In linguistics, the uncertainty of context due to polysemy is widespread, which attracts much attention. Quantum-inspired complex word embedding based on Hilbert space plays an important role in natural language processing (NLP), which fully leverages the similarity between quantum states and word tokens. A word containing multiple meanings could correspond to a single quantum particle which may exist in several possible states, and a sentence could be analogous to the quantum system where particles interfere with each other. Motivated by quantum-inspired complex word embedding, interpretable complex-valued word embedding (ICWE) is proposed to design two end-to-end quantum-inspired deep neural networks (ICWE-QNN and CICWE-QNN representing convolutional complex-valued neural network based on ICWE) for binary text classification. They have the proven feasibility and effectiveness in the application of NLP and can solve the problem of text information loss in CE-Mix [1] model caused by neglecting the important linguistic features of text, since linguistic feature extraction is presented in our model with deep learning algorithms, in which gated recurrent unit (GRU) extracts the sequence information of sentences, attention mechanism makes the model focus on important words in sentences and convolutional layer captures the local features of projected matrix. The model ICWE-QNN can avoid random combination of word tokens and CICWE-QNN fully considers textual features of the projected matrix. Experiments conducted on five benchmarking classification datasets demonstrate our proposed models have higher accuracy than the compared traditional models including CaptionRep BOW, DictRep BOW and Paragram-Phrase, and they also have great performance on F1-score. Eespecially, CICWE-QNN model has higher accuracy than the quantum-inspired model CE-Mix as well for four datasets including SST, SUBJ, CR and MPQA. It is a meaningful and effictive exploration to design quantum-inspired deep neural networks to promote the performance of text classification.

A quantum circuit learning approach is studied to carry out the fast-fitting of Gaussian functions. First, a parameterized structure is designed for quantum circuits based on the boson sampling model. And then, the training procedure of exploiting gradient-based optimizations is presented to iteratively update the gradient of the loss function concerning circuit parameters. For efficiency, two kinds of circuit loss, the kernel maximum mean discrepancy and the mean absolute error, are used in the training procedure, which are both competent to achieve quantum circuit learning well. It is significant that the two circuit losses assist in reducing the variance to $2.54 \times 10^{-6}$ and $6.91 \times 10^{-6}$ , respectively. Finally, a kind of quantum circuit fixed structure is developed with the boson sampling model that can decrease the model complexity as the circuit depth $d$ grows. Sets of experiments have been conducted to evaluate the proposed quantum circuit learning scheme, and demonstrate that our parameterized approach is efficient and promising, and it is worth looking forward to solving practical application problems with quantum computers since valid quantum circuits for Gaussian function fast-fitting can be designed indeed.

For signing quantum messages, the arbitrated quantum signature (AQS) has been widely investigated to date. However, most of the existing AQS protocols are susceptible to different aspects of disavowal and forgery attacks due to the use of quantum one time pad (QOTP) encryption featuring the encryption manner with qubit by qubit and the commutative property of Pauli operations. We develop an AQS protocol with boson sampling-based random unitary encryption. The unique encryption is used to encrypt the message copy (ciphertext) to produce the signature, which can circumvent the drawbacks of the QOTP encryption and stand against the signer Alice’s disavowal and the verifier Bob’s forgery attacks including existential forgery under known message attacks. The employment of a random array via the public board can prevent Bob’s repudiation attacks on the receipt and the integrality of the signature. The quantum walk-based teleportation is applied to teleport the message copy from Alice to Bob, which can avoid preparing the essential entanglement resource beforehand. Security analyses and discussions show that our AQS protocol is with impossibility of disavowal from Alice and Bob and impossibility of forgery from anyone.