Related papers: A Limit on the Speed of Quantum Computation in Det…
To date, quantum computational algorithms have operated on a superposition of all basis states of a quantum system. Typically, this is because it is assumed that some function f is known and implementable as a unitary evolution. However,…
An enduring challenge in computer science is reducing the runtime required to solve computational problems. Quantum computing has attracted significant attention due to its potential to deliver asymptotically faster solutions to certain…
We study parametric integration of functions from the class C^r([0,1]^{d_1+d_2}) to C([0,1]^{d_1}) in the quantum model of computation. We analyze the convergence rate of parametric integration in this model and show that it is always…
Quantum computing's potential is immense, promising super-polynomial reductions in execution time, energy use, and memory requirements compared to classical computers. This technology has the power to revolutionize scientific applications…
A clock is, from an information-theoretic perspective, a system that emits information about time. One may therefore ask whether the theory of information imposes any constraints on the maximum precision of clocks. Here we show a…
A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for…
Majority vote is a basic method for amplifying correct outcomes that is widely used in computer science and beyond. While it can amplify the correctness of a quantum device with classical output, the analogous procedure for quantum output…
In this paper we introduce a measure of genuine quantum incompatibility in the estimation task of multiple parameters, that has a geometric character and is backed by a clear operational interpretation. This measure is then applied to some…
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 examine the effect of previous history on starting a computation on a quantum computer. Specifically, we assume that the quantum register has some unknown state on it, and it is required that this state be cleared and replaced by a…
Quantum fidelity is a central tool in quantum information, quantifying how much two quantum states are similar. Here we propose a limit formula for the quantum fidelity between a mixed state and a pure state. As an example of an…
A general quantum algorithm for solving a problem is discussed. The number of steps required to solve a problem using this method is independent of the number of cases that has to be considered classically. Hence, it is more efficient than…
We consider N quantum systems initially prepared in pure states and address the problem of unambiguously comparing them. One may ask whether or not all $N$ systems are in the same state. Alternatively, one may ask whether or not the states…
Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…
Quantum computing promises to provide the next step up in computational power for diverse application areas. In this review, we examine the science behind the quantum hype, and the breakthroughs required to achieve true quantum advantage in…
We demonstrate the applicability of a universal gate set in the parity encoding, which is a dual to the standard gate model, by exploring several quantum gate algorithms such as the quantum Fourier transform and quantum addition. Embedding…
We examine the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}^N in the black-box model. We show that, in the black-box model, the exponential quantum speed-up obtained for partial functions…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identified when quantum…
While quantum computers hold the promise of significant computational speedups, the limited size of early quantum machines motivates the study of space-bounded quantum computation. We relate the quantum space complexity of computing a…
The integer complexity $f(n)$ of a positive integer $n$ is defined as the minimum number of 1's needed to represent $n$, using additions, multiplications and parentheses. We present two simple and faster algorithms for computing the integer…