Quantum loop programs

Jim D

Yongming Li

Loop is a very important program construct in classical computation. So, it is necessary to study the structure of the quantum Loop programs. This paper defines a general quantum Loop program whose body is a quantum operation, and gives the definitions for termination, almost termination and non-termination of the general quantum Loop program with respect to any input state. It proves the necessary and sufficient conditions for termination of the general quantum Loop programs given input state. As applications, it finally verifies the embedded quantum Loop programs whose body is unitary operation is a general quantum Loop program.

Jingzhe Guo, Mingsheng Ying

We propose a method for performing software pipelining on quantum for-loop programs to exploit parallelism in and across iterations. We redefined concepts useful in program optimization, including array aliasing, instruction dependency, and resource conflict required in optimizing quantum programs. Using these concepts, we present a software pipelining framework exploiting instruction-level parallelism in quantum loop programs. This method is further enhanced with several improvements to reduce total gate count and program depth. The optimization method is then evaluated on some popular quantum algorithms like Grover and QAOA, and compared under different configurations and with several baseline compilers. The evaluation results show that our approach can schedule loop programs with depth close to the depth of the entire loop unrolling while generating smaller code sizes and consuming much less time. This is the first step towards optimization of a quantum program with such loop control flow, as far as we know.

Jeff W. Sanders, Paolo Zuliani

Mingsheng Ying, Yuan Feng

Loop is a powerful program construct in classical computation, but its power is still not exploited fully in quantum computation. The exploitation of such power definitely requires a deep understanding of the mechanism of quantum loop programs. In this paper, we introduce a general scheme of quantum loops and describe its computational process. The notions of termination and almost termination are proposed for quantum loops, and the function computed by a quantum loop is defined. To show their expressive power, quantum loops are applied in describing quantum walks. Necessary and sufficient conditions for termination and almost termination of a general quantum loop on any mixed input state are presented. A quantum loop is said to be (almost) terminating if it (almost) terminates on any input state. We show that a quantum loop is almost terminating if and only if it is uniformly almost terminating. It is observed that a small disturbance either on the unitary transformation in the loop body or on the measurement in the loop guard can make any quantum loop (almost) terminating. Moreover, a representation of the function computed by a quantum loop is given in terms of finite summations of matrices. To illustrate the notions and results obtained in this paper, two simplest classes of quantum loop programs, one qubit quantum loops, and two qubit quantum loops defined by controlled gates, are carefully examined.

Vijayarangan Natarajan