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IEEE International Conference on Quantum Computing and Engineering (QCE)

A Heuristic Error Analysis Framework for Error Bottleneck Identification in Gate-Based Quantum Algorithms

Anika Zaman, Hiu Yung Wong

Published Sep 15, 2024• 1 citation
Publisher

Abstract

In this work, we present an automatic Python framework designed to perform heuristic error analysis of gate-based model algorithms running on a given quantum computer, to identify the source, the nature, and the bottleneck of errors. The information will allow quantum hardware-algorithm co-optimization. This is particularly useful for novel algorithms and hardware. By analyzing the relative contribution of the gate error, propagation error, bit-flip error, and measurement error at each node, one can then use the information to optimize the circuit in terms of the choice of gates and physical qubits. Since it is a model based on the probability of a state being measured, it cannot capture the crossterms and interference. However, it still can be used to deduce the node/stage that has a big error due to failure in interference. In this paper, the Harrow-Hassidim-Lloyd (HHL) quantum algorithm running on the IBM superconducting qubit platform is used as a demonstration of the framework. The bottleneck of the error in the HHL circuit is identified. It should also be noted that this framework can only be used for small problems because simulation is required on a classical computer.

DOI
10.1109/qce60285.2024.10367

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In this work, we present an automatic Python framework designed to perform heuristic error analysis of gate-based model algorithms running on a given quantum computer, to identify the source, the nature, and the bottleneck of errors. The information will allow quantum hardware-algorithm co-optimization. This is particularly useful for novel algorithms and hardware. By analyzing the relative contribution of the gate error, propagation error, bit-flip error, and measurement error at each node, one can then use the information to optimize the circuit in terms of the choice of gates and physical qubits. Since it is a model based on the probability of a state being measured, it cannot capture the crossterms and interference. However, it still can be used to deduce the node/stage that has a big error due to failure in interference. In this paper, the Harrow-Hassidim-Lloyd (HHL) quantum algorithm running on the IBM superconducting qubit platform is used as a demonstration of the framework. The bottleneck of the error in the HHL circuit is identified. It should also be noted that this framework can only be used for small problems because simulation is required on a classical computer.
In this work, we present a Python framework designed to demonstrate various error types within quantum circuits through the utilization of probabilistic data obtained from quantum computers. The framework serves as a valuable tool for monitoring and mitigating errors across all stages of quantum circuits involving multiple qubits and gates. Leveraging the Harrow-Hassidim-Lloyd (HHL) quantum circuit, we conduct an analysis of errors on an IBM quantum computer and subsequently optimize the circuit. The paper introduces an automated methodology for computing single bit-flip errors and propagation errors, and gate errors offering insights into opportunities for mitigating errors in the context of the HHL quantum circuit.
In this paper, we study the error propagation and generation in the Harrow-Hassidim-Lloyd (HHL) quantum algorithm runs on IBM-Q hardware with the help of a MATLAB simulator. HHL is a quantum algorithm that can provide exponential speedup over the fastest classical algorithm (conjugate gradient method) in solving systems of linear equations (SLE). However, without error correction, it cannot give correct results even in a 2-variable system due to its complexity. In this study, an HHL quantum circuit for a 2-variable SLE is implemented in IBM-Q and the error is extracted after each stage of the circuit and compared to a MATLAB simulator. We identified three major sources of errors, namely single-qubit flipping, gate infidelity, and error propagation. We also found that at the ancillary bit rotation stage, the error becomes large but the encoded solution still has high fidelity. However, the solution is mostly lost after the inverse quantum phase estimation which is necessary to extract the solution efficiently. Therefore, it is suggested that error correction resources, if limited, should be added to the second half of the circuit.
The development of quantum computers requires not only experimental advances, but also theoretical efforts to tackle the bottlenecks and identify potential applications. This thesis addresses some essential elements in each stage of the development of quantum computers, from the currently available hardware to the long-term devices. The critical factor that hinders the quantum hardware from performing perfect operations is the presence of noise, however, it can be overcome by error correction codes. We first consider a large-scale quantum processor with asymmetrical noise and preferably a modular structure. By concatenating the surface code with an error-detecting code, and utilising the information from detection with a customised decoder, we find very high thresholds for the designed devices. The second topic is small error correction codes which are more realistic to be implemented in the near future. A measure `integrity' is introduced to benchmark the performance of quantum memories to demonstrate beneficial error correction, associated with four milestones. We show integrity is closely related with other commonly-used measures and can be easily assessed by experimentalists. This framework is then studied in detail in the context of an ion-trap quantum device implemented with the seven qubit code. We present a protocol based on detailed sequences of crystal-reconfiguration operations and stabiliser mappings to perform a full error correction cycle. Realistic error models and parameters from reported works are also given. While experimental efforts continue to battle against the noise, some hybrid quantum-classical algorithms have been developed to be implemented on the near-term noisy devices. The variational algorithm is one of the hybrid algorithms that have been widely applied to simulations of condensed matter physics and quantum chemistry. In the next chapter, we introduce a variational quantum compiler to automatically search for the encoding circuits of small error correction codes. By tailoring the ansatz to optimise the circuit for particular hardware systems, we show some novel circuits discovered with the compiler. The final chapter applies the variational algorithm to solve linear algebra problems including linear systems of equations and matrix-vector multiplications. We show that the linear algebra problems can be solved with near-term devices, with circuit depth linear to the condition number and super-linear to the number of qubits.
Large-scale quantum computation requires a reliable assessment of the main sources of error in the implemented quantum gates. To this aim, we provide a learning-based framework that extracts the contribution of each physical error source to the infidelity of a series of gates, together with an uncertainty estimate for every contribution. Crucially, the uncertainties provided by the underlying Gaussian Process Regression serve as a diagnostic of the assumed noise model itself: if the physical model does not fully explain the experimental observations, the framework signals this instead of returning a falsely precise error budget. We demonstrate the proposed budget learning procedure on a pair of qubits in a transmon array architecture, where we compute the error budgets of the native single- and two-qubit gates. For this purpose, we have also developed an advanced noise model based on the first-principles understanding of the error processes in current superconducting processors, including complex (e.g. non-Markovian) error sources. While the single-qubit budgets are reconstructed with high confidence, the same diagnostic reveals that even this detailed noise model does not fully capture the error dynamics of a state-of-the-art two-qubit gate --- quantitative evidence that uncertainty-aware error budgeting is necessary for the characterization of current quantum hardware.
We introduce two variations of the quantum phase estimation algorithm: quantum shifted phase estimation and quantum punctured phase estimation. The shifted method employs a bit-string left shift to discard the most significant bit and focus on lower-order phase components, and the punctured method removes qubits corresponding to known phase bits, thereby streamlining the circuit. To demonstrate the effectiveness of the two variations, we integrate them into a hybrid quantum-classical implementation of the Harrow--Hassidim--Lloyd algorithm for solving linear systems. The hybrid method leverages both quantum and classical processors to identify and remove unnecessary qubits and gates. As a result, for small-scale linear systems, our method reduces qubit and gate counts relative to previous implementations, yielding lower overall circuit error rates on current hardware. Experimental demonstrations on IBM superconducting hardware confirm the error-mitigation effectiveness on small problem instances.
Due to the fragility of quantum mechanical effects, real quantum computers are plagued by frequent noise effects that cause errors during computations. Quantum error-correcting codes address this problem by providing means to identify and correct corresponding errors. However, most of the research on quantum error correction is theoretical or has been evaluated for specific hardware models only. Moreover, the development of corresponding codes and the evaluation of whether they indeed solve the problem for a particular hardware model, still often rests on tedious trial-and-error thus far. In this work, we propose an open-source framework that supports engineers and researchers in these tasks by automatically applying error-correcting codes for a given application followed by an automatic noise-aware quantum circuit simulation. Case studies showcase that this allows for a substantially more efficient implementation and evaluation of error-correcting codes.