Related papers: ZX-calculus is Complete for Finite-Dimensional Hil…
It was recently shown that a hidden variable model can be constructed for universal quantum computation with magic states on qubits. Here we show that this result can be extended, and a hidden variable model can be defined for quantum…
Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning…
In this paper, we define a realizability semantics for the simply typed $\lambda\mu$-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. This result serves to give characterizations of the…
We propose a generalization of the graphical ZH calculus to qudits of prime-power dimensions $q = p^t$, implementing field arithmetic in arbitrary finite fields. This is an extension of a previous result by Roy which implemented arithmetic…
Quantum computing (QC) represents the future of computing systems, but the tools for reasoning about the quantum model of computation, in which the laws obeyed are those on the quantum mechanical scale, are still a mix of linear algebra and…
Z-complementary code set (ZCCS), an extension of perfect complementary codes (CCs), refers to a set of two-dimensional matrices having zero correlation zone properties. ZCCS can be used in various multi-channel systems to support, for…
A catalysis state is a quantum state that is used to make some desired operation possible or more efficient, while not being consumed in the process. Recent years have seen catalysis used in state-of-the-art protocols for implementing magic…
Systematic discovery of optimization paths in quantum circuit simplification remains a challenge. Today, ZX-calculus, a computing model for quantum circuit transformation, is attracting attention for its highly abstract graph-based…
Quantum error-correcting codes (QECC's) are needed to combat the inherent noise affecting quantum processes. Using ZX calculus, we represent QECC's in a form called a ZX diagram, consisting of a tensor network. In this paper, we present…
We study the topological $\mu$-calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability and FMP over general topological spaces, as well as over $T_0$ and $T_D$ spaces. We also investigate…
Topological quantum computing is a way of allowing precise quantum computations to run on noisy and imperfect hardware. One implementation uses surface codes created by forming defects in a highly-entangled cluster state. Such a method of…
Today's quantum computers operate with a binary encoding that is the quantum analog of classical bits. Yet, the underlying quantum hardware consists of information carriers that are not necessarily binary, but typically exhibit a rich…
Simulating physical systems on near-term quantum computers often requires preparing states within constrained subspaces, like those with fixed particle number or spin. We use Lie algebraic techniques to prove that hardware-efficient gates…
The field of quantum machine learning (QML) explores how quantum computers can be used to more efficiently solve machine learning problems. As an application of hybrid quantum-classical algorithms, it promises a potential quantum advantages…
In the near term, programming quantum computers will remain severely limited by low quantum volumes. Therefore, it is desirable to implement quantum circuits with the fewest resources possible. For the common Clifford+T circuits, most…
This paper presents a novel approach to quantum architecture search by integrating the techniques of ZX-calculus with Genetic Programming (GP) to optimize the structure of parameterized quantum circuits employed in Quantum Machine Learning…
Formal mathematics and computer science proofs are formalized using Hilbert-Russell-style logical systems which are designed to not admit paradoxes and self-refencing reasoning. These logical systems are natural way to describe and reason…
Quantum computing holds great promise for surpassing the limits of classical devices in many fields. Despite impressive developments, however, current research is primarily focused on qubits. At the same time, quantum hardware based on…
Despite outstanding performance in many tasks, language models are notoriously inclined to make factual errors in tasks requiring arithmetic computation. We address this deficiency by creating Calc-X, a collection of datasets that…
The quantum cohomology algebra of a projective manifold X is the cohomology H(X,Q) endowed with a different algebra structure, which takes into account the geometry of rational curves in X. We show that this algebra takes a remarkably…