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This paper is an expanded and more detailed version of our recent work in which the Operator Quantum Error Correction formalism was introduced. This is a new scheme for the error correction of quantum operations that incorporates the known…
When the environmental disturbace to a quantum system has a wavelength much larger than the system size, all qubits localized within a small area are under action of the same error operators. Noiseless subsystem and decoherence free…
Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and…
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,…
We develop a family of perfect quantum error correcting codes that correct for phase errors that arise on any qubit, at any time, during a perfect state transfer experiment. These ensure that we find the optimal operating regime for…
Dynamical decoupling (DD) is a widely-used quantum control technique that takes advantage of temporal symmetries in order to partially suppress quantum errors without the need resource-intensive error detection and correction protocols.…
Today's most advanced ion trap quantum computers have significant overhead due to the need for dual-species operation. Looking ahead, logical qubit register sizes will be limited by the encoding rate needed to correct generic Pauli errors.…
We demonstrate that continuous-variable quantum error correction based on Gaussian ancilla states and Gaussian operations (for encoding, syndrome extraction, and recovery) can be very useful to suppress the effect of non-Gaussian error…
Two initially correlated coherent states, each interacting with its own independent dissipative environment exhibit a sudden transition from classical to quantum decoherence. This change in the dynamics is a turning point in the…
We investigate a family of fault-tolerant quantum error correction schemes based on the concatenation of small error detection or error correction codes with the three-dimensional cluster state. We propose fault-tolerant state preparation…
We present a theoretical framework for state-adaptive quantum error correction that bridges the gap between quantum computing and error correction paradigms. By incorporating knowledge of quantum states into the error correction process, we…
Coherence in an open quantum system is degraded through its interaction with a bath. This decoherence can be avoided by restricting the dynamics of the system to special decoherence-free subspaces. These subspaces are usually constructed…
Quantum error correction is capable of digitizing quantum noise and increasing the robustness of qubits. Typically, error correction is designed with the target of eliminating all errors - making an error so unlikely it can be assumed that…
In quantum error correction, information is encoded in a high-dimensional system to protect it from the environment. A crucial step is to use natural, low-weight operations with an ancilla to extract information about errors without causing…
Encoding quantum information onto bosonic systems is a promising route to quantum error correction. In a cat code, this encoding relies on the confinement of the system's dynamics onto the two-dimensional manifold spanned by Schr\"odinger…
Error correction is essential for modern computing systems, enabling information to be processed accurately even in the presence of noise. Here, we demonstrate a new approach which exploits an error correcting phase that emerges in a system…
Active stabilisation of a quantum system is the active suppression of noise (such as decoherence) in the system, without disrupting its unitary evolution. Quantum error correction suggests the possibility of achieving this, but only if the…
In continuous-variable quantum computing, autonomous quantum error correction (QEC) can dissipatively steer a noisy quantum state into a target state or manifold, enabling robust quantum information processing without explicit syndrome…
We present a unified approach to quantum error correction, called operator quantum error correction. This scheme relies on a generalized notion of noiseless subsystems that is not restricted to the commutant of the interaction algebra. We…
A fundamental challenge for quantum information processing is reducing the impact of environmentally-induced errors. Quantum error detection (QED) provides one approach to handling such errors, in which errors are rejected when they are…