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Physical Review A

Scalable quantum computing in the presence of large detected-error rates

Emanuel H. Knill

Published Apr 14, 2005• 138 citations
Publisher

Abstract

The theoretically tolerable erasure error rate for scalable quantum computing is shown to be well above 0.1, given standard scalability assumptions. This bound is obtained by implementing computations with generic stabilizer code teleportation steps that combine the necessary operations with error correction. An interesting consequence of the technique is that the only errors that affect the maximum tolerable error rate are storage and Bell measurement errors. If storage errors are negligible, then any detected Bell measurement error below is permissible. For practical computation with high detected error rates, the implementation overheads need to be improved.

DOI
10.1103/physreva.71.042322

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The theoretically tolerable erasure error rate for scalable quantum computing is shown to be well above 0.1, given standard scalability assumptions. This bound is obtained by implementing computations with generic stabilizer code teleportation steps that combine the necessary operations with error correction. An interesting consequence of the technique is that the only errors that affect the maximum tolerable error rate are storage and Bell measurement errors. If storage errors are negligible, then any detected Bell measurement error below is permissible. For practical computation with high detected error rates, the implementation overheads need to be improved.
The tolerable erasure error rate for scalable quantum computation is shown to be at least 0.292, given standard scalability assumptions. This bound is obtained by implementing computations with generic stabilizer code teleportation steps that combine the necessary operations with error correction. An interesting consequence of the technique is that the only errors that affect the maximum tolerable error rate are storage and Bell measurement errors. If storage errors are negligible, then any detected Bell measurement error below 1/2 is permissible. Another consequence of the technique is that the maximum tolerable depolarizing error rate is dominated by how well one can prepare the required encoded states. For example, if storage and Bell measurement errors are relatively small, then independent depolarizing errors with error rate close to 0.1 per qubit are tolerable in the prepared states. The implementation overhead is dominated by the efficiency with which the required encoded states can be prepared. At present, this efficiency is very low, particularly for error rates close to the maximum tolerable ones.
Quantum computing stands at the precipice of revolutionizing numerous fields, yet its widespread practical application is obstructed by high error rates, far exceeding those encountered in classical computing. For quantum computers to become viable, these error rates must be significantly reduced, which is a critical challenge in the field. This paper explores the evolving landscape of quantum error correction, focusing on the topological code as a leading strategy for improving the fidelity of quantum computations. topological codes utilize a two-dimensional array of qubits and stabilizer operations to detect and correct quantum errors, offering robust scalability for large-scale quantum systems. The theoretical foundations of topological codes are examined along with their implementation challenges and recent advancements in decoding algorithms. Additionally, stabilizer codes are analyzed and their synergistic role in enhancing quantum error correction schemes. By addressing both theoretical concepts and practical considerations, this study provides insights into overcoming quantum error correction obstacles, moving closer to reliable, fault-tolerant quantum computing systems. The paper also highlights emerging techniques that may shape the future of quantum computing reliability.
We suggest a technique for constructing lower (existence) bounds for the fault-tolerant threshold to scalable quantum computation applicable to degenerate quantum codes with sublinear distance scaling. We give explicit analytic expressions combining probabilities of erasures, depolarizing errors, and phenomenological syndrome measurement errors for quantum low-density parity-check codes with logarithmic or larger distances. These threshold estimates are parametrically better than the existing analytical bound based on percolation.
Fault tolerance is essential for scalable quantum technologies and is enabled by quantum error-correction codes. Bell-state measurements (BSMs) are a fundamental building block for modern quantum technologies such as measurement-based quantum computation and fusion-based quantum computation, as well as quantum networks. Therefore, performing BSMs on error-corrected qubits is a necessary step for achieving fault tolerance in these applications. In this work, we realise a logical BSM using linear optics, based on a two-qubit repetition code, an instance of a quantum parity code that allows detection of bit-flip errors, and experimentally achieve a mean success probability of (70.8 +/- 0.4)%. While standard linear-optical BSMs are fundamentally limited to a maximum success probability of 50%, this increased success probability enables higher secure key rates in quantum communication and facilitates the generation of large graph states for quantum computation. Since fault-tolerant schemes require error-correction codes regardless, this improvement comes at no additional resource overhead. Our results demonstrate that error-correction codes can be used to surpass the linear-optics limit of BSMs, which is an important step towards practical, fault-tolerant, and scalable photonic quantum technologies.
This paper investigates the design and implementation of a fault-tolerant error correction coding scheme for quantum computing, leveraging the inherent robustness of topological quantum computing. The core concept involves constructing a quantum circuit with topological correction properties, employing an error-correcting code to detect and rectify errors within qubits, and utilizing topological quantum entanglement for redundant encoding, thereby enhancing the stability of quantum states. Unlike conventional quantum computing approaches that rely on multiple measurements for error correction, this method offers a more efficient solution by exploiting the topological protection afforded by exotic states of matter. The proposed scheme aims to significantly improve the reliability and scalability of quantum computation. We present a framework for designing such codes and discuss key challenges and potential advancements in this field. The theoretical analysis focuses on the encoding and decoding processes, quantifying the overhead associated with redundancy and evaluating the performance of the scheme in mitigating various types of quantum errors. ---
The threshold theorem indicates that if errors are all local and their rates are below a certain threshold, it is possible to implement large scale quantum computation with arbitrarily small error based on active quantum error correction (QEC). However, most fault-tolerant quantum computation (FTQC) schemes require enormous overhead to achieve this rate by increasing either the concatenation levels for concatenated codes or the distance (hence the size) for topological codes. As a result, a logical qubit is usually encoded in more than thousands of physical qubits, even when the error rate is below the threshold. In this thesis, we try to reduce the resource overhead of FTQC. We first study a quantum computation scheme using clouds of atoms trapped on atomic chips. It suggests that this scheme is robust to noise to some extent and has potential to be scalable. Secondly, we propose a FTQC scheme of encoding many logical qubits into large code blocks. The error performance of such scheme is numerically studied. Preparation of various ancilla states necessary for computation is also explored. Thirdly, we explore the idea of introducing energy gap to suppress thermal noise on each qubit. We show that fault-tolerant holonomic quantum computation (HQC) can be implemented in stabilizer codes with the existence of such energy protection. Especially, we studied fault-tolerant HQC in surface codes in detail. This scheme opens the possibility for self-correcting quantum computation in 2D lattice.