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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…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
Suppressing errors is the central challenge for useful quantum computing, requiring quantum error correction for large-scale processing. However, the overhead in the realization of error-corrected ``logical'' qubits, where information is…
In order to solve problems of practical importance, quantum computers will likely need to incorporate quantum error correction, where a logical qubit is redundantly encoded in many noisy physical qubits. The large physical-qubit overhead…
Generation of logical zero states encoded with a quantum error-correcting code is the first step for fault-tolerant quantum computation, but requires considerably large resource overheads in general. To reduce such overheads, we propose an…
The promise of quantum computers hinges on the ability to scale to large system sizes, e.g., to run quantum computations consisting of more than 100 million operations fault-tolerantly. This in turn requires suppressing errors to levels…
Quantum error correction, which utilizes logical qubits that are encoded as redundant multiple physical qubits to find and correct errors in physical qubits, is indispensable for practical quantum computing. Surface code is considered to be…
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…
Qudit toric codes are a natural higher-dimensional generalization of the well-studied qubit toric code. However standard methods for error correction of the qubit toric code are not applicable to them. Novel decoders are needed. In this…
Quantum error correction protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the…
Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an…
Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this…
Quantum error correction and fault-tolerance make it possible to perform quantum computations in the presence of imprecision and imperfections of realistic devices. An important question is to find the noise rate at which errors can be…
Fault-tolerant logical entangling gates are essential for scalable quantum computing, but are limited by the error rates and overheads of physical two-qubit gates and measurements. To address this limitation, we introduce phantom…
Fault-tolerant quantum computation critically depends on architectures uniting high encoding rates with physical implementability. Quantum low-density parity-check (qLDPC) codes, including bivariate bicycle (BB) codes, achieve dramatic…
Quantum circuits implementing fault-tolerant quantum error correction (QEC) for the three qubit bit-flip code and five-qubit code are studied. To describe the effect of noise, we apply a model based on a generalized effective Hamiltonian…
The surface code, with a simple modification, exhibits ultra-high error correction thresholds when the noise is biased towards dephasing. Here, we identify features of the surface code responsible for these ultra-high thresholds. We provide…
Universal quantum computers require fault-tolerant logical qudits, as qudits naturally align with the simulation of multi-level physical systems. Here, we present a general framework and working examples for encoding fault-tolerant logical…
A major obstacle towards realizing a practical quantum computer is the noise that arises due to system-environment interactions. While it is very well known that quantum error correction (QEC) provides a way to protect against errors that…
Quantum computers require error correction to achieve universal quantum computing. However, current decoding of quantum error-correcting codes relies on classical computation, which is slower than quantum operations in superconducting…