Networks (QCNN). We evaluate the performance of these algorithms in the context of an advanced benchmarking framework for quantum computers designed to estimate resource utilization and calculate application-specific metrics. This allows us to examine the trade-off between run-time execution performance and the quality of solutions for iterative hybrid quantum-classical applications and also highlight the limitations of the algorithms. The benchmarking suite can be executed on simulators as well as existing hardware and is an enhancement to the QED-C's Application-Oriented Benchmark suite.   

Benchmarking quantum processor quality in the utility era

As quantum processors enter the era of utility, it becomes increasingly important to develop benchmarking suites capable of addressing quality, speed, and scale. With scale increasing rapidly for utility, quality benchmarks are needed that can be run at large scales. In this talk, we report developments towards such benchmarks. We present a device benchmark that captures the generic performance of a quantum processor and is scalable to large systems while still capturing important multi-qubit effects like cross-talk. Further, we show in what sense Clifford circuits can be representative of generic circuit performance, and how this can be extended to benchmark applications and error mitigation schemes.   

Optimal twirling depth for classical shadows in the presence of noise.

The classical shadows protocol represents an efficient strategy for estimating properties of an unknown state ρ using a finite number of copies and measurements. In its original form, it involves twirling the state with unitaries randomly selected from a fixed ensemble and measuring the twirled state in a predetermined basis. To compute local properties of the system, it has been demonstrated that optimal sample complexity (the minimal number of required copies) is remarkably achieved when unitaries are drawn from shallow-depth circuits composed of local entangling gates, as opposed to purely local (zero-depth) or global twirling (infinite-depth) ensembles.

In this presentation, I will discuss an improvement of these ideas by considering the sample complexity as a function of the circuit's depth, in the presence of noise. Noise is bound to be present in any experimental implementation of such shallow-depth circuits, which has important implications for determining the optimal twirling ensemble. Under fairly general conditions, I will: i) show that any single-site noise can be accounted for using a depolarizing noise channel with an appropriate damping parameter, f; ii) discuss thresholds f_th at which optimal twirling reduces to local twirling for arbitrary operators; iii) conduct a similar analysis for n^th-order Renyi entropies (where n is greater than or equal to 2); and iv) provide a meaningful upper bound, t_max , on the optimal circuit depth for any finite noise strength f. This upper bound applies to all operators and entanglement entropy measurements. These thresholds strongly constrain the search for optimal strategies to implement the classical shadows protocol and can be easily tailored to the experimental system at hand.   

Characterizing noise in QEC circuits

Quantum error correction (QEC) is essential for fault-tolerant quantum computing. QEC circuits protect quantum information from the effects of noise by encoding it across multiple physical qubits. Knowledge of the relevant characteristics of the noise that exists in devices while they run candidate QEC circuits can potentially enable the design of more efficient and reliable circuits for particular devices. For instance, knowldedge of bias, error spread, and possible error correlations can lead to circuits specifically targeted at correcting such errors as well as tailoring decoders designed for specific devices. Fast and efficient characterization also allows for verification and tailoring of error mitigation techniques, such as dynamic decoupling. I will discuss techniques for efficient characterisation of such noise, both at a holistic circuit level and at a phenomonological level, including data obtained from utilising such techniques on devices. Finally, the scale of data returned by these modern characterization techniques is such that we are rapidly approaching the stage where it will soon be unrealistic to attempt to analyse all the data obtained. I will discuss efficient methods of representing the data through scalable models and discuss how such models can be used in the push towards designing more efficient and reliable QEC circuits.   

Time-resolved shadow tomography of open quantum systems

Shadow tomography is a powerful and resource-frugal characterization technique which permits the estimation of a set of expectation values of an arbitrary quantum state using a number of measurements that scales only logarithmically in the size of the observable set. Allowing the state in question to undergo general non-unitary evolution, we leverage shadow tomography to resolve the time-dependence of this observable set and thereby efficiently estimate parameters of the open system dynamics via compressed sensing.   

Predicting many state properties with robust shallow circuit shadow tomography

Efficient prediction of many quantum state properties is crucial for quantum information processing. Through the use of randomized measurements and shallow circuits, classical shadow tomography emerges as a highly efficient, promising approach compatible with near-term quantum processors. This work presents the Robust Shallow Shadow (RSS) method, designed to operate effectively mitigate correlated noise, and provides a theoretical analysis of RSS behavior within the shallow-circuit region. We further illustrate the efficacy of RSS by demonstrating its performance using superconducting quantum processors.   

Efficiently estimating observables of varying locality using tensor-network-inspired classical shadows

Classical shadow tomography is a powerful randomized measurement technique for estimating $M$ state observables with $O(log M)$ measurements. While global Clifford randomized measurements are sample-optimal for some learning tasks, their implementation remains experimentally inaccessible for large systems because they require a number of gates quadratic in the system size. We show how to recover some aspects of global Clifford scaling using far fewer gates with tensor-network-inspired classical shadows. We consider two implementations: projecting the state of interest into a random matrix product state (MPS) or a random multiscale entanglement renormalization ansatz (MERA) state. We present numerical and analytic evidence that, when estimating observables across a range of scales, these tensor network structures can achieve shadow norms (a figure of merit directly related to measurement sample complexity) with more favorable scaling than the best known bounds on existing shadow schemes. For example, the best-known scheme for learning k-local Pauli observables is shallow shadows, whose variance is upper bounded by $2.28^k$. Both of our implementations outperform this bound, and we provide a framework for implementing our sample-efficient measurements in neutral atom arrays. Our work brings the advantages of randomized measurement protocols closer to experimental realization and highlights the power of making randomized measurements at multiple scales.   

Neural-shadow quantum state tomography: applications for near-term quantum devices

Neural network quantum state is a classical ansatz that has been implemented successfully in reconstructing quantum states from measurement data. In this process, known as neural network quantum state tomography (NNQST), a neural network is trained using a cross-entropy loss function to get the amplitudes and relative phases of a pure quantum state. However, NNQST often has difficulty in determining the relative phases of a quantum state. In this talk, we propose an alternative neural network-based protocol, which we call neural-shadow quantum state tomography (NSQST). NSQST uses infidelity as a loss function and combines classical shadows with computational basis measurements via a pretraining procedure. Here, the infidelity loss function is efficiently estimated using classical shadows of the target state. We demonstrate that NSQST has an advantage over NNQST in learning the relative phases of target quantum states and offers noise robustness in the case of Clifford shadows. We further focus on the implementation and usefulness of this protocol in near-term quantum devices.    

Predicting Arbitrary State Properties from Single Hamiltonian Quench Dynamics

Extracting arbitrary state properties from analog quantum simulations presents a significant challenge due to the necessity of diverse basis measurements. Recent advancements in randomized measurement schemes have successfully reduced measurement sample complexity, yet they demand precise control over each qubit. In this work, we propose the Hamiltonian shadow protocol, which solely depends on quench dynamics with a single Hamiltonian, without any ancillary systems. We provide a theoretical guarantee that our protocol can unbiasedly predict arbitrary state properties. We also derive the sample complexity of this protocol and show it performs similarly to the classical shadow protocol. Hamiltonian shadow protocol does not require any sophisticated control and is universally applicable to various analog quantum systems, as illustrated through numerical demonstrations with Rydberg atom arrays under realistic parameter settings. The new protocol significantly broadens the application of randomized measurements for analog quantum simulators without precise control and ancillary systems.   

Stressing Out Modern Quantum Hardware: Performance Evaluation and Insights

Quantum hardware is progressing at a rapid pace and, alongside this progression, it is vital to challenge the

capabilities of these machines using functionally complex algorithms. Doing so provides direct insights into the

current capabilities of modern quantum hardware and where its breaking points lie. Stress testing is a technique

used to evaluate a system by giving it a computational load beyond its specified thresholds and identifying the

capacity under which it fails. We conduct a qualitative and quantitative evaluation of Quantinuum’s H1 ion-trap

device using a stress test-based protocol. Specifically, we utilize the quantum machine learning (QML) algorithm,

the Quantum Neuron Born Machine, as the computationally intensive load for the device. Then, we linearly

scale the number of repeat-until-success sub-routines within the algorithm to determine the load under which the

hardware fails and where the failure occurred within the quantum stack. Using this proposed method, we (a) assess

the hardware’s capacity to manage a computationally intensive QML algorithm and (b) evaluate the hardware

performance as the functional complexity of the algorithm is scaled. Alongside the quantitative performance

results, we provide a qualitative discussion based on the insights obtained from conducting the stress test with

the QNBM - i.e. we put forth the specific roadblocks that appear throughout the quantum computing stack when

scaling the functional complexity of the algorithm.