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A quantum computer promises efficient processing of certain computational tasks that are intractable with classical computer technology. While basic principles of a quantum computer have been demonstrated in the laboratory, scalability of…
It is shown that in two-state quantum theory, a generic quantum state can be described by a non-computable real number. In terms of this, the criterion for measurement outcome is simply and deterministically defined. This demonstration is…
Quantum circuit compilation comprises many computationally hard reasoning tasks that nonetheless lie inside #$\mathbf{P}$ and its decision counterpart in $\mathbf{PP}$. The classical simulation of general quantum circuits is a core example.…
Realistic simulation of quantum materials is a central goal of quantum computation. Although quantum processors have advanced rapidly in scale and fidelity, it has remained unclear whether pre-fault-tolerant devices can perform…
We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are obtained through sequential probing of quantum systems; no presuppositions…
We give a new theoretical solution to a leading-edge experimental challenge, namely to the verification of quantum computations in the regime of high computational complexity. Our results are given in the language of quantum interactive…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…
We discuss a general model for effective quantum field theories (QFTs), which for example comprises quantum chromodynamics and quantum electrodynamics. We assume in the model a perturbative expansion of the Lagrangian with respect to a…
A quantum computer has now solved a specialized problem believed to be intractable for supercomputers, suggesting that quantum processors may soon outperform supercomputers on scientifically important problems. But flaws in each quantum…
In recent years, applications of quantum simulation have been developed to study properties of strongly interacting theories. This has been driven by two factors: on the one hand, needs from theorists to have access to physical observables…
We propose a model of a programmable quantum processing device realizable with existing nanophotonic technologies and which can be viewed as a basis for new high performance hardware architectures. We present protocols and their physical…
A formulation of quaternionic quantum mechanics ($\mathbb{H}$QM) is presented in terms of a real Hilbert space. Using a physically motivated scalar product, we prove the spectral theorem and obtain a novel quaternionic Fourier series. After…
Quantum computers promise significant speedups in solving problems intractable for conventional computers but, despite recent progress, remain limited in scaling and availability. Therefore, quantum software and hardware development heavily…
Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…
Feynman's prescription for a quantum simulator was to find a hamitonian for a system that could serve as a computer. P\'olya and Hilbert conjecture was to demonstrate Riemann's hypothesis through the spectral decomposition of hermitian…
This article presents an argument for why quantum computers could unlock new methods for machine learning. We argue that spectral methods, in particular those that learn, regularise, or otherwise manipulate the Fourier spectrum of a machine…
This tutorial introduces quantum computing with a focus on the applicability of formal methods in this relatively new domain. We describe quantum circuits and convey an understanding of their inherent combinatorial nature and the…
In quantum process tomography, it is possible to express the experimenter's prior information as a sequence of quantum operations, i.e., trace-preserving completely positive maps. In analogy to de Finetti's concept of exchangeability for…
(Abridged.) Quantum computers promise to solve some problems exponentially faster than traditional computers, but we still do not fully understand why this is the case. While the most studied model of quantum computation uses qubits, which…