Non-Markovian quantum-state diffusion : Perturbation approach.

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N2 - We present a perturbation theory for non-Markovian quantum-state diffusion QSD , the theory of diffusive quantum trajectories for open systems in a bosonic environment [Phys. AB - We present a perturbation theory for non-Markovian quantum-state diffusion QSD , the theory of diffusive quantum trajectories for open systems in a bosonic environment [Phys.

Non-Markovian quantum-state diffusion Perturbation approach. Hungarian Academy of Sciences.

### Decoherent histories and quantum state diffusion (1995)

Abstract We present a perturbation theory for non-Markovian quantum-state diffusion QSD , the theory of diffusive quantum trajectories for open systems in a bosonic environment [Phys. Fingerprint perturbation. It was devised by Lov Grover in Neither search method will allow quantum computers to solve NP-Complete problems in polynomial time. Unlike other quantum algorithms, which may provide exponential speedup over their classical counterparts, Grover's algorithm provides only a quadratic speedup. Grover's algorithm could brute-force a bit symmetric cryptographic key in roughly 2 64 iterations, or a bit key in roughly 2 iterations.

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As a result, it is sometimes suggested [3] that symmetric key lengths be doubled to protect against future quantum attacks. Like many quantum algorithms, Grover's algorithm is probabilistic in the sense that it gives the correct answer with a probability of less than 1. Grover's original paper described the algorithm as a database search algorithm, and this description is still common.

The database in this analogy is a table of all of the function's outputs, indexed by the corresponding input.

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Although the purpose of Grover's algorithm is usually described as "searching a database", it may be more accurate to describe it as "inverting a function". In fact since the oracle for an unstructured database requires at least linear complexity, the algorithm cannot be used for actual databases. Grover's algorithm can also be used for estimating the mean and median of a set of numbers, and for solving the collision problem.

Grover's algorithm could be used to reverse-engineer cryptographic hash functions , allowing an attacker to find a victim's password or generate a series of counterfeit blocks. Consider the problem of determining the index of the database entry that satisfies some search criterion. The operation then represents a conditional inversion NOT gate conditioned by the value of f x on the main system:.

This is a natural way to realize a binary operation using the method of uncomputation. The steps of Grover's algorithm are given as follows.

In other words, both transformations are of Householder transformation type. In order to keep the search algorithm general, we will leave the inner workings of the oracle as a black box, but will explain how the sign is flipped.

## Ian C. Percival - Wikipedia

The oracle is a unitary operator operating on two qubits:. The exact probability of measuring the correct answer is. A natural way to do this is by eigenvalue analysis of a matrix. This matrix happens to have a very convenient Jordan form. Retrieved 3 February Nature News. November Nuclear Physics B.

Bibcode : NuPhB. Retrieved 9 February Retrieved The Astrophysical Journal. Bibcode : ApJ Quantum gravity.

## Ian C. Percival

Bunch—Davies vacuum Hawking radiation Semiclassical gravity Unruh effect. Bosonic string theory M-theory Supergravity Superstring theory. Loop quantum gravity Wheeler—DeWitt equation. Hartle—Hawking state. Causal dynamical triangulation Causal sets Noncommutative geometry Spin foam Group field theory Superfluid vacuum theory Twistor theory Dual graviton.