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Publication# Optimizing Quantum Compilers: Efficient and Effective Algorithms

Abstract

Quantum computing has made significant progress in recent years, with Google and IBM releasing quantum computers with 72 and 50 qubits, respectively. Google has also achieved quantum supremacy with its 54-qubit device, and IBM has announced the release of the Osprey quantum computer with 433 qubits. These developments suggest that quantum computers with even greater qubit counts may be available in the near future.This upcoming period is termed Noisy Intermediate Scale Quantum (NISQ) era, because of the noisy characteristics of near-term devices.Computation on NISQ hardware is modeled using a library of supported quantum gates which can be directly implemented on it and a coupling graph that specifies available qubits interactions for multi-qubit quantum gates. While improvements to quantum hardware are continuously being made by experimentalists, quantum computing experts can contribute to the utility of quantum devices by developing software. This software would aim to adapt textbook quantum algorithms (e.g., for factoring or quantum simulation) to hardware constraints, that include: (1) limited number of qubits, (2) limited connectivity between qubits, (3) limited hardware-specific gate sets, and (4) limited circuit depth due to noise. Algorithms adapted to these constraints will likely look dramatically different from their textbook counterparts. Such software, which performs the task of translating quantum algorithms into quantum circuits according to hardware constraints, is called a quantum compiler. In conclusion, without a good compiler, most quantum algorithms are not applicable in practice.Quantum compilers typically undertake three primary tasks: quantum state preparation, circuit synthesis, and qubit mapping. Quantum state preparation involves preparing the initial state of the quantum system before running the algorithm. The preparation of such a state itself requires a computation performed by a quantum circuit. This task can be challenging, as quantum algorithms assume some specific initial states in superposition before performing the desired application-specific computations. Circuit synthesis involves the process of constructing a quantum circuit that implements the desired quantum algorithm. Qubit mapping is another important task for quantum compilers, which involves mapping the logical qubits of the algorithm to the physical qubits of the quantum computer. In this thesis, I focus on the first two tasks of quantum compilers, quantum state preparation, and circuit synthesis. These tasks are essential for the successful execution of quantum algorithms, and developing efficient and effective algorithms for these tasks is crucial for the continued advancement of quantum computing.

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Ontological neighbourhood

Quantum computing

A quantum computer is a computer that exploits quantum mechanical phenomena. At small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior, specifically quantum superposition and entanglement, using specialized hardware that supports the preparation and manipulation of quantum states. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer.

Quantum programming

Quantum programming is the process of designing or assembling sequences of instructions, called quantum circuits, using gates, switches, and operators to manipulate a quantum system for a desired outcome or results of a given experiment. Quantum circuit algorithms can be implemented on integrated circuits, conducted with instrumentation, or written in a programming language for use with a quantum computer or a quantum processor. With quantum processor based systems, quantum programming languages help express quantum algorithms using high-level constructs.

Quantum supremacy

In quantum computing, quantum supremacy, quantum primacy or quantum advantage is the goal of demonstrating that a programmable quantum computer can solve a problem that no classical computer can solve in any feasible amount of time, irrespective of the usefulness of the problem. The term was coined by John Preskill in 2012, but the concept dates back to Yuri Manin's 1980 and Richard Feynman's 1981 proposals of quantum computing.

Quantum computers have the potential to surpass conventional computing, but they are hindered by noise which induces errors that ultimately lead to the loss of quantum information. This necessitates the development of quantum error correction strategies fo ...

Advancing quantum technologies depends on the precise control of individual quantum systems, the so-called qubits, and the exploitation of their quantum properties. Nowadays, expanding the number of qubits to be entangled is at the core of the developments ...

Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. Access to a computational space that incorporates quantum effects, such as superposition ...