Related papers: Theory of the Quantum Speed Up
Quantum computers are predicted to outperform classical ones for solving partial differential equations, perhaps exponentially. Here we consider a prototypical PDE - the heat equation in a rectangular region - and compare in detail the…
The speed of quantum computation is investigated through the time evolution of the speed of the orthogonality. The external field components for classical treatment beside the detuning and the coupling parameters for quantum treatment play…
(Abridged.) Quantum computers promise to solve some problems exponentially faster than traditional computers, but we still do not fully understand why this is the case. While the most studied model of quantum computation uses qubits, which…
A quantum measurement is logically reversible if the premeasurement density operator of the measured system can be calculated from the postmeasurement density operator and from the outcome of the measurement. This paper analyzes why many…
Quantum measurement is a fundamental concept in the field of quantum mechanics. The action of quantum measurement, leading the superposition state of the measured quantum system into a definite output state, not only reconciles…
We elaborate on the existing notion that quantum mechanics is an emergent phenomenon, by presenting a thermodynamical theory that is dual to quantum mechanics. This dual theory is that of classical irreversible thermodynamics. The linear…
The paper develops the idea that the dynamics of both classical and quantum processes is time reversible. It is shown how this classical analogy allows one to define the measure for the path integral in quantum mechanics.
In former work, we showed that a quantum algorithm requires the number of operations (oracle's queries) of a classical algorithm that knows in advance 50% of the information that specifies the solution of the problem. We gave a preliminary…
In classical mechanics the complexity of a dynamical system is characterized by the rate of local exponential instability which effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum…
The possibility to save and process information in fundamentally indistinguishable states is the quantum mechanical resource that is not encountered in classical computing. I demonstrate that, if energy constraints are imposed, this…
Quantum machine learning promises great speedups over classical algorithms, but it often requires repeated computations to achieve a desired level of accuracy for its point estimates. Bayesian learning focuses more on sampling from…
Quantum computers promise to solve computational problems significantly faster than classical computers. These 'speed-ups' are achieved by utilizing a resource known as magic. Measuring the amount of magic used by a device allows us to…
We present an idiosyncratic view of the race for quantum computational supremacy. Google's approach and IBM challenge are examined. An unexpected side-effect of the race is the significant progress in designing fast classical algorithms.…
We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…
The advent of quantum computers has justified the development of quantum machine learning algorithms , based on the adaptation of the principles of machine learning to the formalism of qubits. Among such quantum algorithms, anomaly…
With the help of recent developments in quantum algorithms for semidefinite programming, we discuss the possibility for quantum speedup for the numerical conformal bootstrap in conformal field theory. We show that quantum algorithms may…
Recent works have independently suggested that Quantum Mechanics might permit for procedures that transcend the power of Turing Machines as well as of `standard' Quantum Computers. These approaches rely on and indicate that Quantum…
Quantum computers hold the promise to solve certain computational task much more efficiently than classical computers. We review the recent experimental advancements towards a quantum computer with trapped ions. In particular, various…
Quantum computing has the potential to provide exponential performance benefits in processing over classical computing. It utilizes quantum mechanics phenomena (such as superposition, entanglement, and interference) to solve a computational…
Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…