Related papers: Quantum Theory from Principles, Quantum Software f…
We present a system of equations between Clifford circuits, all derivable in the ZX-calculus, and formalised as rewrite rules in the Quantomatic proof assistant. By combining these rules with some non-trivial simplification procedures…
We describe how one may go about performing quantum computation with arbitrary "quantum stuff", as long as it has some basic physical properties. Imagine a long strip of stuff, equipped with regularly spaced wires to provide input settings…
Translations between the quantum circuit model and the measurement-based one-way model are useful for verification and optimisation of quantum computations. They make crucial use of a property known as gflow. While gflow is defined for…
The ability to perform a universal set of quantum operations based solely on static resources and measurements presents us with a strikingly novel viewpoint for thinking about quantum computation and its powers. We consider the two major…
The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the…
This paper initiates the study of hidden variables from the discrete, abstract perspective of quantum computing. For us, a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another, into a…
Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n. But using ideas from computational learning theory, we show that "for most practical purposes" one can learn a…
The ZX-calculus is a graphical language for reasoning about quantum computation that has recently seen an increased usage in a variety of areas such as quantum circuit optimisation, surface codes and lattice surgery, measurement-based…
In recent work, Benjamin Schumacher and Michael~D. Westmoreland investigate a version of quantum mechanics which they call "modal quantum theory" but which we prefer to call "discrete quantum theory". This theory is obtained by…
In these proceedings, we review recent advances in applying quantum computing to lattice field theory. Quantum computing offers the prospect to simulate lattice field theories in parameter regimes that are largely inaccessible with the…
Quantum Bayesian Computation (QBC) is an emerging field that levers the computational gains available from quantum computers to provide an exponential speed-up in Bayesian computation. Our paper adds to the literature in two ways. First, we…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules…
This dissertation explores the topics of parameter estimation and model reduction in the context of quantum filtering. Chapters 2 and 3 provide a review of classical and quantum probability theory, stochastic calculus and filtering. Chapter…
These notes introduce quantum computation and quantum error correction, emphasising the importance of stabilisers and the mathematical foundations in basic Lie theory. We begin by using the double cover map $\mathrm{SU}_2 \rightarrow…
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…
We recognize quantum circuit model of computation as factorisable scattering model and propose that a quantum computer is associated with a quantum many-body system solved by the Bethe ansatz. As an typical example to support our…
This book gives a geometry-first, hardware-aware route through quantum-information workflows, with one goal: connect states, circuits, and measurement to deterministic classical pipelines that make hybrid quantum systems run. Part 1…
We present a conceptually clear introduction to quantum theory, deriving the theory from scratch from the point of view of quantum information. Different subsets of these lectures were taught to a wide variety of audiences, including…
I summarize a research program that aims to reconstruct quantum theory from a fundamental physical principle that, while a quantum system has no intrinsic hidden variables, it can be understood using a reference measurement. This program…