Related papers: Quantum Circuits for Elementary Cellular Automata

Over an arbitrary commutative ring $R$, we develop a theory of quantum cellular automata. We then use algebraic K-theory to construct a space $\mathbf{Q}(X)$ of quantum cellular automata (QCA) on a given metric space $X$. In most cases of…

A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…

Gate-level quantum circuits are often derived manually from higher level algorithms. While this suffices for small implementations and demonstrations, ultimately automatic circuit design will be required to realise complex algorithms using…

Two different algorithms are presented for generating a quantum circuit realization of a matrix representing a permutation on $2^n$ letters. All circuits involve $n$ qubits and only use multi--controlled Toffoli gates. The first algorithm…

We define syntax and semantics of quantum circuits, allowing measurement gates and classical channels. We define circuit-based quantum algorithms and prove that, semantically, any such algorithm is equivalent to a single measurement that…

Starting with the basic control system model often employed in NMR pulse design, we derive more realistic control system models taking into account effects such as off-resonant excitation for systems with fixed inter-qubit coupling…

We construct quantum circuits for solving one-dimensional Schr\"odinger equations. Simulations of three typical examples, i.e., harmonic oscillator, square-well and Coulomb potential, show that reasonable results can be obtained with eight…

In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in…

We demonstrate that conditional as well as unconditional basic operations which are prerequisite for universal quantum gates can be performed with almost 100% fidelity within a strongly interacting two-electron quantum ring. Both sets of…

We present a scheme to perform universal quantum computation using global addressing techniques as applied to a physical system of endohedrally doped fullerenes. The system consists of an ABAB linear array of Group V endohedrally doped…

Quantum simulation algorithms often require numerous ancilla qubits and deep circuits, prohibitive for near-term hardware. We introduce a framework for simulating quantum channels using ensembles of low-depth circuits in place of many-qubit…

A key open question in quantum computing is whether quantum algorithms can potentially offer a significant advantage over classical algorithms for tasks of practical interest. Understanding the limits of classical computing in simulating…

This chapter is a short pedagogical introduction to the use of quantum logic for the simulation of complex quantum systems, including a simulation example on actual quantum hardware.

Quantum cellular automata (QCA) constitute space and time homogeneous discrete models for quantum field theories (QFTs). Although QFTs are defined without reference to particles, computations are done in terms of Feynman diagrams, which are…

We propose a classical-quantum hybrid algorithm for machine learning on near-term quantum processors, which we call quantum circuit learning. A quantum circuit driven by our framework learns a given task by tuning parameters implemented on…

We investigate the potential of bio-inspired evolutionary algorithms for designing quantum circuits with specific goals, focusing on two particular tasks. The first one is motivated by the ideas of Artificial Life that are used to reproduce…

Traditional algorithms for simulating quantum computers on classical ones require an exponentially large amount of memory, and so typically cannot simulate general quantum circuits with more than about 30 or so qubits on a typical PC-scale…

Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…

We present evidence that operation of QCA (Quantum Cellular Automaton) cells with four dots is possible with an occupancy of 4N+2 electrons per cell (N being an integer). We show that interaction between cells can be described in terms of a…

In this study, we explore the use of molecules and molecular electronics for quantum computing. We construct one-qubit gates using one-electron scattering in molecules, and two-qubit controlled-phase gates using electron-electron scattering…