Related papers: Entanglement-assisted quantum error-correcting cod…
We prove a new version of the quantum threshold theorem that applies to concatenation of a quantum code that corrects only one error, and we use this theorem to derive a rigorous lower bound on the quantum accuracy threshold epsilon_0. Our…
We derive a family of optimal protocols, in the sense of saturating the quantum Cram\'{e}r-Rao bound, for measuring a linear combination of $d$ field amplitudes with quantum sensor networks, a key subprotocol of general quantum sensor…
We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of…
We present a universal framework for quantum error-correcting codes, i.e., the one that applies for the most general quantum error-correcting codes. This framework is established on the group algebra, an algebraic notation for the nice…
Connecting multiple smaller qubit modules by generating high-fidelity entangled states is a promising path for scaling quantum computing hardware. The performance of such a modular quantum computer is highly dependent on the quality and…
With entanglement-assisted (EA) formalism, arbitrary classical linear codes are allowed to transform into EAQECCs by using pre-shared entanglement between the sender and the receiver. In this paper, based on classical cyclic MDS codes by…
Many quantum algorithms seek to output a specific bitstring solving the problem of interest--or a few if the solution is degenerate. It is the case for the quantum approximate optimization algorithm (QAOA) in the limit of large circuit…
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…
In practical communication and computation systems, errors occur predominantly in adjacent positions rather than in a random manner. In this paper, we develop a stabilizer formalism for quantum burst error correction codes (QBECC) to combat…
Constacyclic codes over finite fields are of theoretical importance as they are closely related to a number of areas of mathematics such as algebra, algebraic geometry, graph theory, combinatorial designs and number theory. However, the…
Entanglement assistance is known to reduce the quantum communication complexity of evaluating functions with distributed inputs. But does the type of entanglement matter, or are EPR pairs always sufficient? This is a natural question…
Proving the quantum Hamming bound for degenerate nonbinary stabilizer codes has been an open problem for a decade. In this note, I prove this bound for double error-correcting degenerate stabilizer codes. Also, I compute the maximum length…
We analytically derive the fundamental lower bound for the preparation fidelity of a maximally-entangled (Bell) state of two atoms involving Rydberg-state interactions. This bound represents the minimum achievable error $E \geq ( 1 + \pi/2…
We show how extra entanglement shared between sender and receiver reduces the memory requirements for a general entanglement-assisted quantum convolutional code. We construct quantum convolutional codes with good error-correcting properties…
Construction of good quantum codes via classical codes is an important task for quantum information and quantum computing. In this work, by virtue of a decomposition of the defining set of constacyclic codes we have constructed eight new…
Estimates of the quantum accuracy threshold often tacitly assume that it is possible to interact arbitrary pairs of qubits in a quantum computer with a failure rate that is independent of the distance between them. None of the many physical…
The problem of correcting transpositions (or swaps) of consecutive symbols in $ q $-ary strings is studied. Lower bounds on asymptotically achievable rates of codes correcting $ t = \tau n $ transpositions are derived. The first bound is…
Creation of entanglement is considered theoretically and numerically in an ensemble of spin chains with dipole-dipole interaction between the spins. The unwanted effect of the long-range dipole interaction is compensated by the optimal…
We prove a general lower bound on the bounded-error entanglement-assisted quantum communication complexity of Boolean functions. The bound is based on the concept that any classical or quantum protocol to evaluate a function on distributed…
Violation of modified Wigner inequality by means binary bipartite quantum system allows the discrimination between the quantum world and the classical local-realistic one, and also ensures the security of Ekert-like quantum key distribution…