The architecture of a quantum programming environment

University of Technology Sydney. Faculty of Engineering and Information Technology.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, two impressive experiments: distinguishing unitary gates and Bell states are given on real quantum computer. Finally, we combine QSI with Microsoft’s LIQUi|> to implement quantum case-statement. These experiments significantly show the quantum power and the scalable framework of the quantum programming environment in practice

The Measurement Calculus

Measurement-based quantum computation has emerged from the physics community as a new approach to quantum computation where the notion of measurement is the main driving force of computation. This is in contrast with the more traditional circuit model which is based on unitary operations. Among measurement-based quantum computation methods, the recently introduced one-way quantum computer stands out as fundamental. We develop a rigorous mathematical model underlying the one-way quantum computer and present a concrete syntax and operational semantics for programs, which we call patterns, and an algebra of these patterns derived from a denotational semantics. More importantly, we present a calculus for reasoning locally and compositionally about these patterns. We present a rewrite theory and prove a general standardization theorem which allows all patterns to be put in a semantically equivalent standard form. Standardization has far-reaching consequences: a new physical architecture based on performing all the entanglement in the beginning, parallelization by exposing the dependency structure of measurements and expressiveness theorems. Furthermore we formalize several other measurement-based models: Teleportation, Phase and Pauli models and present compositional embeddings of them into and from the one-way model. This allows us to transfer all the theory we develop for the one-way model to these models. This shows that the framework we have developed has a general impact on measurement-based computation and is not just particular to the one-way quantum computer.Comment: 46 pages, 2 figures, Replacement of quant-ph/0412135v1, the new version also include formalization of several other measurement-based models: Teleportation, Phase and Pauli models and present compositional embeddings of them into and from the one-way model. To appear in Journal of AC

Programming with Quantum Communication

This work develops a formal framework for specifying, implementing, and analysing quantum communication protocols. We provide tools for developing simple proofs and analysing programs which involve communication, both via quantum channels and exhibiting the LOCC (local operations, classical communication) paradigm

Quantitative Robustness Analysis of Quantum Programs (Extended Version)

Quantum computation is a topic of significant recent interest, with practical advances coming from both research and industry. A major challenge in quantum programming is dealing with errors (quantum noise) during execution. Because quantum resources (e.g., qubits) are scarce, classical error correction techniques applied at the level of the architecture are currently cost-prohibitive. But while this reality means that quantum programs are almost certain to have errors, there as yet exists no principled means to reason about erroneous behavior. This paper attempts to fill this gap by developing a semantics for erroneous quantum while-programs, as well as a logic for reasoning about them. This logic permits proving a property we have identified, called $\epsilon$-robustness, which characterizes possible "distance" between an ideal program and an erroneous one. We have proved the logic sound, and showed its utility on several case studies, notably: (1) analyzing the robustness of noisy versions of the quantum Bernoulli factory (QBF) and quantum walk (QW); (2) demonstrating the (in)effectiveness of different error correction schemes on single-qubit errors; and (3) analyzing the robustness of a fault-tolerant version of QBF.Comment: 34 pages, LaTeX; v2: fixed typo

Concrete resource analysis of the quantum linear system algorithm used to compute the electromagnetic scattering cross section of a 2D target

We provide a detailed estimate for the logical resource requirements of the quantum linear system algorithm (QLSA) [Phys. Rev. Lett. 103, 150502 (2009)] including the recently described elaborations [Phys. Rev. Lett. 110, 250504 (2013)]. Our resource estimates are based on the standard quantum-circuit model of quantum computation; they comprise circuit width, circuit depth, the number of qubits and ancilla qubits employed, and the overall number of elementary quantum gate operations as well as more specific gate counts for each elementary fault-tolerant gate from the standard set {X, Y, Z, H, S, T, CNOT}. To perform these estimates, we used an approach that combines manual analysis with automated estimates generated via the Quipper quantum programming language and compiler. Our estimates pertain to the example problem size N=332,020,680 beyond which, according to a crude big-O complexity comparison, QLSA is expected to run faster than the best known classical linear-system solving algorithm. For this problem size, a desired calculation accuracy 0.01 requires an approximate circuit width 340 and circuit depth of order $10^{25}$ if oracle costs are excluded, and a circuit width and depth of order $10^8$ and $10^{29}$, respectively, if oracle costs are included, indicating that the commonly ignored oracle resources are considerable. In addition to providing detailed logical resource estimates, it is also the purpose of this paper to demonstrate explicitly how these impressively large numbers arise with an actual circuit implementation of a quantum algorithm. While our estimates may prove to be conservative as more efficient advanced quantum-computation techniques are developed, they nevertheless provide a valid baseline for research targeting a reduction of the resource requirements, implying that a reduction by many orders of magnitude is necessary for the algorithm to become practical.Comment: 37 pages, 40 figure