Related papers: Improved constructions of quantum automata

Time-space tradeoff has been studied in a variety of models, such as Turing machines, branching programs, and finite automata, etc. While communication complexity as a technique has been applied to study finite automata, it seems it has not…

We introduce a quantum cellular automaton that achieves approximate phase-covariant cloning of qubits. The automaton is optimized for 1-to-2N economical cloning. The use of the automaton for cloning allows us to exploit different foliations…

The (meta)logic underlying classical theory of computation is Boolean (two-valued) logic. Quantum logic was proposed by Birkhoff and von Neumann as a logic of quantum mechanics more than sixty years ago. The major difference between Boolean…

We study two-level q-deformed angular momentum states and us- ing q-deformed harmonic oscillators, we provide a framework for con- structing qubits and quantum gates. We also present the construction of some basic quantum gates including…

Using quantum algorithms, we obtain, for accuracy $\epsilon>0$ and confidence $1-\delta,0<\delta<1,$ a new sample complexity upper bound of $O((\mbox{log}(\frac{1}{\delta}))/\epsilon)$ as $\epsilon,\delta\rightarrow 0$ for a general…

Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant…

Quantum computers are believed to bring computational advantages in simulating quantum many body systems. However, recent works have shown that classical machine learning algorithms are able to predict numerous properties of quantum systems…

Quantum computing offers advantages over classical computation, yet the precise features that set the two apart remain unclear. In the standard quantum circuit model, adding a 1-qubit basis-changing gate -- commonly chosen to be the…

We give the quantum subset construction of orthomodular lattice-valued finite automata, then we show the equivalence between orthomodular lattice-valued finite automata, orthomodular lattice-valued deterministic finite automata and…

One of the key challenges in quantum machine learning is finding relevant machine learning tasks with a provable quantum advantage. A natural candidate for this is learning unknown Hamiltonian dynamics. Here, we tackle the supervised…

Randomization of quantum states is the quantum analogue of the classical one-time pad. We present an improved, efficient construction of an approximately randomizing map that uses O(d/epsilon^2) Pauli operators to map any d-dimensional…

A simple probabilistic cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions. Occupation numbers for fermions are classical bits or Ising spins. The automaton acts deterministically…

1-way quantum finite automata are deterministic and reversible in nature, which greatly reduces its accepting property. In fact the set of languages accepted by 1-way quantum finite automata is a proper subset of regular languages. In this…

We outline refined versions of two major quantum algorithms for performing principal component analysis and solving linear equations. Our methods are exponentially faster than their classical counterparts and even previous quantum…

We introduce a versatile method for preparing a quantum state whose amplitudes are given by some known function. Unlike existing approaches, our method does not require handcrafted reversible arithmetic circuits, or quantum table reads, to…

The common structure of the space of pure states $P$ of a classical or a quantum mechanical system is that of a Poisson space with a transition probability. This is a topological space equipped with a Poisson structure, as well as with 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…

Motivated by the randomized generation of slowly synchronizing automata, we study automata made of permutation letters and a merging letter of rank $ n\!-\!1 $. We present a constructive randomized procedure to generate synchronizing…

We study structural restrictions on biautomata such as, e.g., acyclicity, permutation-freeness, strongly permutation-freeness, and orderability, to mention a few. We compare the obtained language families with those induced by deterministic…

A major hurdle to the deployment of quantum linear systems algorithms and recent quantum simulation algorithms lies in the difficulty to find inexpensive reversible circuits for arithmetic using existing hand coded methods. Motivated by…