In quantum communication systems, quantum error-correcting codes (QECCs) are known to exhibit improved performance with the use of error-free entanglement bits (ebits). In practical situations, ebits inevitably suffer...
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In quantum communication systems, quantum error-correcting codes (QECCs) are known to exhibit improved performance with the use of error-free entanglement bits (ebits). In practical situations, ebits inevitably suffer from errors, and as a result, the error-correcting capability of the code is diminished. Previous studies have proposed two different schemes as a solution. One study uses only one QECC to correct errors on the receiver side (i.e., Bob) and sender side (i.e., Alice). The other uses different QECCs on each side. In this paper, we present a method to correct errors on both sides by using single nonadditive entanglement-assisted codeword stabilized quantum error-correcting code (EACWS QECC). We use the property that the number of effective error patterns decreases as much as the number of ebits. This property results in a greater number of logical codewords using the same number of physical qubits. (C) 2016 The Korean Institute of Communications Information Sciences. Publishing Services by Elsevier B.V.
We reconsider the black hole firewall puzzle, emphasizing that quantumerror-correction, computational complexity, and pseudorandomness are crucial concepts for understanding the black hole interior. We assume that th...
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ISBN:
(纸本)9781450380539
We reconsider the black hole firewall puzzle, emphasizing that quantumerror-correction, computational complexity, and pseudorandomness are crucial concepts for understanding the black hole interior. We assume that the Hawking radiation emitted by an old black hole is pseudorandom, meaning that it cannot be distinguished from a perfectly thermal state by any efficient quantum computation acting on the radiation alone. We then infer the existence of a subspace of the radiation system which we interpret as an encoding of the black hole interior. This encoded interior is entangled with the late outgoing Hawking quanta emitted by the old black hole, and is inaccessible to computationally bounded observers who are outside the black hole. Specifically, efficient operations acting on the radiation, those with quantum computational complexity polynomial in the entropy of the remaining black hole, commute with a complete set of logical operators acting on the encoded interior, up to corrections which are exponentially small in the entropy. Thus, under our pseudorandomness assumption, the black hole interior is well protected from exterior observers as long as the remaining black hole is macroscopic. On the other hand, if the radiation is not pseudorandom, an exterior observer may be able to create a firewall by applying a polynomial-time quantum computation to the radiation.
A new method to obtain self-orthogonal codes over finite field F(2) is presented. Based on this method, we provide a construction for quantum error-correcting codes starting from cyclic codes over finite ring R = F(2)...
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A new method to obtain self-orthogonal codes over finite field F(2) is presented. Based on this method, we provide a construction for quantum error-correcting codes starting from cyclic codes over finite ring R = F(2) + uF(2). As an example, we present infinite families of quantum error-correcting codes which are derived from cyclic codes over the ring R = F(2) + uF(2).
In this paper, from special code chains C-1 superset of C-2 superset of C-3 such that C-1(perpendicular to h) subset of C 3 and C-2(perpendicular to h) subset of C-2, some Hermitian dual-containing (HDC) matrix-produc...
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In this paper, from special code chains C-1 superset of C-2 superset of C-3 such that C-1(perpendicular to h) subset of C 3 and C-2(perpendicular to h) subset of C-2, some Hermitian dual-containing (HDC) matrix-product (MP) codes are presented, where C-3 is not HDC. By studying some constacyclic codes of lengths n = q(2) +/- 1 and n = q(2) - 1/2, we construct many HDC MP codes of length 3n. Consequently, many q-ary quantumcodes with larger designed distance d >= q + 1 are obtained from these MP codes, where 4 <= q <= 9.
In this paper, we present a computer-supported method of searching for quantum caps. By means of this method and relevant knowledge of combinatorics, many quantum caps in PG(3, 9) and PG(4, 9) are constructively prove...
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In this paper, we present a computer-supported method of searching for quantum caps. By means of this method and relevant knowledge of combinatorics, many quantum caps in PG(3, 9) and PG(4, 9) are constructively proven to exist. Then, according to the theorem that each quantum cap corresponds to a quantum error-correcting code with d = 4, we obtain 278 quantum error-correcting codes. Most of these results break theGVbound, and a number of them are optimal quantumcodes or have improved parameters.
The lattice surgery approach allows for an efficient implementation of universal quantum gate sets with topological quantumerrorcorrectingcodes that achieve a high threshold and are composed of only the nearest gat...
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The lattice surgery approach allows for an efficient implementation of universal quantum gate sets with topological quantumerrorcorrectingcodes that achieve a high threshold and are composed of only the nearest gate operations and low-weight stabilizers. Here, we propose two types of lattice surgery-based logical qubit architectures using the logical remote-controlled-not operation and circuit mapping method. Our architectures enhanced the qubit efficiency, and when combined with our qubit initialization and routing process, they reduced the running time and quantum volume of several quantum circuits by removing time-expensive logical SWAP operations and enabling fast logical CNOT operations. The quantum volume was compared between three cases, one in which the magic state distillation technique was not applied, one in which the multiple magic state distillation circuits are used to reduce the circuit execution time, and the other in which one magic state distillation circuit are used to reduce the number of qubit used.
In this paper, a channel-optimized quantum communication scheme with imperfect Bell states is being considered, based on quantum teleportation and error correction codes technology. In this scheme, a novel "combi...
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In this paper, a channel-optimized quantum communication scheme with imperfect Bell states is being considered, based on quantum teleportation and error correction codes technology. In this scheme, a novel "combination code" technique is proposed to protect the pre-shared Bell states from storage errors and to safeguard the information-encoded states from noisy channels. Ultimately, it is revealed by Monte Carlo simulation results that the channel fidelity of the proposed channel-optimized quantum communication scheme with imperfect Bell states is significantly advantageous over standard quantum error-correcting code (QECC) and entanglement-assisted quantum error-correcting code (EAQECC) communication schemes.
Generally, it is difficult to construct the generator matrices of quantum stabilizer codes for large length N. In this work, we employ the recursive relations of matrices to solve this problem so that quantumerror-co...
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Generally, it is difficult to construct the generator matrices of quantum stabilizer codes for large length N. In this work, we employ the recursive relations of matrices to solve this problem so that quantum error-correcting codes with large length N can be constructed easily.
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