Related papers: Quantum error correction under numerically exact o…
It is a standard result in the theory of quantum error-correcting codes that no code of length n can fix more than n/4 arbitrary errors, regardless of the dimension of the coding and encoded Hilbert spaces. However, this bound only applies…
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not…
Fault tolerant protocol assumes the application of error correction after every quantum gate. However, correcting errors is costly in terms of time and number of qubits. Here we demonstrate that quantum error correction can be applied…
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…
A quantum error correction (QEC) code uses $N_{\rm c}$ quantum bits to construct one "logical" quantum bits of better quality than the original "physical" ones. QEC theory predicts that the failure probability $p_L$ of logical qubits…
The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting a single error per error correction cycle. Yet, time-correlated error are common for physical implementations of…
We analyze simple quantum error detection and quantum error correction protocols relevant to current experiments with superconducting qubits. We show that for qubits with energy relaxation the repetitive N-qubit codes cannot be used for…
We use density matrix simulations to study the performance of three distance three quantum error correcting codes in the context of the rare-earth-ion-doped crystal (RE) platform for quantum computing. We analyze pseudothresholds for these…
We develop a protocol for continuous operation of a quantum error correcting code for protection of coherent evolution due to an encoded Hamiltonian against environmental errors, using the three qubit bit flip code and bit flip errors as a…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
The demonstration of quantum error correction (QEC) is one of the most important milestones in the realization of fully-fledged quantum computers. Toward this, QEC experiments using the surface codes have recently been actively conducted.…
Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this…
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…
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…
Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…
Many physical systems considered promising qubit candidates are not, in fact, two-level systems. Such systems can leak out of the preferred computational states, leading to errors on any qubits that interact with leaked qubits. Without…
Realizing the potential of quantum computing will require achieving sufficiently low logical error rates. Many applications call for error rates in the $10^{-15}$ regime, but state-of-the-art quantum platforms typically have physical error…
Quantum error correcting codes have been shown to have the ability of making quantum information resilient against noise. Here we show that we can use quantum error correcting codes as diagnostics to characterise noise. The experiment is…
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…
Radiation impacts are a current challenge with computing on superconducting-based quantum devices because they can lead to widespread correlated errors across the device. Such errors can be problematic for quantum error correction (QEC)…