Learnable antinoise-receiver algorithm based on a quantum feedforward neural network in optical quantum communication

The quantum communication process usually consists of three stages: the sender who prepares encoded carriers, the transmission in noisy channels, and the quantum receivers. The transmitted quantum information can be inevitably affected by kinds of quantum noise in the environment. Thus, quantum protocols are extensively studied to improve communication efficiency and accuracy under the influence of quantum noise. The optimization strategies usually occur in these three stages. In this paper, we focus on the optimization strategy of quantum receivers in the third stage. In quantum receiver algorithms, the key to distinguish received non-orthogonal coherent states in free-space optical quantum communication is to construct an optimum displacement operator for transforming the current coherent state into a state that is easier to distinguish than before. To improve the antinoise ability and accuracy of quantum communication, this paper proposes a universal optimization strategy of quantum receivers called learnable antinoise receiver (LAN receiver). In this strategy, a parametrized quantum circuit is constructed as a quantum feedforward neural network as the displacement operator to improve the antinoise ability. The parameters used in the quantum circuit are updated by gradient descent continuously to find the best parameter combination of the quantum circuit that minimizes the error rate and the qubits affected by quantum noise are used as training and testing data. The simulation of the proposed algorithm shows that the LAN receiver can resist different kinds of strong quantum noise. The average error rate of the proposed algorithm LAN receiver under the strong noise channel is 0.18, which has better performance than other type of receivers under the influence of strong quantum noise.

Figure 1

LAN-receiver-based quantum communication system.

Figure 2

Preprocessing circuit (a): conversion of the format of input classical data and feature extraction.

Figure 3

Preprocessing circuit (b): feature encoding circuit where ${\theta }_{mn}>{\theta }_{mn+1}$ and ${\theta }_{mn}\in \left[0,\pi \right]$.

Figure 4

Quantum neural network circuit for training displacement. Here, $p\in \left\{x,y,z\right\}$ and $\left\{{\delta }_i,i=1...k\right\}$ denotes the rotation angle of the corresponding rotation operation $R_p\left({\delta }_i\right)$.

Figure 5

Detailed description of the multiparticle-controlled circuit.

Figure 6

The basic module of quantum neural network: the physical realization of arbitrary unitary operations

Figure 7

Physical realization of quantum neural network circuit.

Figure 8

Fidelity comparison under four kinds of single noise, amplitude damping (AD), bit flip (BF), phase flip (PF), and depolarizing (D).

Figure 9

Simulation results under the influence of amplitude damping noise, bit-flip noise, phase-flip noise and depolarizing noise.

Figure 10

The change of fidelity of the system with different combinations of noise factors ${\gamma }_{AD}, {\gamma }_{BF}, {\gamma }_{PF}$, and ${\gamma }_D$.

Figure 11

Simulation result under the influence of amplitude damping noise and bit-flip noise.

Figure 12

Simulation result under the influence of amplitude damping noise and phase-flip noise.

Figure 13

Simulation result under the influence of amplitude damping noise and depolarizing noise.

Figure 14

Simulation result under the influence of phase-flip noise and bit-flip noise.

Figure 15

Simulation result under the influence of depolarizing noise and bit-flip noise.

Figure 16

Simulation result under the influence of depolarizing noise and phase-flip noise.