Quantum computers have already shown high potential in solving complex computational problems much more efficiently compared to the typical conventional supercomputers. One major challenge in the field of quantum computing is to implement the major operations of the conventional computers using the available quantum hardware (quantum gates). Such operations are the arithmetic operations as well as decoding and multiplexing. An obvious burden is the absence of quantum gates that directly implement the fundamental Boolean operations like AND and OR. Moreover, care should be taken in order to reduce the costs involved when implementing a quantum circuit. In this paper, we present an oracle-based approach to implement quantum decoding and multiplexing in a joint circuit. The use of oracles necessarily implies that some type of quantum programming will be used. A quantum program is a process organized in a sequence of computations whose data elements are selected from the set of the known quantum gates. In our approach, the oracles are used as pre-programmed black boxes that determine if a datum should be directed from the input to the output. The important idea behind our scheme is that the oracles operate in parallel, therefore their selection decisions are taken simultaneously, while the approaches found in the literature implement sequential circuits with feedbacks from the outputs to inputs that burden the overall performance. We have used Qiskit open-source software development kit to verify the correctness of our design through extensive simulations.
Quantum computers have already shown high potential in solving complex computational problems much more efficiently compared to the typical conventional supercomputers. One major challenge in the field of quantum computing is to implement the major operations of the conventional computers using the available quantum hardware (quantum gates). Such operations are the arithmetic operations as well as decoding and multiplexing. An obvious burden is the absence of quantum gates that directly implement the fundamental Boolean operations like AND and OR. Moreover, care should be taken in order to reduce the costs involved when implementing a quantum circuit. In this paper, we present an oracle-based approach to implement quantum decoding and multiplexing in a joint circuit. The use of oracles necessarily implies that some type of quantum programming will be used. A quantum program is a process organized in a sequence of computations whose data elements are selected from the set of the known quantum gates. In our approach, the oracles are used as pre-programmed black boxes that determine if a datum should be directed from the input to the output. The important idea behind our scheme is that the oracles operate in parallel, therefore their selection decisions are taken simultaneously, while the approaches found in the literature implement sequential circuits with feedbacks from the outputs to inputs that burden the overall performance. We have used Qiskit open-source software development kit to verify the correctness of our design through extensive simulations.
Although the concept of quantum computing has existed for decades, the technology needed to successfully implement a quantum computing system has not yet reached the level of sophistication, reliability, and scalability necessary for commercial viability until very recently. Significant progress on this front was made in the past few years, with IBM planning to create a 1000-qubit chip by the end of 2023, and Google already claiming to have achieved quantum supremacy. Other major industry players such as Intel and Microsoft have also invested significant amounts of resources into quantum computing research. Any viable computing system requires both hardware and software to work together harmoniously in order to perform useful computations. While the achievements of IBM and other companies represent a large step forward for quantum hardware, many gaps remain to be filled with respect to the corresponding software. Specifically, there is currently no clear path towards a complete process for translating quantum algorithms into physical operations that are directly executable on quantum hardware. Such a process is analogous to a compiler that translates programs written in a high-level language into executable machine instructions on a conventional digital computer, and it is necessary if quantum computers are to be harnessed to perform practically useful computations. Existing work has addressed individual components of this process, but so far no unified method for translating the whole of a quantum algorithm into executable operations has been described. I make substantial progress towards filling this gap by describing a set of high-level and low-level quantum circuit design techniques, which when taken together reduce the need of a circuit designer to be concerned with low-level details. On the high-level side, I describe an approach or strategy to designing quantum oracles for Grover's algorithm that allows it to be applied to several types of problems. This approach involves designing oracles in terms of high-level blocks such as counters, multiplexers, comparators, and arbitrary Boolean functions. The implementations of these blocks in terms of lower-level quantum gates are demonstrated in a way that makes it clear that scaled-up versions of them can be generated in a completely automated fashion. For a specific class of problems, which I call state-space path planning problems, I also introduce a paradigm for quantum oracle design that involves representing the problem in terms of individual states and moves. Problems of this sort have applications in robotics and games. Low-level techniques that I introduce
Quantum computers have already shown significant potential to solve specific problems more efficiently than conventional supercomputers. A major challenge towards noisy intermediate-scale quantum computing is characterizing and reducing the various control costs. Quantum programming describes the process of quantum computation as a sequence, whose elements are selected from a finite set of universal quantum gates. Quantum compilation translates quantum programs to ordered pulses to the quantum control devices subsequently and quantum compilation optimization provides a high-level solution to reduce the control cost efficiently. Here, we propose a high-performance compilation strategy for multiplexing quantum control architecture. For representative benchmarks, the utilization efficiency of control devices increased by 49.44% on average in our work, with an acceptable circuit depth expansion executing on several real superconducting quantum computers of IBM.
Oracle quantum programs are a fundamental class of quantum programs that serve as a critical bridge between quantum computing and classical computing. Many important quantum algorithms are built upon oracle quantum programs, making it essential to ensure their correctness during development. Although software testing is a well-established approach for improving program reliability, no systematic method has been developed to test oracle quantum programs. This paper proposes a black-box testing framework designed for general oracle quantum programs. We formally define these programs, establish the foundational theory for their testing, and propose a detailed testing framework. We develop a prototype tool and conduct extensive experimental evaluations to evaluate the effectiveness of the framework. Our results demonstrate that the proposed framework significantly aids developers in testing oracle quantum programs, providing insights to enhance the reliability of quantum software.
Practical realizations of quantum computers are poised to deliver outstanding computational capabilities far beyond the reach of any classical supercomputer. While classical systems are reliably implemented using CMOS technology, the fabrication of quantum hardware has not yet reached a commercially viable level of maturity. Nowadays, many different technologies are being developed as competing candidates to build the first error-corrected quantum computer. Among the software resources required to operate such a system, quantum compilers translate a high-level description of a quantum algorithm into low-level, technology-dependent quantum instructions. Many quantum algorithms, including Shor's and Grover's algorithms, require to compute some classical logic functions on the quantum computer. The first part of this thesis deals with the problem of compiling quantum circuits that perform such classical Boolean functions, called oracles, into a fault-tolerant set of instructions. Oracle circuits often demand many resources in terms of the number of qubits and gates. The focus is on compiling quantum circuits starting from multi-level logic networks representing large Boolean functions while minimizing the resource footprint of the obtained quantum circuits. At the same time, the trade-off between memory resources and the number of operations typical of such a compilation process is explored. As part of the effort in reducing the resources required to perform a given quantum program, I also present some quantum circuit optimization techniques. The researched algorithms leverage data structures and techniques borrowed and adapted from classical logic synthesis, e.g., SAT solvers, LUT mapping, and multi-level logic networks. I implemented all the compilation algorithms presented in this thesis as part of open-source projects. In particular, I develop and maintain caterpillar---a C++ header-only library dedicated to the quantum compilation of oracles and quantum memory management. The second part of this thesis describes how to equip quantum programming language compilers with automatic accuracy management. Despite the availability of many of such languages, resource estimation of quantum algorithms does not yet support taking approximation errors into account. This general methodology is applicable to any programming language and I demonstrate its integration into the Q# compiler. The technique consists of providing language support to ease the accuracy-aware programming task. The user can define accuracy parameters that will be automatically optimized according to a constraint and a cost function directly generated from the source code. In the presented practical evaluations, the constraint function is the overall allowed accuracy, while the cost function is application-dependent and related to the number of gates. During the optimization process, such functions are evaluated hundreds of times. For this reason, we extract them as (near-)symbolic expressions, whose evaluation time does not depend on the quantum algorithm size. The algorithms and the methodologies presented in this thesis are part of a widespread effort of the research community to build a complete and efficient software stack to program and control the first practical universal quantum computer.
The topic of this dissertation stands at the crossroads of two emerging technologies: highly-parallel computing and quantum computing. Both seek to go beyond the limits of current computing practice: in the absence of further miniaturization, highly-parallel computing seeks to increase the available computer power substantially. Quantum Computing looks beyond the classical approach to computation, leveraging quantum-mechanical effects to increase computing power in a fundamental way. In the absence and also in the presence of actual quantum computers it is crucial to support the development of quantum computer applications by creating an appropriate software framework. Creating such a framework currently faces two major research challenges. First, one needs to separate the realization of the quantum computer from the software running on it, whether it is an actual physical or a simulated realization. Our first contribution lies with defining a layered software architecture, ranging from a design tool at the higher abstraction levels to a simulated execution layer underneath. At its core sits a ‘Quantum Virtual Machine’ using the Measurement Calculus as the underlying quantum computational model. Such a virtual machine layer makes the application developed on top of it oblivious to how it is executed. The simulated execution of this quantum virtual machine is fundamentally a computationally intensive task. Parallel computing offers a way to throw more computational resources at the problem, in the light of the saturation of sequential performance of current computers. Simulation is the domain of the second challenge, as it has very high performance requirements. The simulation problem thus becomes: how does one expose the inherent parallelism of quantum computing simulation in a fundamental way, so as to be usable for the highly-parallel computers to come? Our second contribution is to provide a formal translation of quantum programs to highly-parallel dataflow computations, and to develop a virtual environment that compiles and executes such programs. This work demonstrates several properties of both the formal as well as the virtual level of computation that validate our approach.
This paper introduces a comprehensive quantum calculator using Qiskit that integrates quantum arithmetic and logic functions into a single calculator. The calculator relies on quantum Fourier transforms (QFT), controlled-phase gates, and quantum modular arithmetic to perform basic arithmetic operations such as addition, subtraction, and multiplication. These arithmetic techniques used quantum parallelism and interference to perform calculations more efficiently, particularly for tasks involving large numerical inputs. Numerical values are stored in qubit registers and processed using QFT-based circuits, which enable efficient and reversible mathematical computations. In addition to arithmetic operations, the calculator also implements quantum logic algorithms, including Grover’s Search and the Deutsch-Jozsa algorithm. Grover’s algorithm is an unstructured search algorithm that operates by constructing an oracle and iteratively amplifying the probability amplitude of the target solution. This amplitude amplification significantly increases the likelihood of measuring the desired outcome. Due to this property, Grover’s algorithm has practical relevance in applications such as database searching and solving combinatorial optimization problems. The Deutsch-Jozsa algorithm determines whether or not a certain Boolean function is constant or balanced and offers an exponential speed up compared to classical methods for this class of problem. A key fundamental function of the calculator is the ability to generate hybrid quantum circuits that support both arithmetic and logical functions. That allows the exploration of simple as well as complex problem-solving strategies that take advantage of both quantum arithmetic and decision-making algorithms. For instance, combining Grover’s amplification with function characterizations from the Deutsch-Jozsa algorithm provides not only interesting circuit configurations but also adds value to the possibilities of the algorithms. This research offers a modular idea and allows exploring the fundamental principles of quantum computing generally speaking and will be a valuable resource for educational as well as research purposes in the rapidly growing field of quantum algorithm development.