To advance the field of quantum computing, quantum error correction codes are essential to preserve and elaborate quantum information. Among the various candidates for near-term quantum error correction, surface codes stand out due to their structure and the availability of efficient decoding strategies. Performance assessments of these codes have been focused mainly on the qubit error probability, overlooking the impact of decoherence over time when decoders with different latencies are employed. In this paper, we present a simple framework to address this limitation, deriving performance metrics that incorporate the time complexity of the decoding process.
To advance the field of quantum computing, quantum error correction codes are essential to preserve and elaborate quantum information. Among the various candidates for near-term quantum error correction, surface codes stand out due to their structure and the availability of efficient decoding strategies. Performance assessments of these codes have been focused mainly on the qubit error probability, overlooking the impact of decoherence over time when decoders with different latencies are employed. In this paper, we present a simple framework to address this limitation, deriving performance metrics that incorporate the time complexity of the decoding process.
Quantum technologies have the potential to solve certain computationally hard problems with polynomial or super-polynomial speedups when compared to classical methods. Unfortunately, the unstable nature of quantum information makes it prone to errors. For this reason, quantum error correction is an invaluable tool to make quantum information reliable and enable the ultimate goal of fault-tolerant quantum computing. Surface codes currently stand as the most promising candidates to build near term error corrected qubits given their two-dimensional architecture, the requirement of only local operations, and high tolerance to quantum noise. Decoding algorithms are an integral component of any error correction scheme, as they are tasked with producing accurate estimates of the errors that affect quantum information, so that they can subsequently be corrected. A critical aspect of decoding algorithms is their speed, since the quantum state will suffer additional errors with the passage of time. This poses a connundrum, where decoding performance is improved at the expense of complexity and viceversa. In this review, a thorough discussion of state-of-the-art decoding algorithms for surface codes is provided. The target audience of this work are both readers with an introductory understanding of the field as well as those seeking to further their knowledge of the decoding paradigm of surface codes. We describe the core principles of these decoding methods as well as existing variants that show promise for improved results. In addition, both the decoding performance, in terms of error correction capability, and decoding complexity, are compared. A review of the existing software tools regarding surface codes decoding is also provided.
ABSTRACT Quantum computing can effectively solve certain specific problems that classical computing cannot address efficiently. However, due to the vulnerability of qubits to noise, quantum error‐correcting codes need to be introduced in the process of implementing quantum computing. Fault‐tolerant quantum computing is achieved through the encoding and decoding of qubits. There are various types of quantum error‐correcting codes, among which the surface code is favored by researchers for its simple topological structure, requirement of only local operations, and relatively high threshold. For quantum error‐correcting codes, corresponding decoders are necessary for decoding. Driven by the demand for fault‐tolerant quantum computing, the decoding of quantum error‐correcting codes must support real‐time functionality, which means there are specific requirements for the decoding speed of decoders. In this review, we focus on work related to real‐time decoding for the surface code, and presents recent advances in this field, particularly those that have been implemented on hardware platforms or show potential for implementation.
As the field of quantum computing moves towards the realization of Quantum Error Correction (QEC), an increasing amount of attention has been paid to the implementation of decoders-classical systems analyzing the state of error on the quantum device in real-time. However, today there is a lack of tools available to characterize and compare the performance of decoders. In this work, we address this need and introduce decoder-bench, a framework for benchmarking decoders on relevant QEC code traces. decoder-bench integrates with Stim, a high performance tool for analyzing stabilizer circuits, to create traces for a variety of QEC codes and fault-tolerant subroutines. We use decoder-bench to evaluate the accuracy and latency performance of multiple decoders for circuit-level simulations of color code memory experiments, bivariate-bicycle code memory experiments, surface code memory experiments, and surface code lattice surgery experiments.
Quantum computers require large-scale error correction codes to circumvent the limited fidelity of physical qubits. However, current error decoders are either not scalable to practical code sizes or cannot meet the strict real-time decoding requirements. This work presents a novel decoder for stabilizer error correction codes that exploits hyperdimensional computing to offer an efficient hardware implementation for large-scale codes, thus achieving low latency and high throughput. Next to a universal approach for generating the necessary hypervectors, an efficient method specific to surface codes is devised. In this very first implementation, the proposed decoder outclasses popular graph-based decoders for small surface codes with depolarizing noise and efficiently scales to large codes, thus representing both a suitable solution for near-term real-time error correction and a promising alternative for future large-scale codes.
Fault-tolerant quantum computing is essential for realizing the substantial computational speedups that quantum computing can bring, but it requires real-time error decoding with high performance. Speculative window decoding improves performance by reducing the time spent waiting for dependencies from prior decoding windows.
However, speculative decoders have only been evaluated under the regime of superconducting qubits with fast gate speeds, surface codes, and matching decoders. Since different quantum technologies can have slower gate speeds, we evaluate the performance of speculative decoding under slow gate speeds. We also examine its sensitivity to speculation accuracy, decoder latency, processor count, and workload parallelism, which can vary across different quantum error correction codes, decoders, and hardware platforms.
This work presents design principles for identifying when speculative decoding yields the greatest performance improvements. It also reveals the conditions under which non-speculative decoders outperform speculative decoders.
Radiation impacts are a current challenge with computing on superconducting-based quantum devices because they can lead to widespread correlated errors across the device. Such errors can be problematic for quantum error correction (QEC) codes, which are generally designed to correct independent errors. To address this, we have developed a computational model to simulate the effects of radiation impacts on QEC performance. This is achieved by building from recently developed models of quasiparticle density, mapping radiation-induced qubit error rates onto a quantum error channel and simulation of a simple surface code. We also provide a performance metric to quantify the resilience of a QEC code to radiation impacts. Additionally, we sweep various parameters of chip design to test mitigation strategies for improved QEC performance. Our model approach is holistic, allowing for modular performance testing of error mitigation strategies and chip and code designs.