Related papers: Fault-tolerant conversion between stabilizer codes…
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that…
Quantum error correction offers a promising path to suppress errors in quantum processors, but the resources required to protect logical operations from noise, especially non-Clifford operations, pose a substantial challenge to achieve…
Code switching is an established technique that facilitates a universal set of FT quantum gate operations by combining two QEC codes with complementary sets of gates, which each by themselves are easy to implement fault-tolerantly. In this…
We present a set of efficiently implementable logical multi-qubit gates in concatenated quantum error correction codes using parity qubits. In particular, we show how fault-tolerant high-weight rotation gates of arbitrary angle can be…
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…
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…
Hypergraph product codes are a class of quantum low density parity check (LDPC) codes discovered by Tillich and Z\'emor. These codes have a constant encoding rate and were recently shown to have a constant fault-tolerant error threshold.…
We propose a Clifford noise reduction (CliNR) scheme that provides a reduction of the logical error rate of Clifford circuit with lower overhead than error correction and without the exponential sampling overhead of error mitigation. CliNR…
We propose a systematic scheme for the construction of graphs associated with binary stabilizer codes. The scheme is characterized by three main steps: first, the stabilizer code is realized as a codeword-stabilized (CWS) quantum code;…
Quantum error correction is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation…
In quantum error correction using imperfect primitives, errors of high weight arising from a few faults are major concerns since they might not be correctable by the quantum error correcting code. Fortunately, some errors of different…
The preparation of a quantum state using a noisy quantum computer (gate noise strength $\delta$), will necessarily affect an O($\delta$)-fraction of the qubits, no matter which protocol is used. Here, we show that fault-tolerant quantum…
We introduce a family of scalable planar fault-tolerant circuits that implement logical non-Clifford operations on a 2D color code, such as a logical $T$ gate or a logical non-Pauli measurement that prepares a magic $|T\rangle$ state. The…
The construction of a quantum computer remains a fundamental scientific and technological challenge, in particular due to unavoidable noise. Quantum states and operations can be protected from errors using protocols for fault-tolerant…
Fault tolerance is widely regarded as indispensable for achieving scalable and reliable quantum computing. However, the spacetime overhead required for fault-tolerant quantum computating remains prohibitively large. A critical challenge…
We compare two different implementations of fault-tolerant entangling gates on logical qubits. In one instance, a twelve-qubit trapped-ion quantum computer is used to implement a non-transversal logical CNOT gate between two five qubit…
Fault-tolerant complexes describe surface-code fault-tolerant protocols from a single geometric object. We first introduce fusion complexes that define a general family of fusion-based quantum computing (FBQC) fault-tolerant quantum…
Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored…
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…
Stabilizer codes form an important class of quantum error correcting codes which have an elegant theory, efficient error detection, and many known examples. Constructing stabilizer codes of length $n$ is equivalent to constructing subspaces…