Related papers: Unitary application of the quantum error correctio…
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…
A universal set of quantum gates is constructed for the recently developed jump-error correcting quantum codes. These quantum codes are capable of correcting errors arising from the spontaneous decay of distinguishable qubits into…
By introducing an operator sum representation for arbitrary linear maps, we develop a generalized theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This theory…
We propose a single auxiliary-assisted purification-based framework for quantum error correction, capable of correcting errors that drive a system from its ground-state subspace into excited-state sectors. The protocol consists of a joint…
Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal…
Correcting errors is a vital but expensive component of fault tolerant quantum computation. Standard fault tolerant protocol assumes the implementation of error correction, via syndrome measurements and possible recovery operations, after…
Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensure certain simple form for the measurements involved in realizing an unambiguous unitary quantum…
We present a construction scheme for quantum error correcting codes. The basic ingredients are a graph and a finite abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph…
The discovery of quantum error correction has greatly improved the long-term prospects for quantum computing technology. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the…
Large-scale universal quantum computing requires the implementation of quantum error correction (QEC). While the implementation of QEC has already been demonstrated for quantum memories, reliable quantum computing requires also the…
In this paper we investigate the encoding of operator quantum error correcting codes i.e. subsystem codes. We show that encoding of subsystem codes can be reduced to encoding of a related stabilizer code making it possible to use all the…
This research extends quantum singular value transformation (QSVT) for general bounded operators embedded in unitary operators on possibly infinite-dimensional Hilbert spaces. Through in-depth mathematical exploration, we have achieved a…
The accurate identification of faulty hardware is a fundamental requirement for reliable quantum information processing. We address this problem in a quantum setting, where a series of $n$ devices is intended to apply the same unitary…
In this work, we present active and passive linear optical setups for error correction in quantum communication systems that employ polarization of single-photon and mesoscopic coherent states. Applications in quantum communication systems…
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…
Quantum error correction (QEC) is essential for quantum computers to perform useful algorithms, but large-scale fault-tolerant computation remains out of reach due to demanding requirements on operation fidelity and the number of…
Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit…
We consider a unitary transformation which maps any given state of an $n$-qubit quantum register into another one. This transformation has applications in the initialization of a quantum computer, and also in some quantum algorithms.…
The entanglement of formation gives a necessary and sufficient condition for the existence of a perfect quantum error correction procedure.
Reliable quantum information processing in the face of errors is a major fundamental and technological challenge. Quantum error correction protects quantum states by encoding a logical quantum bit (qubit) in multiple physical qubits. To be…