Related papers: Codeword Stabilized Codes from m-Uniform Graph Sta…
Quantum error correction is the art of protecting fragile quantum information through suitable encoding and active interventions. After encoding $k$ logical qubits into $n>k$ physical qubits using a stabilizer code, this amounts to…
Neural-network quantum states (NQS) have become a powerful tool in many-body physics. Of the numerous possible architectures in which neural-networks can encode amplitudes of quantum states the simplicity of the Restricted Boltzmann Machine…
We develop a unified quantum framework for subgraph counting in graphs. We encode a graph on $N$ vertices into a quantum state on $2\lceil \log_2 N \rceil$ working qubits and $2$ ancilla qubits using its adjacency list, with worst-case gate…
For every stabiliser $N$-qudit absolutely maximally entangled state, we present a method for determining the stabiliser generators and logical operators of a corresponding quantum error correction code. These codes encode $k$ qudits into…
We report the implementation of a 3-qubit quantum error correction code (QECC) on a quantum information processor realized by the magnetic resonance of Carbon nuclei in a single crystal of Malonic Acid. The code corrects for phase errors…
The realization of effective quantum error correction protocols remains a central challenge in the development of scalable quantum computers. Employing high-dimensional quantum systems (qudits) can offer more hardware-efficient protocols…
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…
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 considered a deciding component in enabling practical quantum computing. Stabilizer codes, and in particular topological surface codes, are promising candidates for implementing QEC by redundantly encoding…
One of the limitations to the quantum computing capability of a continuous-variable system is determined by our ability to cool it to the ground state, because pure logical states, in which we accurately encode quantum information, are…
In the context of measurement-based quantum computation a way of maintaining the coherence of a graph state is to measure its stabilizer operators. Aside from performing quantum error correction, it is possible to exploit the information…
We extend the relation between absolutely maximally entangled (AME) states and quantum maximum distance separable (QMDS) codes by constructing whole families of QMDS codes from their parent AME states. We introduce a reduction-friendly form…
Stabilizer states and graph states find application in quantum error correction, measurement-based quantum computation and various other concepts in quantum information theory. In this work, we study party-local Clifford (PLC)…
Graph theory is important in information theory. We introduce a quantization process on graphs and apply the quantized graphs in quantum information. The quon language provides a mathematical theory to study such quantized graphs in a…
In quantum coding theory, stabilizer codes are probably the most important class of quantum codes. They are regarded as the quantum analogue of the classical linear codes and the properties of stabilizer codes have been carefully studied in…
Quantum superpositions of macroscopically distinct classical states, so-called Schr\"{o}dinger cat states, are a resource for quantum metrology, quantum communication, and quantum computation. In particular, the superpositions of two…
The construction of large, coherent quantum systems necessary for quantum computation remains an entreating but elusive goal, due to the ubiquitous nature of decoherence. Recent progress in quantum error correction schemes have given new…
Quantum error-correcting codes aim to protect information in quantum systems to enable fault-tolerant quantum computations. The most prevalent method, stabilizer codes, has been well developed for many varieties of systems, however, largely…
We introduce a theory of quantum error correction (QEC) for a subclass of states within a larger Hilbert space. In the standard theory of QEC, the set of all encoded states is formed by an arbitrary linear combination of the codewords.…
The present paper is concerned with the concept of the one-way quantum computer, beyond binary-systems, and its relation to the concept of stabilizer quantum codes. This relation is exploited to analyze a particular class of quantum…