Related papers: On Computational Power of Quantum Read-Once Branch…
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box and the aim is to compute function value for arbitrary input using as few queries as possible. We concentrate on quantum…
The query model (or black-box model) has attracted much attention from the communities of both classical and quantum computing. Usually, quantum advantages are revealed by presenting a quantum algorithm that has a better query complexity…
In this paper we propose a new approach to quantum neural networks. Our multi-layer architecture avoids the use of measurements that usually emulate the non-linear activation functions which are characteristic of the classical neural…
Loading functions into quantum computers represents an essential step in several quantum algorithms, such as quantum partial differential equation solvers. Therefore, the inefficiency of this process leads to a major bottleneck for the…
Loop is a powerful program construct in classical computation, but its power is still not exploited fully in quantum computation. The exploitation of such power definitely requires a deep understanding of the mechanism of quantum loop…
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box, but the aim is to compute function value for arbitrary input using as few queries as possible. In this paper we…
Quantum computing is the process of performing calculations using quantum mechanics. This field studies the quantum behavior of certain subatomic particles for subsequent use in performing calculations, as well as for large-scale…
In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs, which provide a graphic description of sequential quantum algorithms. In the first part of the…
The theory of matchgates is of interest in various areas in physics and computer science. Matchgates occur in e.g. the study of fermions and spin chains, in the theory of holographic algorithms and in several recent works in quantum…
We study the computational power of polynomial threshold functions, that is, threshold functions of real polynomials over the boolean cube. We provide two new results bounding the computational power of this model. Our first result shows…
This paper initiates the study of quantum computing within the constraints of using a polylogarithmic ($O(\log^k n), k\geq 1$) number of qubits and a polylogarithmic number of computation steps. The current research in the literature has…
We describe how one may go about performing quantum computation with arbitrary "quantum stuff", as long as it has some basic physical properties. Imagine a long strip of stuff, equipped with regularly spaced wires to provide input settings…
We prove that quantum computation is polynomially equivalent to classical probabilistic computation with an oracle for estimating the value of simple sums, quadratically signed weight enumerators. The problem of estimating these sums can be…
Quantum algorithms leverage the use of quantumly-controlled data in order to achieve computational advantage. This implies that the programs use constructs depending on quantum data and not just classical data such as measurement outcomes.…
We study supervised learning algorithms in which a quantum device is used to perform a computational subroutine - either for prediction via probability estimation, or to compute a kernel via estimation of quantum states overlap. We design…
A monotone Boolean (OR,AND) circuit computing a monotone Boolean function f is a read-k circuit if the polynomial produced (purely syntactically) by the arithmetic (+,x) version of the circuit has the property that for every prime implicant…
One-time programs are modelled after a black box that allows a single evaluation of a function, and then self-destructs. Because software can, in principle, be copied, general one-time programs exists only in the hardware token model: it…
We introduce partial differential encodings of Boolean functions as a way of measuring the complexity of Boolean functions. These encodings enable us to derive from group actions non-trivial bounds on the Chow-Rank of polynomials used to…
We propose an approach to quantum computing in which quantum gate strengths are parametrized by quantum degrees of freedom, and the capability of the quantum computer to perform desired tasks is monitored and gradually improved by…
Quantum formulas, defined by Yao [FOCS '93], are the quantum analogs of classical formulas, i.e., classical circuits in which all gates have fanout one. We show that any read-once quantum formula over a gate set that contains all…