Related papers: Fault-tolerance of the [[8,1,3]] non-CSS code
We show that a simple modification of the surface code can exhibit an enormous gain in the error correction threshold for a noise model in which Pauli Z errors occur more frequently than X or Y errors. Such biased noise, where dephasing…
A critical component of any quantum error-correcting scheme is detection of errors by using an ancilla system. However, errors occurring in the ancilla can propagate onto the logical qubit, irreversibly corrupting the encoded information.…
Quantum error correction (QEC) with single-shot decoding enables reduction of errors after every single round of noisy stabilizer measurement, easing the time-overhead requirements for fault tolerance. Notably, several classes of quantum…
To ensure resilience against the unavoidable noise in quantum computers, quantum information needs to be encoded using an error-correcting code, and circuits must have a particular structure to be fault-tolerant. Compilation of…
Decoding stabilizer codes such as the surface and toric codes involves evaluating free-energy differences in a disordered statistical mechanics model, in which the randomness comes from the observed pattern of error syndromes. We study the…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
In this paper we introduce a general fault-tolerant quantum error correction protocol using flag circuits for measuring stabilizers of arbitrary distance codes. In addition to extending flag error correction beyond distance-three codes for…
Noise is an important factor that influences the reliability of information acquisition, transmission, processing, and storage. In order to suppress the inevitable noise effects, a fault-tolerant information processing approach via quantum…
Efficient decoding to estimate error locations from outcomes of syndrome measurement is the prerequisite for quantum error correction. Decoding in presence of circuit-level noise including measurement errors should be considered in case of…
Quantum error correcting code can diagnose potential errors and correct them based on measured outcomes by leveraging syndrome measurement. However, mid-circuit measurement has been technically challenging for early fault-tolerant quantum…
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…
We present a nonintrusive method for reliably estimating the noise level during quantum computation and quantum communication protected by quantum error-correcting codes. As preprocessing of quantum error correction, our scheme estimates…
Quantum error correction is essential for robust quantum information processing with noisy devices. As bosonic quantum systems play a crucial role in quantum sensing, communication, and computation, it is important to design error…
We prove an accuracy threshold theorem for fault-tolerant quantum computation based on error detection and postselection. Our proof provides a rigorous foundation for the scheme suggested by Knill, in which preparation circuits for ancilla…
We report new construction of nine-qubit error-correcting code, which introduces two new nine-qubit codes and one new three-qubit code. Because both the new two nine-qubit codes have the normal logical operators, as opposed to the…
Quantum computers will eventually reach a size at which quantum error correction becomes imperative. Quantum information can be protected from qubit imperfections and flawed control operations by encoding a single logical qubit in multiple…
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 -…
The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…
In this paper, we propose an efficient method to reduce error floors in quantum error correction using non-binary low-density parity-check (LDPC) codes. We identify and classify cycle structures in the parity-check matrix where estimated…
A classical coding across a block of logical qubits is presented. We characterize subgroups of the product stabilizer group on a block of logical qubits corresponding to dual codes of classical error correcting codes. We prove conditions on…