Physical Layer Encryption of OFDM-PON Based on Quantum Noise Stream Cipher with Polar Code

Orthogonal frequency division multiplexing passive optical network(OFDM-PON) has superior anti-dispersion property to operate in the C-band of fiber for increased optical power budget. However,the downlink broadcast exposes the physical layer vulnerable to the threat of illegal eavesdropping. Quantum noise stream cipher(QNSC) is a classic physical layer encryption method and well compatible with the OFDM-PON. Meanwhile, it is indispensable to exploit forward error correction(FEC) to control errors in data transmission. However, when QNSC and FEC are jointly coded, the redundant information becomes heavier and thus the code rate of the transmitted signal will be largely reduced. In this work, we propose a physical layer encryption scheme based on polar-code-assisted QNSC. In order to improve the code rate and security of the transmitted signal, we exploit chaotic sequences to yield the redundant bits and utilize the redundant information of the polar code to generate the higher-order encrypted signal in the QNSC scheme with the operation of the interleaver.We experimentally demonstrate the encrypted 16/64-QAM, 16/256-QAM, 16/1024-QAM, 16/4096-QAM QNSC signals transmitted over 30-km standard single mode fiber. For the transmitted 16/4096-QAM QNSC signal, compared with the conventional QNSC method, the proposed method increases the code rate from 0.1 to 0.32 with enhanced security.

Performance of entanglement-assisted quantum codes with noisy ebits over asymmetric and memory channels

Entanglement-assisted quantum error correction codes(EAQECCs)play an important role in quantum communications with noise.Such a scheme can use arbitrary classical linear code to transmit qubits over noisy quantum channels by consuming some ebits between the sender(Alice)and the receiver(Bob).It is usually assumed that the preshared ebits of Bob are error free.However,noise on these ebits is unavoidable in many cases.In this work,we evaluate the performance of EAQECCs with noisy ebits over asymmetric quantum channels and quantum channels with memory by computing the exact entanglement fidelity of several EAQECCs.We consider asymmetric errors in both qubits and ebits and show that the performance of EAQECCs in entanglement fidelity gets improved for qubits and ebits over asymmetric channels.In quantum memory channels,we compute the entanglement fidelity of several EAQECCs over Markovian quantum memory channels and show that the performance of EAQECCs is lowered down by the channel memory.Furthermore,we show that the performance of EAQECCs is diverse when the error probabilities of qubits and ebits are different.In both asymmetric and memory quantum channels,we show that the performance of EAQECCs is improved largely when the error probability of ebits is reasonably smaller than that of qubits.

On the complete weight distributions of quantum error-correcting codes

In a recent paper, Hu et al. defined the complete weight distributions of quantum codes and proved the Mac Williams identities, and as applications they showed how such weight distributions may be used to obtain the singleton-type and hamming-type bounds for asymmetric quantum codes. In this paper we extend their study much further and obtain several new results concerning the complete weight distributions of quantum codes and applications. In particular, we provide a new proof of the Mac Williams identities of the complete weight distributions of quantum codes. We obtain new information about the weight distributions of quantum MDS codes and the double weight distribution of asymmetric quantum MDS codes. We get new identities involving the complete weight distributions of two different quantum codes. We estimate the complete weight distributions of quantum codes under special conditions and show that quantum BCH codes by the Hermitian construction from primitive, narrow-sense BCH codes satisfy these conditions and hence these estimate applies.

Quantum Codes Do Not Increase Fidelity against Isotropic Errors

In this article, we study the ability of error-correcting quantum codes to increase the fidelity of quantum states throughout a quantum computation. We analyze arbitrary quantum codes that encode all qubits involved in the computation, and we study the evolution of n-qubit fidelity from the end of one application of the correcting circuit to the end of the next application. We assume that the correcting circuit does not introduce new errors, that it does not increase the execution time (i.e. its application takes zero seconds) and that quantum errors are isotropic. We show that the quantum code increases the fidelity of the states perturbed by quantum errors but that this improvement is not enough to justify the use of quantum codes. Namely, we prove that, taking into account that the time interval between the application of the two corrections is multiplied (at least) by the number of qubits n (due to the coding), the best option is not to use quantum codes, since the fidelity of the uncoded state over a time interval n times smaller is greater than that of the state resulting from the quantum code correction.

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 quantum blind signature scheme based on dense coding for non-entangled states

In some schemes, quantum blind signatures require the use of difficult-to-prepare multiparticle entangled states. By considering the communication overhead, quantum operation complexity, verification efficiency and other relevant factors in practical situations, this article proposes a non-entangled quantum blind signature scheme based on dense encoding. The information owner utilizes dense encoding and hash functions to blind the information while reducing the use of quantum resources. After receiving particles, the signer encrypts the message using a one-way function and performs a Hadamard gate operation on the selected single photon to generate the signature. Then the verifier performs a Hadamard gate inverse operation on the signature and combines it with the encoding rules to restore the message and complete the verification.Compared with some typical quantum blind signature protocols, this protocol has strong blindness in privacy protection,and higher flexibility in scalability and application. The signer can adjust the signature operation according to the actual situation, which greatly simplifies the complexity of the signature. By simultaneously utilizing the secondary distribution and rearrangement of non-entangled quantum states, a non-entangled quantum state representation of three bits of classical information is achieved, reducing the use of a large amount of quantum resources and lowering implementation costs. This improves both signature verification efficiency and communication efficiency while, at the same time, this scheme meets the requirements of unforgeability, non-repudiation, and prevention of information leakage.

Recurrent neural network decoding of rotated surface codes based on distributed strategy

Quantum error correction is a crucial technology for realizing quantum computers.These computers achieve faulttolerant quantum computing by detecting and correcting errors using decoding algorithms.Quantum error correction using neural network-based machine learning methods is a promising approach that is adapted to physical systems without the need to build noise models.In this paper,we use a distributed decoding strategy,which effectively alleviates the problem of exponential growth of the training set required for neural networks as the code distance of quantum error-correcting codes increases.Our decoding algorithm is based on renormalization group decoding and recurrent neural network decoder.The recurrent neural network is trained through the ResNet architecture to improve its decoding accuracy.Then we test the decoding performance of our distributed strategy decoder,recurrent neural network decoder,and the classic minimum weight perfect matching(MWPM)decoder for rotated surface codes with different code distances under the circuit noise model,the thresholds of these three decoders are about 0.0052,0.0051,and 0.0049,respectively.Our results demonstrate that the distributed strategy decoder outperforms the other two decoders,achieving approximately a 5%improvement in decoding efficiency compared to the MWPM decoder and approximately a 2%improvement compared to the recurrent neural network decoder.

Mechanism of Universal Quantum Computation in the Brain

In this paper, the authors extend [1] and provide more details of how the brain may act like a quantum computer. In particular, positing the difference between voltages on two axons as the environment for ions undergoing spatial superposition, we argue that evolution in the presence of metric perturbations will differ from that in the absence of these waves. This differential state evolution will then encode the information being processed by the tract due to the interaction of the quantum state of the ions at the nodes with the “controlling’ potential. Upon decoherence, which is equal to a measurement, the final spatial state of the ions is decided and it also gets reset by the next impulse initiation time. Under synchronization, several tracts undergo such processes in synchrony and therefore the picture of a quantum computing circuit is complete. Under this model, based on the number of axons in the corpus callosum alone, we estimate that upwards of 50 million quantum states might be prepared and evolved every second in this white matter tract, far greater processing than any present quantum computer can accomplish.

A Novel Deterministic Quantum Communication Scheme Using Stabilizer Quantum Code

Exploiting the encoding process of the stabilizer quantum code [[n, k, d]], a deterministic quantum communication scheme, in which n - 1 photons are distributed forward and backward in two-way channel, is proposed to transmit the secret messages with unconditional security. The present scheme can be implemented to distribute the secret quantum （or classical） messages with great capacity in imperfect quantum channel since the utilized code encodes k-qubit messages for each scheme run.

Constructing Non-binary Asymmetric Quantum Codes via Graphs

The theory of quantum error correcting codes is a primary tool for fighting decoherence and other quantum noise in quantum communication and quantum computation. Recently, the theory of quantum error correcting codes has developed rapidly and been extended to protect quantum information over asymmetric quantum channels, in which phase-shift and qubit-flip errors occur with different probabilities. In this paper, we generalize the construction of symmetric quantum codes via graphs (or matrices) to the asymmetric case, converting the construction of asymmetric quantum codes to finding matrices with some special properties. We also propose some asymmetric quantum Maximal Distance Separable (MDS) codes as examples constructed in this way.

Quantum quasi-cyclic low-density parity-check error-correcting codes

In this paper, we propose the approach of employing circulant permutation matrices to construct quantum quasicyclic （QC） low-density parity-check （LDPC） codes. Using the proposed approach one may construct some new quantum codes with various lengths and rates of no cycles-length 4 in their Tanner graphs. In addition, these constructed codes have the advantages of simple implementation and low-complexity encoding. Finally, the decoding approach for the proposed quantum QC LDPC is investigated.

ON CLASSICAL BCH CODES AND QUANTUM BCH CODES

It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its designed distance. In this paper, we give the sufficient and necessary condition for arbitrary classical BCH codes with self-orthogonal property through algorithms. We also give a better upper bound of the designed distance of a classical narrow-sense BCH code which contains its Euclidean dual. Besides these, we also give one algorithm to compute the dimension of these codes. The complexity of all algorithms is analyzed. Then the results can be applied to construct a series of quantum BCH codes via the famous CSS constructions.

Entanglement fidelity of channel adaptive quantum codes

We study the performances of quantum channel adaptive [4,1] code transmitting in a joint amplitude damping and dephasing channel, the [6,2] code transmitting in an amplitude damping channel by combining the encoding, noise process, and decoding as one effective channel. We explicitly obtain the entanglement fidelities. The recovery operators of the [6,2] code are given. The performance is nearly optimal compared with that of the optimal method of semidefinite programming.

Jointly-check iterative decoding algorithm for quantum sparse graph codes

For quantum sparse graph codes with stabilizer formalism, the unavoidable girth-four cycles in their Tanner graphs greatly degrade the iterative decoding performance with standard belief-propagation （BP） algorithm. In this paper, we present a jointly-check iterative algorithm suitable for decoding quantum sparse graph codes efficiently. Numerical simulations show that this modified method outperforms standard BP algorithm with an obvious performance improvement.

Determination of quantum toric error correction code threshold using convolutional neural network decoders

Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers.In order to find the best syndrome of the stabilizer code in quantum error correction,we need to find a fast and close to the optimal threshold decoder.In this work,we build a convolutional neural network(CNN)decoder to correct errors in the toric code based on the system research of machine learning.We analyze and optimize various conditions that affect CNN,and use the RestNet network architecture to reduce the running time.It is shortened by 30%-40%,and we finally design an optimized algorithm for CNN decoder.In this way,the threshold accuracy of the neural network decoder is made to reach 10.8%,which is closer to the optimal threshold of about 11%.The previous threshold of 8.9%-10.3%has been slightly improved,and there is no need to verify the basic noise.

Quantum secret sharing based on quantum error-correcting codes

Quantum secret sharing（QSS） is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2k- 1, 1, k] quantum error-correcting code （QECC） to implement a quantum （k, 2k-1） threshold scheme. It also takes advantage of classical enhancement of the [2k-1, 1, k] QECC to establish a QSS scheme which can share classical information and quantum information simultaneously. Because information is encoded into QECC, these schemes can prevent intercept-resend attacks and be implemented on some noisy channels.

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.

Degenerate asymmetric quantum concatenated codes for correcting biased quantum errors

In most practical quantum mechanical systems,quantum noise due to decoherence is highly biased towards dephasing.The quantum state suffers from phase flip noise much more seriously than from the bit flip noise.In this work,we construct new families of asymmetric quantum concatenated codes(AQCCs)to deal with such biased quantum noise.Our construction is based on a novel concatenation scheme for constructing AQCCs with large asymmetries,in which classical tensor product codes and concatenated codes are utilized to correct phase flip noise and bit flip noise,respectively.We generalize the original concatenation scheme to a more general case for better correcting degenerate errors.Moreover,we focus on constructing nonbinary AQCCs that are highly degenerate.Compared to previous literatures,AQCCs constructed in this paper show much better parameter performance than existed ones.Furthermore,we design the specific encoding circuit of the AQCCs.It is shown that our codes can be encoded more efficiently than standard quantum 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.