Learning algorithm and application of quantum BP neural networks based on universal quantum gates

A quantum BP neural networks model with learning algorithm is proposed. First, based on the universality of single qubit rotation gate and two-qubit controlled-NOT gate, a quantum neuron model is constructed, which is composed of input, phase rotation, aggregation, reversal rotation and output. In this model, the input is described by qubits, and the output is given by the probability of the state in which （1） is observed. The phase rotation and the reversal rotation are performed by the universal quantum gates. Secondly, the quantum BP neural networks model is constructed, in which the output layer and the hide layer are quantum neurons. With the application of the gradient descent algorithm, a learning algorithm of the model is proposed, and the continuity of the model is proved. It is shown that this model and algorithm are superior to the conventional BP networks in three aspects： convergence speed, convergence rate and robustness, by two application examples of pattern recognition and function approximation.

Full-Blind Delegating Private Quantum Computation

The delegating private quantum computation(DQC)protocol with the universal quantum gate set{X,Z,H,P,R,CNOT}was firstly proposed by Broadbent et al.[Broadbent(2015)],and then Tan et al.[Tan and Zhou(2017)]tried to put forward a half-blind DQC protocol(HDQC)with another universal set{H,P,CNOT,T}.However,the decryption circuit of Toffoli gate(i.e.T)is a little redundant,and Tan et al.’s protocol[Tan and Zhou(2017)]exists the information leak.In addition,both of these two protocols just focus on the blindness of data(i.e.the client’s input and output),but do not consider the blindness of computation(i.e.the delegated quantum operation).For solving these problems,we propose a full-blind DQC protocol(FDQC)with quantum gate set{H,P,CNOT,T},where the desirable delegated quantum operation,one of{H,P,CNOT,T},is replaced by a fixed sequence(H,P,CZ,CNOT,T)to make the computation blind,and the decryption circuit of Toffoli gate is also optimized.Analysis shows that our protocol can not only correctly perform any delegated quantum computation,but also holds the characteristics of data blindness and computation blindness.

<i>C</i>¹²- <i>C</i>¹³Diamond Quantum Computer with Longitudinal rf-Magnetic Field

In the diamond C12 (nuclear spin zero) structure with a linear chain of C13 (nuclear spin one half) atoms is applied to a transverse static field with respect of this linear chain, having a gradient along the linear chain, and it is also applied to an rf-magnetic field in a plane with a component in the direction of the static field. It is shown that one qubit rotation, the Controlled-Not (CNOT), the Controlled-Controlled-NoT (CCNOT) quantum gates, and teleportation algorithm can be implemented on this structure using integer multiples of electromagnetic π-pulses. Therefore, a quantum computer can be constructed in this form.

Foundations of Holographic Quantum Computation

We present a comprehensive mathematical framework establishing the foundations of holographic quantum computing, a novel paradigm that leverages holographic phenomena to achieve superior error correction and algorithmic efficiency. We rigorously demonstrate that quantum information can be encoded and processed using holographic principles, establishing fundamental theorems characterizing the error-correcting properties of holographic codes. We develop a complete set of universal quantum gates with explicit constructions and prove exponential speedups for specific classes of computational problems. Our framework demonstrates that holographic quantum codes achieve a code rate scaling as O(1/logn), superior to traditional quantum LDPC codes, while providing inherent protection against errors via geometric properties of the code structures. We prove a threshold theorem establishing that arbitrary quantum computations can be performed reliably when physical error rates fall below a constant threshold. Notably, our analysis suggests certain algorithms, including those involving high-dimensional state spaces and long-range interactions, achieve exponential speedups over both classical and conventional quantum approaches. This work establishes the theoretical foundations for a new approach to quantum computation that provides natural fault tolerance and scalability, directly addressing longstanding challenges of the field.

Programmable quantum processor implemented with superconducting circuit

A quantum processor might execute certain computational tasks exponentially faster than a classical processor.Here,using superconducting quantum circuits we design a powerful universal quantum processor with the structure of symmetric all-to-all capacitive connection.We present the Hamiltonian and use it to demonstrate a full set of qubit operations needed in the programmable universal quantum computations.With the device the unwanted crosstalk and ZZ-type couplings between qubits can be effectively suppressed by tuning gate voltages,and the design allows efficient and high-quality couplings of qubits.Within available technology,the scheme may enable a practical programmable universal quantum computer.