Development of Hybrid ARQ Protocol for the Quantum Communication System on Stabilizer Codes

In this paper,we develop a novel hybrid automatic-repeat-request(ARQ)protocol for the quantum communication system using quantum stabilizer codes.The quantum information is encoded by stabilizer codes to against the channel noise.The twophoton entangled state is prepared for codeword secure transmission.Hybrid ARQ protocol rules the recognition and retransmission of error codewords.In this protocol,the property of quantum entangled state ensures the security of information,the theory of hybrid ARQ system improves the reliability of transmission,the theory of quantum stabilizer codes corrects the flipping errors of codewords.Finally,we verify the security and throughput efficiency of this protocol.

Low-overhead fault-tolerant error correction scheme based on quantum stabilizer codes

Fault-tolerant error-correction(FTEC)circuit is the foundation for achieving reliable quantum computation and remote communication.However,designing a fault-tolerant error correction scheme with a solid error-correction ability and low overhead remains a significant challenge.In this paper,a low-overhead fault-tolerant error correction scheme is proposed for quantum communication systems.Firstly,syndrome ancillas are prepared into Bell states to detect errors caused by channel noise.We propose a detection approach that reduces the propagation path of quantum gate fault and reduces the circuit depth by splitting the stabilizer generator into X-type and Z-type.Additionally,a syndrome extraction circuit is equipped with two flag qubits to detect quantum gate faults,which may also introduce errors into the code block during the error detection process.Finally,analytical results are provided to demonstrate the fault-tolerant performance of the proposed FTEC scheme with the lower overhead of the ancillary qubits and circuit depth.

Encoding entanglement-assisted quantum stabilizer codes

We address the problem of encoding entanglement-assisted （EA） quantum error-correcting codes （QECCs） and of the corresponding complexity. We present an iterative algorithm from which a quantum circuit composed of CNOT, H, and S gates can be derived directly with complexity O（n2） to encode the qubits being sent. Moreover, we derive the number of each gate consumed in our algorithm according to which we can design EA QECCs with low encoding complexity. Another advantage brought by our algorithm is the easiness and efficiency of programming on classical computers.

THE CONSTRUCTION METHOD OF STABILIZER CODES FOR CONTINUOUS VARIABLES

The paper analyzes the basic principles of stabilizer codes, focusing on how to construct stabilizer codes for achieving the continuous-variable quantum error correction. Stabilizer codes can be used in the reconciliation of continuous-variable quantum key distribution system. The construction method of stabilizer codes is very important and it can be turned into finding the check matrix for stabilizer codes. In this paper, a new algorithm called region elimination algorithm for finding the check matrix of stabilizer codes was presented which can seek the voluntary check matrix for continu-ous-variable stabilizer codes within 8 bit code length quickly and effectively, and it was simulated by Visual C++. The algorithm is mainly realized by initializing search region, reducing the search region and then keeping searching till finding all the commuting generators. The finding of check matrix of stabilizer codes lays important foundations for the further development of stabilizer codes in the con-tinuous-variable quantum key distribution.

Decoding topological XYZ^(2) codes with reinforcement learning based on attention mechanisms

Quantum error correction, a technique that relies on the principle of redundancy to encode logical information into additional qubits to better protect the system from noise, is necessary to design a viable quantum computer. For this new topological stabilizer code-XYZ^(2) code defined on the cellular lattice, it is implemented on a hexagonal lattice of qubits and it encodes the logical qubits with the help of stabilizer measurements of weight six and weight two. However topological stabilizer codes in cellular lattice quantum systems suffer from the detrimental effects of noise due to interaction with the environment. Several decoding approaches have been proposed to address this problem. Here, we propose the use of a state-attention based reinforcement learning decoder to decode XYZ^(2) codes, which enables the decoder to more accurately focus on the information related to the current decoding position, and the error correction accuracy of our reinforcement learning decoder model under the optimisation conditions can reach 83.27% under the depolarizing noise model, and we have measured thresholds of 0.18856 and 0.19043 for XYZ^(2) codes at code spacing of 3–7 and 7–11, respectively. our study provides directions and ideas for applications of decoding schemes combining reinforcement learning attention mechanisms to other topological quantum error-correcting codes.

A NOVEL CONSTRUCTION OF QUANTUM LDPC CODES BASED ON CYCLIC CLASSES OF LINES IN EUCLIDEAN GEOMETRIES

The dual-containing (or self-orthogonal) formalism of Calderbank-Shor-Steane (CSS) codes provides a universal connection between a classical linear code and a Quantum Error-Correcting Code (QECC). We propose a novel class of quantum Low Density Parity Check (LDPC) codes constructed from cyclic classes of lines in Euclidean Geometry (EG). The corresponding constructed parity check matrix has quasi-cyclic structure that can be encoded flexibility, and satisfies the requirement of dual-containing quantum code. Taking the advantage of quasi-cyclic structure, we use a structured approach to construct Generalized Parity Check Matrix (GPCM). This new class of quantum codes has higher code rate, more sparse check matrix, and exactly one four-cycle in each pair of two rows. Ex-perimental results show that the proposed quantum codes, such as EG(2,q)II-QECC, EG(3,q)II-QECC, have better performance than that of other methods based on EG, over the depolarizing channel and decoded with iterative decoding based on the sum-product decoding algorithm.

Research of the CICC Stability by the Numerical Code Gandalf

The basic approach to computer analysis of the CICC in superconducting Tokamak HT-7U is given and discussed. We will apply a 1-D mathematical model (Gandalf) to investigate the stability of CICC at real operating modes of Tokamak. 1-D model can be directly adopted to follow the evolution of the zone when the energy input is large enough and the coil quenches. In this report, we will analyze the stability of typical CICC (including pure copper) and discuss effect of copper on the stability of CICC.

Lecture notes on quantum entanglement:From stabilizer states to stabilizer channels

We study mathematical,physical and computational aspects of the stabilizer formalism arising in quantum information and quantum computation.The measurement process of Pauli observables with its algorithm is given.It is shown that to detect genuine entanglement we need a full set of stabilizer generators and the stabilizer witness is coarser than the GHZ(Greenberger-Horne-Zeilinger)witness.We discuss stabilizer codes and construct a stabilizer code from a given linear code.We also discuss quantum error correction,error recovery criteria and syndrome extraction.The symplectic structure of the stabilizer formalism is established and it is shown that any stabilizer code is unitarily equivalent to a trivial code.The structure of graph codes as stabilizer codes is identified by obtaining the respective stabilizer generators.The distance of embeddable stabilizer codes in lattices is obtained.We discuss the Knill-Gottesman theorem,tableau representation and frame representation.The runtime of simulating stabilizer gates is obtained by applying stabilizer matrices.Furthermore,an algorithm for updating global phases is given.Resolution of quantum channels into stabilizer channels is shown.We discuss capacity achieving codes to obtain the capacity of the quantum erasure channel.Finally,we discuss the shadow tomography problem and an algorithm for constructing classical shadow is given.

Enhanced Efficiency and Durability of Organic Electroluminescent Devices by Doping in Emitting Layer

Remarkable improvement in efficiency and stability has been observed in a doped organic electroluminescence device, which consists of a hole-transport layer, an electron-transport layer and a luminescent layer. The hole-transport layer is a N,N’-bis(3-methyphenyl)-N,N’-diphenylbenzidine film. The doped emitting layer consists of 8-(quinolinolate)-aluminum as the host and rubrene as the emission dopant. The doped device demonstrated a brightness in excess of 40 000 cd/m 2 and the maximum external quantum efficiency of 3.4%, which is about six times and four times respectively greater than those of the undoped device. For no packaged deviced, a luminance half-life on the order of about 230 h has been achieved under a constant current density of 15 mA/cm 2, starting at 500 cd/m 2 at the room temperature.

Construction of nonbinary quantum cyclic codes by using graph method

Using the graph method proposed by Schlingemann and Werner, this paper introduces a technique to construct nonbinary quantum cyclic codes and provides a specific example. We also construct the quantum codes [[8, 2, 4]]p and [[n, n - 2, 2]]p for all odd primes p by the graph method.