Related papers: Classical and quantum computation with small space…
Deutsch, Feynman, and Manin viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum Turing machines has shown how these machines can simulate an arbitrary unitary transformation on a…
We introduce Merlin-Arthur (MA) automata where Merlin provides a certificate at the beginning of computation and it is scanned by Arthur before reading the input. We define Merlin-Arthur deterministic, probabilistic, and quantum finite…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
Quantum computers promise to surpass the most powerful classical supercomputers when it comes to solving many critically important practical problems, such as pharmaceutical and fertilizer design, supply chain and traffic optimization, or…
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other…
We show that the algorithmic complexity of any classical algorithm written in a Turing-complete programming language polynomially bounds the number of quantum bits that are required to run and even symbolically execute the algorithm on a…
A large spectrum of problems in classical physics and engineering, such as turbulence, is governed by nonlinear differential equations, which typically require high-performance computing to be solved. Over the past decade, however, the…
The development of quantum computational techniques has advanced greatly in recent years, parallel to the advancements in techniques for deep reinforcement learning. This work explores the potential for quantum computing to facilitate…
Variational quantum algorithms (VQAs) have established themselves as a central computational paradigm in the Noisy Intermediate-Scale Quantum (NISQ) era. By coupling parameterized quantum circuits (PQCs) with classical optimization, they…
This work endeavors to juxtapose the efficacy of machine learning algorithms within classical and quantum computational paradigms. Particularly, by emphasizing on Support Vector Machines (SVM), we scrutinize the classification prowess of…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
We define a quantum computational model over infinite words, called Measure-Many Quantum B\"uchi Automata (MMQBA), which extends Measure-many Quantum Finite automata (MMQFA) to the infinite word setting with B\"uchi acceptance condition. In…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
We find an application in quantum finite automata for the ideas and results of [JL21] and [JL22]. We reformulate quantum finite automata with multiple-time measurements using the algebraic notion of near-ring. This gives a unified…
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…
Broadly applicable quantum advantage, particularly in classical data processing and machine learning, has been a fundamental open problem. In this work, we prove that a small quantum computer of polylogarithmic size can perform large-scale…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
Quantum finite automata (QFAs) literature offers an alternative mathematical model for studying quantum systems with finite memory. As a superiority of quantum computing, QFAs have been shown exponentially more succinct on certain problems…
Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Since quantum systems produce counter-intuitive patterns believed not to be efficiently…
This paper combines quantum computation with classical neural network theory to produce a quantum computational learning algorithm. Quantum computation uses microscopic quantum level effects to perform computational tasks and has produced…