Related papers: Three-dimensional color code thresholds via statis…
We study the performance of distance-three surface code layouts under realistic multi-parameter noise models. We first calculate their thresholds under depolarizing noise. We then compare a Pauli-twirl approximation of amplitude and phase…
Continuous quantum error correction has been found to have certain advantages over discrete quantum error correction, such as a reduction in hardware resources and the elimination of error mechanisms introduced by having entangling gates…
Motivated by limitations and capabilities of neutral atom qubits, we examine whether measurement-free error correction can produce practical error thresholds. We show that this can be achieved by extracting redundant syndrome information,…
Qudits can be described by a state vector in a $q$-dimensional Hilbert space, enabling a more extensive encoding and manipulation of information compared to qubits. This implies that conducting fault-tolerant quantum computations using…
We introduce a new topological quantum code, the three-dimensional subsystem toric code (3D STC), which is a generalization of the stabilizer toric code. The 3D STC can be realized by measuring geometrically-local parity checks of weight at…
Knill demonstrated a fault-tolerant quantum computation scheme based on concatenated error-detecting codes and postselection with a simulated error threshold of 3% over the depolarizing channel. %We design a two-dimensional architecture for…
Quantum computers promise to solve problems that are intractable for classical computers, but qubits are vulnerable to many sources of error, limiting the depth of the circuits that can be reliably executed on today's quantum hardware.…
Quantum data is susceptible to decoherence induced by the environment and to errors in the hardware processing it. A future fault-tolerant quantum computer will use quantum error correction (QEC) to actively protect against both. In the…
Quantum error correcting codes have a distance parameter, conveying the minimum number of single spin errors that could cause error correction to fail. However, the success thresholds of finite per-qubit error rate that have been proven for…
Mapping quantum error correcting codes to classical disordered statistical mechanics models and studying the phase diagram of the latter has proven a powerful tool to study the fundamental error robustness and associated critical error…
The error correcting capabilities of the Calderbank-Shor-Steane [[7,1,3]] quantum code, together with a fault-tolerant syndrome extraction by means of several ancilla states, have been numerically studied. A simple probability expression to…
Fault-tolerant quantum computation traditionally incurs substantial resource overhead, with both qubit and time overheads scaling polylogarithmically with the size of the computation. While prior work by Gottesman showed that constant qubit…
In this work, the efficient quantum error-correction protocol against the general independent noise is constructed with the three-qubit codes. The rules of concatenation are summarized according to the error-correcting capability of the…
Twists are defects that are used to encode and process quantum information in topological codes like surface and color codes. Color codes can host three basic types of twists viz., charge-permuting, color-permuting and domino twists. In…
Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and…
Current experiments are taking the first steps toward noise-resilient logical qubits. Crucially, a quantum computer must not merely store information, but also process it. A fault-tolerant computational procedure ensures that errors do not…
With fault-tolerant quantum computing (FTQC) on the horizon, it is critical to understand sources of logical error in plausible hardware implementations of quantum error-correcting codes (QECC). In this work, we consider logical error rates…
Mid-circuit measurements are a major bottleneck for superconducting quantum processors because they are slower and noisier than gates. Measurement-free quantum error correction (mfec) replaces repeated measurements and classical…
Quantum information theory has shown strong connections with classical statistical physics. For example, quantum error correcting codes like the surface and the color code present a tolerance to qubit loss that is related to the classical…
We analyze and study the effects of locality on the fault-tolerance threshold for quantum computation. We analytically estimate how the threshold will depend on a scale parameter r which estimates the scale-up in the size of the circuit due…