Related papers: Codeword Stabilized Codes from m-Uniform Graph Sta…
We address the task of verifying whether a quantum computer, designed to be protected by a specific stabilizer code, correctly encodes the corresponding logical qubits. To achieve this, we develop a general framework for subspace…
Many $q$-ary stabilizer quantum codes can be constructed from Hermitian self-orthogonal $q^2$-ary linear codes. This result can be generalized to $q^{2 m}$-ary linear codes, $m > 1$. We give a result for easily obtaining quantum codes from…
Quantum error-correcting code (QECC) is the central ingredient in fault-tolerant quantum information processing. An emerging paradigm of dynamical QECC shows that one can robustly encode logical quantum information both temporally and…
The realization of quantum error correction is an essential ingredient for reaching the full potential of fault-tolerant universal quantum computation. Using a range of different schemes, logical qubits can be redundantly encoded in a set…
We present a description of encoding/decoding for a concatenated quantum code that enables both protection against quantum computational errors and the occurrence of one quantum erasure. For this, it is presented how encoding and decoding…
Non-symmetric GHZ states ($n$-GHZ$_\alpha$), defined by unequal superpositions of $|00...0>$ and $|11...1>$, naturally emerge in experiments due to decoherence, control errors, and state preparation imperfections. Despite their relevance in…
Quantum computing is an emerging technology that has the potential to achieve exponential speedups over their classical counterparts. To achieve quantum advantage, quantum principles are being applied to fields such as communications,…
In previous work, we have shown that pseudocodewords can be used to characterize the behavior of decoders not only for classical codes but also for quantum stabilizer codes. With the insights obtained from this pseudocodewords-based…
The five-qubit quantum error correcting code encodes one logical qubit to five physical qubits, and protects the code from a single error. It was one of the first quantum codes to be invented, and various encoding circuits have been…
Protection of quantum information from noise is a massive challenge. One avenue people have begun to explore is reducing the number of particles needing to be protected from noise and instead use systems with more states, so called qudit…
We experimentally explore the state space of three qubits on an NMR quantum information processor. We construct a scheme to experimentally realize a canonical form for general three-qubit states up to single-qubit unitaries. This form…
The pair coherent state (PCS) is a theoretical extension of the Glauber coherent state to two harmonic oscillators. It is an interesting class of non-Gaussian continuous-variable entangled state and is also at the heart of a promising…
The construction of quantum error-correcting codes (QECCs) with good parameters is a hot topic in the area of quantum information and quantum computing. Quantum maximum distance separable (QMDS) codes are optimal because the minimum…
Graph states, which include for example Bell states, GHZ states and cluster states, form a well-known class of quantum states with applications ranging from quantum networks to error-correction. Deciding whether two graph states are…
In quantum computing and quantum information processing, graph states are a specific type of quantum states which are commonly used in quantum networking and quantum error correction. A recurring problem is finding a transformation from a…
We study a linear computation problem over a quantum multiple access channel (LC-QMAC), where $S$ servers share an entangled state and separately store classical data streams $W_1,\cdots, W_S$ over a finite field $\mathbb{F}_d$. A user aims…
We introduce multivariate multicycle (MM) codes, a new family of quantum error-correcting codes (QECCs) that unifies bivariate bicycle, multivariate bicycle, abelian two-block group algebra, generalized bicycle, trivariate tricycle, and…
Consider a general quantum stochastic source that emits at discrete time steps quantum pure states which are chosen from a finite alphabet according to some probability distribution which may depend on the whole history. Also, fix two…
Preparing arbitrary logical states is a central primitive for universal fault-tolerant quantum computation and the cost of encoded-state preparation contributes directly to the overall resource overhead. This makes the synthesis of…
A generalization of the stabilizer code construction presented by Gottesman is described, which allows for the construction of quantum error-correcting codes for continuous-variable systems. This formalism describes all continuous-variable…