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Robustness and Performance Scaling of Large-Scale Quantum Computers with Faulty Gates

Yunseong Nam

Published Jan 1, 2016• 0 citations
Publisher

Abstract

This thesis presents an overview of my published work on streamlining and optimizing quantum processors. Complete, microscopic, quantum-gate–by–quantum-gate simulations of a variety of quantum circuits are implemented and executed on state-of-the-art multi-processor parallel computers. A host of analytical scaling formulas addressing the quality of quantum processors, e.g., in the presence of realistic gate errors and defects, are presented. These formulas reliably describe the practically interesting, large-number-of-qubit regime, inaccessible to simulations on classical computers. Much of the technical details may be found in my published articles, which appear in the Appendix. This thesis also presents the generic and specific directions into which my current investigations are headed. In addition, several preliminary results are presented and discussed.

DOI
10.14418/wes01.3.59

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This thesis presents an overview of my published work on streamlining and optimizing quantum processors. Complete, microscopic, quantum-gate–by–quantum-gate simulations of a variety of quantum circuits are implemented and executed on state-of-the-art multi-processor parallel computers. A host of analytical scaling formulas addressing the quality of quantum processors, e.g., in the presence of realistic gate errors and defects, are presented. These formulas reliably describe the practically interesting, large-number-of-qubit regime, inaccessible to simulations on classical computers. Much of the technical details may be found in my published articles, which appear in the Appendix. This thesis also presents the generic and specific directions into which my current investigations are headed. In addition, several preliminary results are presented and discussed.
Quantum computing promises to solve some problems that are intractable by classical computers. Several quantum processors based on different technologies and consisting of a few tens of noisy qubits have already been developed. However, qubits are fragile as they tend to decohere extremely quickly and quantum operations are faulty, making reliable computation very difficult. Moreover, quantum processors have hardware constraints such as limited qubit connectivity and shared classical control, making quantum algorithms not directly executable. This thesis focuses on some of the challenges of the implementation of quantum algorithms on near-termintermediate-scale and future large-scale quantum processors. More precisely, it investigates how to perform reliable quantum computation using fault-tolerant protocols and how to execute quantum algorithms on hardware-constrained processors using circuit-mapping techniques.
Understanding the performance of realistic noisy encoded circuits is an important task for the development of large-scale practical quantum computers. Specifically, the development of proposals for quantum computation must be well informed by both the qualities of the low-level physical system of choice, and the properties of the high-level quantum error correction and fault-tolerance schemes. Gaining insight into how a particular computation will play out on a physical system is in general a difficult problem, as the classical simulation of arbitrary noisy quantum circuits is inefficient. Nevertheless, important classes of noisy circuits can be simulated efficiently. Such simulations have led to numerical estimates of threshold errors rates and resource estimates in topological codes subject to efficiently simulable error models. \n \nThis thesis describes and analyzes a method that my collaborators and I have introduced for leveraging efficient simulation techniques to understand the performance of large quantum processors that are subject to errors lying outside of the efficient simulation algorithm's applicability. The idea is to approximate an arbitrary gate error with an error from the efficiently simulable set in a way that ``honestly'' represents the original error's ability to preserve or distort quantum information. After introducing and analyzing the individual gate approximation method, its utility as a means for estimating circuit performance is studied. In particular, the method is tested within the use-case for which it was originally conceived; understanding the performance of a hypothetical physical implementation of a quantum error-correction protocol. It is found that the method performs exactly as desired in all cases. That is, the circuits composed of the approximated error models honestly represent the circuits composed of the errors derived from the physical models.
State of the art quantum computing architectures are founded on the decision to use scalable but faulty quantum hardware in conjunction with an efficient error correcting code capable of tolerating high error rates. The promised effect of this decision is that the first large-scale practical quantum computer is within reach. Coming to grips with the strategy and the challenges of preparing reliable executions of an arbitrary quantum computation is not difficult. Moreover, the article explains why defects are good.
Removing a single logical gate from a classical information processor renders this processor useless. This is not so for a quantum information processor. A large number of quantum gates may be removed without significantly affecting the processor's performance. In this paper, focusing on the quantum Fourier transform (QFT) and quantum adder, we show even more: Even if most of its gates are eliminated and the remaining gates are selected from a randomly generated set, the QFT, one of the most useful quantum processors, and the quantum adder, one of the most basic building blocks of a universal quantum computer, still operate with satisfactory success probability, comparable to that of a quantum computer constructed with perfect gates. We support these conclusions by first laying out a general analytical framework and then deriving analytical scaling relations, which are in excellent agreement with our numerical simulations. The demonstrated robustness of the QFT and quantum adder, to the point where randomly generated quantum gates take the place of the exact gates, is an important boon for the construction of quantum computers, since it shows that stringent gate error tolerances do not have to be met to obtain satisfactory performance of the corresponding quantum processors. Our analytical techniques are powerful enough to generate asymptotic scaling laws for any gate defect model of quantum information processors and we illustrate this point by explicitly computing asymptotic analytical scaling formulas for several other defect models as well.
Quantum computing promises to revolutionize several scientific and technological domains through fundamentally new ways of processing information. Among its most compelling applications is digital quantum simulation, where quantum computers are used to replicate the behavior of other quantum systems. This could enable the study of problems that are otherwise intractable on classical computers, transforming fields such as quantum chemistry, condensed matter physics, and materials science. Despite this potential, realizations of practical quantum advantage for relevant problems are hindered by imperfections of current devices. This also affects quantum hardware based on superconducting circuits which is among the most advanced and scalable platforms. The envisaged long-term solution of fault-tolerant quantum computers that correct their own errors remains out of reach mainly due to the associated qubit number overhead. As a result, the field has developed strategies that combine quantum and classical resources, exploit hardware-native operations, and employ error mitigation techniques to extract meaningful results from noisy data. This doctoral thesis contributes to this broader effort by exploring methods for advancing quantum simulation across the full computational stack, including hardware-level innovations, refined techniques for noise modeling and error mitigation, and algorithmic improvements enabled by efficient measurement processing.
Quantum computing promises to address problems in simulation, optimization, and chemistry, but current hardware operates in the noisy intermediate-scale (NISQ) regime where coherence limits, gate imperfections, and readout errors restrict performance. Improving calibration and mitigating errors therefore remain essential. This thesis analyzes error reduction on superconducting transmon qubits through calibration, gate analysis, and circuit-level mitigation. It compares single-qubit amplitude calibration methods and analyzes two-qubit gates based on the cross-resonance interaction, identifying differences in precision, convergence, and performance. In addition, it develops Inverted-Circuit Zero-Noise-Extrapolation (IC-ZNE) which measures effective error strength using inverted circuits. Compared to standard ZNE, IC-ZNE achieves results closer to ideal values and reduces observable errors. Overall, the presented methods improve the reliability of near-term quantum processors.