Related papers: On The Power of Exact Quantum Polynomial Time
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
We construct an oracular (i.e., black box) problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different…
In classical computation, a "write-only memory" (WOM) is little more than an oxymoron, and the addition of WOM to a (deterministic or probabilistic) classical computer brings no advantage. We prove that quantum computers that are augmented…
In this note we study the power of so called query-limited computers. We compare the strength of a classical computer that is allowed to ask two questions to an NP-oracle with the strength of a quantum computer that is allowed only one such…
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…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
Quantum computers are widely believed have an advantage over classical computers, and some have even published some empirical evidence that this is the case. However, these publications do not include a rigorous proof of this advantage,…
Quantum information science explores the frontier of highly complex quantum states, the "entanglement frontier." This study is motivated by the observation (widely believed but unproven) that classical systems cannot simulate highly…
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…
The potential of the exact quantum information processing is an interesting, important and intriguing issue. For examples, it has been believed that quantum tools can provide significant, that is larger than polynomial, advantages in the…
It is well known, and appreciated, that quantum computers have the potential to be the most powerful computational devices ever created. This newfound power comes from a quantum parallelism effect that allows the computer to be in multiple…
We demonstrate the superior capabilities of the recently proposed Lorentz quantum computer (LQC) compared to conventional quantum computers. We introduce an associated computational complexity class termed bounded-error Lorentz quantum…
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…
Quantum computers leverage the principles of quantum mechanics to do computation with a potential advantage over classical computers. While a single classical computer transforms one particular binary input into an output after applying one…
A proof of quantumness is a protocol through which a classical machine can test whether a purportedly quantum device, with comparable time and memory resources, is performing a computation that is impossible for classical computers.…
An efficient quantum algorithm is proposed to solve in polynomial time the parity problem, one of the hardest problems both in conventional quantum computation and in classical computation, on NMR quantum computers. It is based on the…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
It is a widely believed, though unproven, conjecture that the capability of postselection increases the language recognition power of both probabilistic and quantum polynomial-time computers. It is also unknown whether polynomial-time…
Quantum algorithm is constructed which verifies the formulas of predicate calculus in time $O(\sqrt N)$ with bounded error probability, where $N$ is the time required for classical algorithms. This algorithm uses the polynomial number of…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…