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Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all known algorithms at constant rate require exponential time.…
We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This…
We propose a linear optics scheme with SPDC process to test the fault tolerance property of quantum error correction code. To transmit an unknown qubit robustly through the noisy channel, one may first encode it into a certain quantum error…
We present and analyze protocols for fault-tolerant quantum computing using color codes. We present circuit-level schemes for extracting the error syndrome of these codes fault-tolerantly. We further present an integer-program-based…
A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes, in which logical qubits are encoded by several physical qubits, enable…
Quantum error correction is a crucial technology for fault tolerant quantum computing. On superconducting platforms, hardware defects in large scale quantum processors can disrupt the regular lattice structure of topological codes and…
Quantum error correction is crucial for protecting quantum information against decoherence. Traditional codes like the surface code require substantial overhead, making them impractical for near-term, early fault-tolerant devices. We…
In adversarial settings, where attackers can deliberately and strategically corrupt quantum data, standard quantum error correction reaches its limits. It can only correct up to half the code distance and must output a unique answer.…
Fast, reliable logical operations are essential for realizing useful quantum computers. By redundantly encoding logical qubits into many physical qubits and using syndrome measurements to detect and correct errors, one can achieve low…
To unleash the potential of quantum computers, noise effects on qubits' performance must be carefully managed. The decoders responsible for diagnosing noise-induced computational errors must use resources efficiently to enable scaling to…
Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale…
Geometrically local quantum codes, which are error correction codes embedded in $\mathbb{R}^D$ with checks acting only on qubits within a fixed spatial distance, have garnered significant interest. Recently, it has been demonstrated how to…
Quantum error detection can produce unbiased expectation values that exponentially converge to noiseless results as the code distance is increased. Despite this, its performance as an error mitigation technique is relatively understudied on…
Dissipative quantum error correction (QEC) autonomously protects quantum information using engineered dissipation and offers a promising alternative to error correction via measurement and feedback. However, scalability remains a challenge,…
To avoid prohibitive overheads in performing fault-tolerant quantum computation, the decoding problem needs to be solved accurately and at speeds sufficient for fast feedback. Existing decoding systems fail to satisfy both of these…
This paper investigates quantum error correction schemes for fully-correlated noise channels on an $n$-qubit system, where error operators take the form $W^{\otimes n}$, with $W$ being an arbitrary $2\times 2$ unitary operator. In previous…
Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits,…
In this short review, I draw attention to new developments in the theory of fault tolerance in quantum computation that may give concrete direction to future work in the development of superconducting qubit systems. The basics of quantum…
Atom loss is a dominant error source in neutral-atom quantum processors, yet its correlated structure remains largely unexploited by existing quantum error correction decoders. We analyze the performance of the surface code equipped with…
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…