Related papers: Direct measurement of Bacon-Shor code stabilizers
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…
We consider realistic, multi-parameter error models and investigate the performance of the surface code for three possible fault-tolerant superconducting quantum computer architectures. We map amplitude and phase damping to a diagonal Pauli…
We present a fault-tolerant universal gate set consisting of Hadamard and controlled-controlled-Z (CCZ) on Bacon-Shor subsystem codes. Transversal non-Clifford gates on these codes are intriguing in that higher levels of the Clifford…
We present a scalable scheme for executing the error-correction cycle of a monolithic surface-code fabric composed of fast-flux-tuneable transmon qubits with nearest-neighbor coupling. An eight-qubit unit cell forms the basis for repeating…
The stabilizer code is the most general algebraic construction of quantum error-correcting codes proposed so far. A stabilizer code can be constructed from a self-orthogonal subspace of a symplectic space over a finite field. We propose a…
Quantum error correction is essential for bridging the gap between the error rates of physical devices and the extremely low logical error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting…
We study the performance of quantum error correction codes (QECCs) under the detection-induced coherent error due to the imperfectness of practical implementations of stabilizer measurements, after running a quantum circuit. Considering the…
The typical model for measurement noise in quantum error correction is to randomly flip the binary measurement outcome. In experiments, measurements yield much richer information - e.g., continuous current values, discrete photon counts -…
Quantum computation must be performed in a fault-tolerant manner to be realizable in practice. Recent progress has uncovered quantum error-correcting codes with sparse connectivity requirements and constant qubit overhead. Existing schemes…
We optimize fault-tolerant quantum error correction to reduce the number of syndrome bit measurements. Speeding up error correction will also speed up an encoded quantum computation, and should reduce its effective error rate. We give both…
Quantum data-syndrome (QDS) codes are a class of quantum error-correcting codes that protect against errors both on the data qubits and on the syndrome itself via redundant measurement of stabilizer group elements. One way to define a QDS…
Benchmarking the performance of quantum error correction codes in physical systems is crucial for achieving fault-tolerant quantum computing. Current methodologies, such as (shadow) tomography or direct fidelity estimation, fall short in…
We discuss single-shot decoding of quantum Calderbank-Shor-Steane codes with faulty syndrome measurements. We state the problem as a joint source-channel coding problem. By adding redundant rows to the code's parity-check matrix we obtain…
Flag-style fault-tolerance has become a linchpin in the realization of small fault-tolerant quantum-error correction experiments. The flag protocol's utility hinges on low qubit overhead, which is typically much smaller than in other…
In this work, we analyze a framework for constructing fault-tolerant measurement schedules of varying lengths by combining stabilizer generators, and prove results about the distance of such schedules by combining according to classical…
We analyze the performance of quantum stabilizer codes, one of the most important classes for practical implementations, on both symmetric and asymmetric quantum channels. To this aim, we first derive the weight enumerator (WE) for the…
We present an error correcting protocol that enhances the lifetime of stabilizer code based qubits which are susceptible to the creation of pairs of localized defects (due to string-like error operators) at finite temperature, such as the…
The Pauli stabilizer formalism is perhaps the most thoroughly studied means of procuring quantum error-correcting codes, whereby the code is obtained through commutative Pauli operators and ``stabilized'' by them. In this work we will show…
Current quantum technology is approaching the system sizes and fidelities required for quantum error correction. It is therefore important to determine exactly what is needed for proof-of-principle experiments, which will be the first major…
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…