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The topological color code and the toric code are two leading candidates for realizing fault-tolerant quantum computation. Here we show that the color code on a $d$-dimensional closed manifold is equivalent to multiple decoupled copies of…
A geometrical description of three qubit entanglement is given. A part of the transformations corresponding to stochastic local operations and classical communication on the qubits is regarded as a gauge degree of freedom. Entangled states…
We explore the concept of a graph homomorphism through the lens of C$^*$-algebras and operator systems. We start by studying the various notions of a quantum graph homomorphism and examine how they are related to each other. We then define…
We present a native three-qubit entangling gate that exploits engineered interactions to realize control-control-target and control-target-target operations in a single coherent step. Unlike conventional decompositions into multiple…
Here a finite-Lieb-lattice quantum computing circuit consisting of spin-1/2 quantum bits (qubits) and triplet couplers is designed. Important gradient - quantum entanglement - is analysed. This type of design could be realised in a vast…
We construct a quantum extension of the (classical) three-coloring model introduced by Baxter [J.Math.Phys.11, 784 (1970)] for which the ground state can be computed exactly along a continuous line of Rokhsar-Kivelson solvable points. The…
Optical computing harnesses the speed of light to perform vector-matrix operations efficiently. It leverages interference, a cornerstone of quantum computing algorithms, to enable parallel computations. In this work, we interweave quantum…
Universal quantum computation may be realized based on quantum walk, by formulating it as a scattering problem on a graph. In this paper, we simulate quantum gates through electric circuits, following a recent report that a one-dimensional…
We define the Bloch spectrum of a quantum graph to be the collection of the spectra of a family of Schrodinger operators parametrized by the cohomology of the quantum graph. We show that the Bloch spectrum determines the Albanese torus, the…
We define solvable quantum mechanical systems on a Hilbert space spanned by bipartite ribbon graphs with a fixed number of edges. The Hilbert space is also an associative algebra, where the product is derived from permutation group…
We illustrate an isomorphic representation of the observable algebra for quantum mechanics in terms of the functions on the projective Hilbert space, and its Hilbert space analog, with a noncommutative product in terms of explicit…
The development of quantum codes with good error correction parameters and useful sets of transversal gates is a problem of major interest in quantum error-correction. Abundant prior works have studied transversal gates which are restricted…
In this expository paper we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we focus on quantum information geometry and ZX-calculus,…
Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have…
We introduce a novel quantum algorithm for determining graph connectedness using a constant number of measurements. The algorithm can be extended to find connected components with a linear number of measurements. It relies on non-unitary…
Quantum computing in terms of geometric phases, i.e. Berry or Aharonov-Anandan phases, is fault-tolerant to a certain degree. We examine its implementation based on Zeeman coupling with a rotating field and isotropic Heisenberg interaction,…
We examine a generic three state mechanism which realizes all fundamental single and double qubit quantum logic gates operating under the effect of adiabatically controllable static (radiation free) bias couplings between the states. At the…
In this paper we describe and thoroughly discuss three reported experiments in quantum optics (QO) involving interferometers and non-linear crystals. We show that by using a graphical method and an over-simplified model of the parametric…
We study twists of the Burkhardt quartic threefold over non-algebraically closed base fields of characteristic different from 2,3,5. We show they all admit quartic models in projective four-space. We identify a Galois-cohomological…
In this work, we develop a graphical calculus for multi-qudit computations with generalized Clifford algebras, building off the algebraic framework developed in our prior work. We build our graphical calculus out of a fixed set of graphical…