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Continuous-time quantum error correction (CTQEC) is a technique for protecting quantum information against decoherence, where both the decoherence and error correction processes are considered continuous in time. Given any [[n,k,d]] quantum…
Quantum computers are highly vulnerable to noise, necessitating the use of error-correcting codes to protect stored data. Errors must be continuously corrected over time to counteract decoherence using appropriate decoders. Therefore, fast…
Executing quantum applications with quantum error correction (QEC) faces the gate non-universality problem imposed by the Eastin-Knill theorem. As one resource-time-efficient solution, code switching changes the encoding of logical qubits…
Usual scenarios of fault-tolerant computation are concerned with the fault-tolerant realization of quantum algorithms that compute classical functions, such as Shor's algorithm for factoring. In particular, this means that input and output…
The minimum weight perfect matching (MWPM) decoder is the standard decoding strategy for quantum surface codes. However, it suffers a harsh decrease in performance when subjected to biased or non-identical quantum noise. In this work, we…
The realization of fault-tolerant quantum computers hinges on the construction of high-speed, high-accuracy, real-time decoding systems. The persistent challenge lies in the fundamental trade-off between speed and accuracy: efforts to…
Holistic resource estimates are essential for guiding the development of fault-tolerant quantum algorithms and the computers they will run on. This is particularly true when we focus on highly-constrained early fault-tolerant devices. Many…
Recent experimental advances have made it possible to implement logical multi-qubit transversal gates on surface codes in a multitude of platforms. A transversal controlled-NOT (tCNOT) gate on two surface codes introduces correlated errors…
Noisy Intermediate-Scale Quantum Computing (NISQ) has dominated headlines in recent years, with the longer-term vision of Fault-Tolerant Quantum Computation (FTQC) offering significant potential albeit at currently intractable resource…
Real-time decoding is crucial for fault-tolerant quantum computing but likely requires specialized hardware such as field-programmable gate arrays (FPGAs), whose parallelism can alter relative algorithmic performance. We analyze…
QR decomposition is an essential operation for solving linear equations and obtaining least-squares solutions. In high-performance computing systems, large-scale parallel QR decomposition often faces node faults. We address this issue by…
Practical quantum computation heavily relies on the ability to perform quantum error correction in a fault-tolerant manner. Fault-tolerant encoding is a critical first step, and careful consideration of the error correction cycle that…
It is hard to achieve a theoretical quantum advantage on NISQ devices. Besides the attempts to reduce error using error mitigation and dynamical decoupling, small quantum error correction and fault-tolerant schemes that reduce the high…
Attaining fault tolerance while maintaining low overhead is one of the main challenges in a practical implementation of quantum circuits. One major technique that can overcome this problem is the flag technique, in which high-weight errors…
A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error…
This work addresses the open question of implementing fault-tolerant QRLCs with feasible computational overhead. We present a new decoder for quantum random linear codes (QRLCs) capable of dealing with imperfect decoding operations. A first…
Running quantum algorithms protected by quantum error correction requires a real time, classical decoder. To prevent the accumulation of a backlog, this decoder must process syndromes from the quantum device at a faster rate than they are…
For many decades, quantum chemical method development has been dominated by algorithms which involve increasingly complex series of tensor contractions over one-electron orbital spaces. Procedures for their derivation and implementation…
Code-switching offers a route to universal, fault-tolerant quantum computation by circumventing the limitation implied by the Eastin-Knill theorem against a universal transversal gate set within a single quantum code. Here, we present a…
Hybridizing different degrees of freedom or physical platforms potentially offers various advantages in building scalable quantum architectures. We here introduce a fault-tolerant hybrid quantum computation by taking the advantages of both…