Related papers: The Power of Adiabatic Quantum Computation with No…
We discuss models of computing that are beyond classical. The primary motivation is to unearth the cause of nonclassical advantages in computation. Completeness results from computational complexity theory lead to the identification of very…
Quantum annealing (QA) is a method for solving combinatorial optimization problems. We can estimate the computational time for QA using the adiabatic condition. The adiabatic condition consists of two parts: an energy gap and a transition…
Quantum decoherence is of primary importance for relaxation to an equilibrium distribution and, accordingly, for equilibrium processes. We demonstrate how coherence breaking implies evolution to a microcanonical distribution…
We report the realization of a nuclear magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm. Adiabatic quantum algorithms offer new insight into how quantum resources can be used to…
The oracle model of computation is believed to allow a rigorous proof of quantum over classical computational superiority. Since quantum and classical oracles are essentially different, a correspondence principle is commonly implicitly used…
We demonstrate provable (sub)exponential quantum speedups in both discrete and continuous optimization, achieved through simple and natural quantum optimization algorithms, namely the quantum adiabatic algorithm for discrete optimization…
We consider a classical and superadiabatic version of an iterative quantum adiabatic algorithm to solve combinatorial optimization problems. This algorithm is deterministic because it is based on purely classical dynamics, that is, it does…
Adiabatic quantum computation is a paradigmatic model aiming to solve a computational problem by finding the many-body ground state encapsulating the solution. However, its use of an adiabatic evolution depending on the spectral gap of an…
Adiabatic quantum optimization offers a new method for solving hard optimization problems. In this paper we calculate median adiabatic times (in seconds) determined by the minimum gap during the adiabatic quantum optimization for an NP-hard…
In this paper, we consider a quantum algorithm for solving the following problem: ``Suppose $f$ is a function given as a black box (that is also called an oracle) and $f$ is invariant under some AND-mask. Examine a property of $f$ by…
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…
This paper investigates the power of polynomial-time quantum computation in which only a very limited number of qubits are initially clean in the |0> state, and all the remaining qubits are initially in the totally mixed state. No…
Attempts to separate the power of classical and quantum models of computation have a long history. The ultimate goal is to find exponential separations for computational problems. However, such separations do not come a dime a dozen: while…
We present straightforward proofs of estimates used in the adiabatic approximation. The gap dependence is analyzed explicitly. We apply the result to interpolating Hamiltonians of interest in quantum computing.
In this paper we give a framework for describing how abstract systems can be used to compute if no randomness or error is involved. Using this we describe a class of classical "physical" computation systems whose computational capabilities…
In the standard oracle model, an oracle efficiently evaluates an unknown classical function independent of the quantum algorithm itself. Quantum algorithms have a complex interrelationship to their oracles; for example the possibility of…
Computational devices may be supplied with external sources of information (oracles). Quantum oracles may transmit phase information which is available to a quantum computer but not a classical computer. One consequence of this observation…
A dynamical quantum model assigns an eigenstate to a specified observable even when no measurement is made, and gives a stochastic evolution rule for that eigenstate. Such a model yields a distribution over classical histories of a quantum…
This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…
Quantum models of computation are widely believed to be more powerful than classical ones. Efforts center on proving that, for a given problem, quantum algorithms are more resource efficient than any classical one. All this, however,…