In this paper,the termination(almost termination)of generalized quantum loop program(for short GQLoop)is firstly investigated,where the loop bodies of GQLoop are described by bit flip channel,depolarizing channel,amplitude damping channel and phase damping channel,respectively.Secondly,when the loop bodies are the embedding of two kinds of GQLoop,the conditions of the termination(almost termination)of GQLoop are addressed.It shows that the conditions of the termination(almost termination)of GQLoop depend on the parameters occuring in the quantum channels.Finally,when the loop bodies are an unitary operation on the principle system and the environment under the open quantum system,after implementing unitary operation,the computed processing of the quantum program is discussed by performing a partial trace over the environment.
In this paper,the termination(almost termination)of generalized quantum loop program(for short GQLoop)is firstly investigated,where the loop bodies of GQLoop are described by bit flip channel,depolarizing channel,amplitude damping channel and phase damping channel,respectively.Secondly,when the loop bodies are the embedding of two kinds of GQLoop,the conditions of the termination(almost termination)of GQLoop are addressed.It shows that the conditions of the termination(almost termination)of GQLoop depend on the parameters occuring in the quantum channels.Finally,when the loop bodies are an unitary operation on the principle system and the environment under the open quantum system,after implementing unitary operation,the computed processing of the quantum program is discussed by performing a partial trace over the environment.
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.
To address the termination problem of the generalized quantum Loop program, in this paper, we first introduce two definitions of termination and almost termination. We show that their expressive power regarding the termination of a program is not sufficient. To compensate for this, we define two other definitions:the nth termination with a specified probability and terminability, and we obtain some conclusions by comparing these four definitions. Secondly, we introduce the definition of the quantum (regular) safety property, which is an important kind of linear-time property of quantum Markov chains. We show that the satisfiability probability of the quantum (regular) safety property is equivalent to the unreachability probability of the termination state in the product of the quantum Markov chains. Then, we discuss a checking technique for the quantum regular safety property. By applying this technique, we reduce the termination problem of the generalized quantum Loop program into the satisfiability problem of the quantum regular safety property, and we propose an algorithm to calculate the probability and the termination state of the nth termination and the terminability. To determine the termination state and the probability of a multi-qubit (single-qubit) quantum system, compound quantum system, and nested quantum system, we derive the probability and the termination state of their nth termination and their terminability, and we present expressions for calculating them. Finally, we prove the necessary and sufficient conditions for the finite-step termination and terminability of the generalized quantum Loop program.
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.
This thesis presents the architecture of quantum programming environment, called QSI, along with its related modules and several quantum experiments. The environment is based on one specific quantum language, namely quantum while-language. Some partial experimental results are also presented within QSI.
The first part relates to the architecture, the designing and the implementation of quantum programming environment which provides a new, powerful and flexible environment for developing and implementing quantum programs. First, we study the possible structure of the programming environment which supports a measurement-based case statement and a measurement-based while-loop. These two program constructs are extremely convenient for describing large-scale quantum algorithms, such as quantum random walk-based algorithms. We also define a new assembly language called f-QASM (Quantum Assembly Language with feedback) as an interactive command set. The assembly language is compatible with other low-level instruction sets and can be used to directly drive quantum hardware. Moreover, the simulation of syntax of quantum program and the behaviours within the architecture on the classical computer are discussed. Finally, we consider the work-flow which contains the decomposition of unitary matrix to achieve the goal that executing on Noisy Intermediate-Scale Quantum Computer.
The second part concerns the modules based on quantum programming environment: termination analysis module, detective separable unitary module and quantum control module. Along with the architecture, we bring an essential module - termination analysis module for the loop structure. It can analyze sub-bodies of quantum program and suggest the critical termination information. In addition, we improve the Jordan decomposition step in the original algorithm which consumes extended period for analyzing. This improvement also makes the module more robust on executing. A fast permutation algorithm module clarifies the re-ordering algorithm in case of qubits system. It regenerates the program (unitary operator) which is not in pre-ordered sequence. In the detective separable unitary module, we prove sufficient conditions for separable unitary and its approximate scenario. The result shows there does not exist a universal algorithm for potential parallel executing quantum programs without communications (classical or quantum communications). However, in approximate, there exists a scheme for parallel computing without the help of communication. In this part, two examples for parallel computing are given. Last, in quantum control module, an algorithm is suggested towards automatically generating quantum circuits for quantum case-statement. We believe these analysis modules can help the compiler to optimize the implementation of quantum algorithms.
The third part is devoted to quantum experiment. First, we focus several experiments which can be operated directly by QSI : Qloop, BB84 protocol and Grover search algorithm. After that, with the help of IBM’s QISKit,…
A scheme is proposed for cyclic-controlled quantum operation teleportation (CCQOT) for three sides with EPR and cluster states. Under the control of David, Alice can implement an unknown single-qubit unitary operation on the remote Bob’s quantum system, while Bob can execute a single-qubit unitary operation on Charlie’s quantum system and Charlie can also perform an unknown single-qubit unitary operation on Alice’s quantum system. Our scheme can be generalized to [Formula: see text]) agents involved in the cycle to realize the transmission of single-qubit operations. Moreover, by replacing the quantum channels, we can change the cyclic direction of controlled qunatum operation teleportation (CQOT) from clockwise to counterclockwise. In addition, we discuss our scheme in four types of noisy environments (amplitude-damping, phase-damping, bit-flip and phase-flip noisy environment), and use fidelity to analyze the amount of information lost in the process of CCQOT due to noise. The results show that the fidelity is determined by decoherence rate and amplitude parameters of the final state.
Harmonic oscillator is significantly important in quantum gravity for its dynamical properties. Dynamics of the harmonic oscillator can be modified by inserting a modified uncertainty relation considered in quantum cosmology models such as string theory and quantum loop gravity theory. In this paper, the equation of damped quantum harmonic oscillator has been solved with respect to the modified uncertainty relation and the effects of this modification have been probed in the case of the damped oscillating system.