Related papers: On Transversality Across Two Distinct Quantum Erro…
One of the main problems for the future of practical quantum computing is to stabilize the computation against unwanted interactions with the environment and imperfections in the applied operations. Existing proposals for quantum memories…
A method for concatenating quantum error-correcting codes is presented. The method is applicable to a wide class of quantum error-correcting codes known as Calderbank-Shor-Steane (CSS) codes. As a result, codes that achieve a high rate in…
Quantum repeaters that incorporate quantum error correction codes have been shown to be a promising alternative compared with the original quantum repeaters that rely upon probabilistic quantum error detection depending on classical…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels.…
Quantum optical states are fragile and can become corrupted when passed through a lossy communication channel. Unlike for classical signals, optical amplifiers cannot be used to recover quantum signals. Quantum repeaters have been proposed…
We propose fault-tolerant encoders for quantum low-density parity check (LDPC) codes. By grouping qubits within a quantum code over contiguous blocks and applying preshared entanglement across these blocks, we show how transversal…
A permutationally invariant n-bit code for quantum error correction can be realized as a subspace stabilized by the non-Abelian group S_n. The code corresponds to bases for the trivial representation, and all other irreducible…
Multi user orthogonal chirp spread spectrum (OCSS) can improve the spectral inefficiency of chirp spread spectrum (CSS) but is only feasible with perfect synchronism and without any channel dispersion. Asynchronism, channel dispersion, or…
One of the main challenge for an efficient implementation of quantum information technologies is how to counteract quantum noise. Quantum error correcting codes are therefore of primary interest for the evolution towards quantum computing…
The surface code is a promising candidate for fault-tolerant quantum computation, achieving a high threshold error rate with nearest-neighbor gates in two spatial dimensions. Here, through a series of numerical simulations, we investigate…
We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This…
With respect to the transversal gate group (an invariant of quantum codes), we demonstrate that non-additive codes can outperform stabilizer codes. We do this by constructing spin codes that correspond to permutation-invariant multiqubit…
A quantum shift register circuit acts on a set of input qubits and memory qubits, outputs a set of output qubits and updated memory qubits, and feeds the memory back into the device for the next cycle (similar to the operation of a…
CSS codes are a subfamily of stabilizer codes especially appropriate for fault-tolerant quantum computations. A very simple method is proposed to encode a general qudit when a Calderbank-Shor-Steane quantum code, defined over a q-ary…
We extend quantum rate distortion theory by considering auxiliary resources that might be available to a sender and receiver performing lossy quantum data compression. The first setting we consider is that of quantum rate distortion coding…
Transversal gates play a crucial role in suppressing error propagation in fault-tolerant quantum computation, yet they are intrinsically constrained: any nontrivial code encoding a single logical qubit admits only a finite subgroup of…
We investigate in this work a quantum error correction on a five-qubits graph state used for secret sharing through five noisy channels. We describe the procedure for the five, seven and nine qubits codes. It is known that the three codes…
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…
Using transversal gates is a straightforward and efficient technique for fault-tolerant quantum computing. Since transversal gates alone cannot be computationally universal, they must be combined with other approaches such as magic state…