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As quantum computing resources remain scarce and error rates high, minimizing the resource consumption of quantum circuits is essential for achieving practical quantum advantage. Here we consider the natural problem of, given a circuit $C$,…
We study the quantum complexity of the static set membership problem: given a subset S (|S| \leq n) of a universe of size m (m \gg n), store it as a table of bits so that queries of the form `Is x \in S?' can be answered. The goal is to use…
It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical…
Many computational problems are subject to a quantum speed-up: one might find that a problem having an O(n^3)-time or O(n^2)-time classic algorithm can be solved by a known O(n^1.5)-time or O(n)-time quantum algorithm. The question…
The concept of quantum computing has inspired a whole new generation of scientists, including physicists, engineers, and computer scientists, to fundamentally change the landscape of information technology. With experimental demonstrations…
We describe Qiskit, a software development kit for quantum information science. We discuss the key design decisions that have shaped its development, and examine the software architecture and its core components. We demonstrate an…
Quantum computing is entering a period in which progress will be shaped as much by advances in computer science as by improvements in hardware. The central thesis of this report is that early fault-tolerant quantum computing shifts many of…
As we enter the era of useful quantum computers we need to better understand the limitations of classical support hardware, and develop mitigation techniques to ensure effective qubit utilisation. In this paper we discuss three key…
We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem $k$-QSAT on large random graphs. As an approximation strategy, we optimize the solution…
We present quantum complexity lower and upper bounds for independent set problems in graphs. In particular, we give quantum algorithms for computing a maximal and a maximum independent set in a graph. We present applications of these…
Quantum error correction (QEC) is essential for operating quantum computers in the presence of noise. Here, we accurately decode arbitrary Calderbank-Shor-Steane (CSS) codes via the maximum satisfiability (MaxSAT) problem. We show how to…
Quantum computing promises exponential improvements in solving large systems of partial differential equations (PDE), which forms a bottleneck in high-resolution computational fluid dynamics (CFD) simulations, in, among others, aerospace…
An algorithm for a particular problem may find some instances of the problem easier and others harder to solve, even for a fixed input size. We numerically analyse the relative hardness of MAX 2-SAT problem instances for various…
In this dissertation, we study the intersection of quantum computing and supervised machine learning algorithms, which means that we investigate quantum algorithms for supervised machine learning that operate on classical data. This area of…
More than a speculative technology, quantum computing seems to challenge our most basic intuitions about how the physical world should behave. In this thesis I show that, while some intuitions from classical computer science must be…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…
Quantum information science explores the frontier of highly complex quantum states, the "entanglement frontier." This study is motivated by the observation (widely believed but unproven) that classical systems cannot simulate highly…
To date, all proposed quantum algorithms for simulating quantum field theory (QFT) simulate (continuous-time) Hamiltonian lattice QFT as a stepping stone. Two overlooked issues are how large we can take the timestep in these simulations…
Despite the fundamental role the Quantum Satisfiability (QSAT) problem has played in quantum complexity theory, a central question remains open: At which local dimension does the complexity of QSAT transition from "easy" to "hard"? Here, we…
Significant advances in the development of computing devices based on quantum effects and the demonstration of their use to solve various problems have rekindled interest in the nature of the "quantum computational advantage." Although…