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This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure…
Staircase codes, a new class of forward-error-correction (FEC) codes suitable for high-speed optical communications, are introduced. An ITU-T G.709-compatible staircase code with rate R=239/255 is proposed, and FPGA-based simulation results…
We exhibit a simple, systematic procedure for detecting and correcting errors using any of the recently reported quantum error-correcting codes. The procedure is shown explicitly for a code in which one qubit is mapped into five. The…
A fully fault-tolerant implementation of the quantum error-detecting Iceberg $[[2m, 2m-2, 2]]$ code applied to a Toffoli circuit achieved beyond-break-even error detection on a leading trapped-ion quantum computer, where the effect of…
We consider linear codes over a field in which the error values are restricted to a subgroup of its unit group. This scenario captures Lee distance codes as well as codes over the Gaussian or Eisenstein integers. Codes correcting restricted…
Typically, fault-tolerant operations and code concatenation are reserved for quantum error correction due to their resource overhead. Here, we show that fault tolerant operations have a large impact on the performance of symmetry based…
Quantum error correction codes are usually designed to correct errors regardless of their physical origins. In large-scale devices, this is an essential feature. In smaller-scale devices, however, the main error sources are often…
When sending quantum information over a channel, we want to ensure that the message remains intact. Quantum error correction and quantum authentication both aim to protect (quantum) information, but approach this task from two very…
Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high…
For high-speed quantum key distribution systems, error reconciliation is often the bottleneck affecting system performance. By exchanging common information through a public channel, the identical key can be generated on both communicating…
A successful quantum error correction protocol would allow quantum computers to run algorithms without suffering from the effects of noise. However, fully fault-tolerant quantum error correction is too resource intensive for existing…
We present an algorithm for finding sparse solutions of the system of linear equations $\Phi\mathbf{x}=\mathbf{y}$ with rectangular matrices $\Phi$ of size $n\times N$, where $n<N$, when measurement vector $\mathbf{y}$ is corrupted by a…
Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high…
Bosonic quantum error-correcting codes offer a viable direction towards reducing the hardware overhead required for fault-tolerant quantum information processing. A broad class of bosonic codes, namely rotation-symmetric codes, can be…
We consider the impact of the unitary averaging framework on single and two-mode linear optical gates. We demonstrate that this allows a trade-off between the probability of success and gate fidelity, with perfect fidelity gates being…
Quantum error correction is important to quantum information processing, which allows us to reliably process information encoded in quantum error correction codes. Efficient quantum error correction benefits from the knowledge of error…
We propose a scalable trapped-ion quantum-computing architecture that efficiently incorporates quantum error correction. The chip design exploits orthogonal qubit connectivity by assigning horizontal trap regions to transversal logical…
The use of reconfigurable computing, and FPGAs in particular, to accelerate computational kernels has the potential to be of great benefit to scientific codes and the HPC community in general. However, whilst recent advanced in FPGA tooling…
Orthogonal Fractional Factorial Designs and in particular Orthogonal Arrays are frequently used in many fields of application, including medicine, engineering and agriculture. In this paper we present a methodology and an algorithm to find…