Related papers: Quantum Error Correction of Time-Correlated Errors
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard…
Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of error information--error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose the idea…
One of the main problems in quantum information systems is the presence of errors due to noise, and for this reason quantum error-correcting codes (QECCs) play a key role. While most of the known codes are designed for correcting generic…
We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result --…
Detecting mitigating and correcting errors in quantum control is among the most pertinent contemporary problems in quantum technologies. We consider three of the most common bosonic error correction codes -- the CLY, binomial and dual rail…
We propose a new method to autonomously correct for errors of a logical qubit induced by energy relaxation. This scheme encodes the logical qubit as a multi-component superposition of coherent states in a harmonic oscillator, more…
Experimental realization of automated error correction is demonstrated through IBM Quantum Experience for Bell and GHZ states using a measurement based approach upon ancilla qubits. The measurement automatically activates error correcting…
Using nuclear magnetic resonance techniques, we experimentally investigated the effects of applying a two bit phase error detection code to preserve quantum information in nuclear spin systems. Input states were stored with and without…
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…
In quantum error-correcting code (QECC), many quantum operations and measurements are necessary to correct errors in logical qubits. In the stabilizer formalism, which is widely used in QECC, generators $G_i (i=1,2,..)$ consist of multiples…
Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to…
Fault tolerant quantum computing relies on the ability to detect and correct errors, which in quantum error correction codes is typically achieved by projectively measuring multi-qubit parity operators and by conditioning operations on the…
Designs for quantum error correction depend strongly on the connectivity of the qubits. For solid state qubits, the most straightforward approach is to have connectivity constrained to a planar graph. Practical considerations may also…
Topological stabilizer codes with different spatial dimensions have complementary properties. Here I show that the spatial dimension can be switched using gauge fixing. Combining 2D and 3D gauge color codes in a 3D qubit lattice,…
Qubit loss is a major source of error in quantum computation, as it invalidates the algebraic structure of the standard stabilizer formalism for quantum error-correcting codes. On the one hand, it complicates decoding; on the other hand, it…
Methods to control errors will be essential for quantum information processing. It is widely believed that fault-tolerant quantum error correction is the leading contender to achieve this goal. Although the theory of fault-tolerant quantum…
We present a full quantum error correcting procedure with the semion code: an off-shell extension of the double semion model. We construct open strings operators that recover the quantum memory from arbitrary errors and closed string…
Based on the group structure of a unitary Lie algebra, a scheme is provided to systematically and exhaustively generate quantum error correction codes, including the additive and nonadditive codes. The syndromes in the process of…
We propose a method for applying the quantum error-correction method for errors that occur during quantum gates. Using a perturbation treatment of the noise that allows us to separate it from the ideal evolution of the quantum gate, we…
The error correcting capabilities of the Calderbank-Shor-Steane [[7,1,3]] quantum code, together with a fault-tolerant syndrome extraction by means of several ancilla states, have been numerically studied. A simple probability expression to…