Related papers: Efficient classical simulation of the Deutsch-Jozs…
Quantum computers are believed to surpass the classical ones. Moreover, it is claimed that this belief reaches the level of a mathematically proven fact within the oracle model of computation. Here we impair the whole class of the so-called…
We study the advantage of pure-state quantum computation without entanglement over classical computation. For the Deutsch-Jozsa algorithm we present the maximal subproblem that can be solved without entanglement, and show that the algorithm…
Deutsch-Jozsa (DJ) problem is one of the most important problems demonstrating the power of quantum algorithm. DJ problem can be described as a Boolean function $f$: $\{0,1\}^n\rightarrow \{0,1\}$ with promising it is either constant or…
Digital quantum computers promise exponential speedups in performing quantum time-evolution, providing an opportunity to simulate quantum dynamics of complex systems in physics and chemistry. However, the task of extracting desired quantum…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
Insofar as quantum computation is faster than classical, it appears to be irreversible. In all quantum algorithms found so far the speed-up depends on the extra-dynamical irreversible projection representing quantum measurement. Quantum…
State-of-the-art cosmological simulations on classical computers are limited by time, energy, and memory usage. Quantum computers can perform some calculations exponentially faster than classical computers, using exponentially less energy…
In the effort to develop useful quantum computers simulating quantum machines with conventional computing resources is a key capability. Such simulations will always face limits preventing the emulation of quantum computers of substantial…
Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability…
Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and…
The Church-Turing thesis asserts that if a partial strings-to-strings function is effectively computable then it is computable by a Turing machine. In the 1930s, when Church and Turing worked on their versions of the thesis, there was a…
It is generally believed that entanglement is essential for quantum computing. We present here a few simple examples in which quantum computing without entanglement is better than anything classically achievable, in terms of the reliability…
Let a classical algorithm be determined by sequential applications of a black box performing one step of this algorithm. If we consider this black box as an oracle which gives a value F(a) for any query a, we can compute T sequential…
Quantum algorithms could efficiently solve certain classically intractable problems by exploiting quantum parallelism. To date, whether the quantum entanglement is useful or not for quantum computing is still a question of debate. Here, we…
Two models of computer, a quantum and a classical "chemical machine" designed to compute the relevant part of Shor's factoring algorithm are discussed. The comparison shows that the basic quantum features believed to be responsible for the…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
The speed-up provided by quantum algorithms with respect to their classical counterparts is at the origin of scientific interest in quantum computation. However, the fundamental reasons for such a speed-up are not yet completely understood…
Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory, but offer higher accuracy. Accordingly, quantum computers have been…
The Deustch-Jozsa problem is one of the most basic ways to demonstrate the power of quantum computation. Consider a Boolean function f : {0,1}^n to {0,1} and suppose we have a black-box to compute f. The Deutsch-Jozsa problem is to…