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.
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.
Quantum error correction codes are essential for fault-tolerant quantum computing. They are a method of detecting and correcting errors in a quantum computer by encoding logical qubits across multiple physical qubits. Several prominent error correction codes have been developed and larger and more complex codes are being developed continuously. However, evaluating the fault-tolerance of these larger codes is becoming exponentially more complicated. While conventional methods of proving and evaluating the fault-tolerance of these circuits have worked thus far, they are soon to be obsolete. The aim of this thesis is to develop a framework that automatically evaluates the fault-tolerance of a quantum error correction circuit across different hardware architectures. The framework works as follows: it takes a noiseless quantum error correction code; injects hardware-realistic noise into it; and evaluates the fault-tolerance of the resulting noisy circuit by estimating its logical error rate through Monte Carlo sampling. For the injection of hardware-realistic noise, this thesis considers noise stemming from five different quantum computing hardware architectures: superconducting qubits, neutral atoms, trapped ions, photonic qubits, and spin qubits. The noise model was constructed by extracting single-qubit gate, two-qubit gate and measurement error fidelities from current experimental literature. The noise model and circuit generation is implemented in Python, circuit representation and noise injection is executed in Stim and decoding and estimating the logical error rate is achieved through PyMatching. The framework is evaluated on the repetition code, the surface code, and the color code; the logical error rate is estimated across all five hardware architectures under the noise model; and the results are discussed in the context of hardware compatibility for the given codes.
The QCAD which has been technologically advanced during last few years to support basic transformations, simulating multi-dimensional quantum devices and circuits. It is most important to demonstrate the theoretical operation of quantum computer using the simulator. Besides of describing various noise models in terms of quantum gates, a direct support of quantum error correction codes. Using the quantum error correction codes, the effects of applying single bit or phase flip error to the quantum circuits are reported along with the error recovery method for different qubit codes. The results are generated using the QCAD simulator. A simulation model for evaluating single qubit error in the proposed quantum circuit is also given. The working software prototype of an extremely efficient quantum computer simulator which is an attractive and versatile tool for both research and education.
Recent advancements in quantum computing software are gradually increasing the scope and size of quantum programs being developed. At the same time, however, these larger programs provide more possibilities for functional errors that are harder to detect and resolve. Meanwhile, debugging tools that could aid developers in resolving these errors are still barely existent and far from what we take for granted in classical design automation and software engineering. As a result, even if one manages to identify the incorrect behavior of a developed quantum program, detecting and resolving the underlying errors in the program remains a time-consuming and tedious task. Moreover, the exponential growth of the state space in quantum programs makes the efficient manual investigation of errors radically difficult even for respectively simple algorithms, and almost impossible as the number of qubits increases. To address this problem, this work proposes a debugging framework, available as an open-source implementation at https://github.com/cda-tum/mqt-debugger. It assists developers in debugging errors in quantum programs, allowing them to efficiently identify the existence of errors and diagnose their causes. Users are given the ability to place assertions in the code that test for the correctness of a given algorithm and are evaluated using classical simulations of the underlying quantum program. Once an assertion fails, the proposed framework employs different diagnostic methods to point towards possible error causes. This way, the debugging workload for quantum programs is drastically reduced.
Quantum computing has demonstrated the potential to transform our world, with applications ranging from drug discovery to logistics. One of the largest problems standing in the way of practical quantum computers is the fragility of the quantum states that power them. This fragility inevitably leads to computational errors that require detection and correction. This review leverages peer-reviewed foundational papers published about quantum mechanics, quantum computing and error correction with emphasis on the most recently published research. It a ims to provide an overview of Quantum Error Correction (QEC) for those who have a grasp on the fundamentals of quantum computing and want to explore the gaps in knowledge, recent developments, and future research directions in QEC. Key challenges such as quantum noise, code distance, error threshold, and real-time decoders are presented. Core principles, and the current state of the art in QEC, explaining the strengths and weaknesses of each method, are discussed. The findings of published research in literature are showcased, encompassing the most recent developments. Noting the fascinating progress made in this time frame, it can be concluded that, with cautious optimism, we can expect the creation of QEC schemes capable of facilitating practical quantum computers in the future.
A mathematical model of computation is an idealized abstraction. We design algorithms and perform analysis on the assumption that the mathematical operations we specify will be carried out exactly, and without error. Physical devices that implement an abstract model of computation are imperfect and of limited precision. For example, when a digital circuit is implemented on a physical circuit board, unwanted electrical noise in the environment may cause components to behave differently than expected, and may cause voltage levels (bit-values) to change. These sources of error must be controlled or compensated for, or else the resulting loss of efficiency may reduce the power of the information-processing device. If individual steps in a computation succeed with probability p, then a computation involving t sequential steps will have a success probability that decreases exponentially as pt. Although it may be impossible to eliminate the sources of errors, we can devise schemes to allow us to recover from errors using a reasonable amount of additional resources. Many classical digital computing devices use error-correcting codes to perform detection of and recovery from errors. The theory of error-correcting codes is itself a mathematical abstraction, but it is one that explicitly accounts for errors introduced by the imperfection and imprecision of realistic devices. This theory has proven extremely effective in allowing engineers to build computing devices that are resilient against errors. Quantum computers are more susceptible to errors than classical digital computers, because quantum mechanical systems are more delicate and more difficult to control. If large-scale quantum computers are to be possible, a theory of quantum error correction is needed. The discovery of quantum error correction has given researchers confidence that realistic large-scale quantum computing devices can be built despite the presence of errors. We begin by considering fundamental concepts for error correction in a classical setting. We will focus on three of these concepts: (a) the characterization of the error model, (b) the introduction of redundancy through encoding, and (c) an error recovery procedure. We will later see that these concepts generalize quite naturally for quantum error correction.
Quantum Error Correction (QEC) is an essential field of research towards the realization of large-scale quantum computers. On the theoretical side, a lot of effort is put into designing error-correcting codes that protect quantum data from errors, which inevitably happen due to the noisy nature of quantum hardware and quantum bits (qubits). Protecting data with an error-correcting code necessitates means to recover the original data, given a potentially corrupted data set---a task referred to as decoding. It is vital that decoding algorithms can recover error-free states in an efficient manner. While theoretical properties of certain QEC methods have been extensively studied, good techniques to analyze their performance in practically more relevant settings is still a widely unexplored area. In this work, we propose a set of software tools that facilitate numerical experiments with so-called Quantum Low-Density Parity-Check codes (QLDPC codes)---a broad class of codes, some of which have recently been shown to be asymptotically good. Based on that, we provide an implementation of a general decoder for QLDPC codes. On top of that, we propose a highly efficient heuristic decoder that eliminates the runtime bottlenecks of the general QLDPC decoder while still maintaining comparable decoding performance. These tools eventually make it possible to confirm theoretical results around QLDPC codes in a more practical setting and showcase the value of software tools (in addition to theoretical considerations) for investigating codes for practical applications. The resulting tool, which is publicly available at https://github.com/cda-tum/qecc as part of the Munich Quantum Toolkit (MQT), is meant to provide a playground for the search for "practically good" quantum codes.