Quantum Algorithm for the Collision Problem, 1998; Brassard, Hoyer, Tapp

2011 ◽  
Keyword(s):  
Quantum Algorithm ◽  
Collision Problem

scholarly journals Quantum Algorithm for the Collision Problem

2016 ◽  
pp. 1662-1664 ◽  
Author(s):  
Gilles Brassard ◽  
Peter Høyer ◽  
Alain Tapp
Keyword(s):  
Quantum Algorithm ◽  
Collision Problem

scholarly journals Impossibility of succinct quantum proofs for collision-freeness

2012 ◽  
Vol 12 (1&2) ◽  
pp. 21-28 ◽  
Author(s):  
Scott Aaronson
Keyword(s):  
Lower Bound ◽  
Quantum Algorithm ◽  
Simple Extension ◽  
Class A ◽  
Collision Problem ◽  
Open Question

We show that any quantum algorithm to decide whether a function f[n] \rightarrow [n] is a permutation or far from a permutation\ must make \Omega( n^{1/3}/w) queries to f, even if the algorithm is given a w-qubit quantum witness in support of f being a permutation. This implies that there exists an oracle A such that {SZK}^{A}\not \subset {QMA}^{A}, answering an eight-year-old open question of the author. \ Indeed, we show that relative to some oracle, {SZK} is not in the counting class {A}_0{PP} defined by Vyalyi. The proof is a fairly simple extension of the quantum lower bound for the collision problem.

scholarly journals Quantum Algorithm for the Collision Problem

2015 ◽  
pp. 1-2 ◽  
Author(s):  
Gilles Brassard ◽  
Peter Høyer ◽  
Alain Tapp
Keyword(s):  
Quantum Algorithm ◽  
Collision Problem

scholarly journals A quantum lower bound for distinguishing random functions from random permutations

2014 ◽  
Vol 14 (13&14) ◽  
pp. 1089-1097
Author(s):  
Henry Yuen
Keyword(s):  
Lower Bound ◽  
Quantum Algorithm ◽  
Input Function ◽  
Random Permutation ◽  
Query Complexity ◽  
Random Permutations ◽  
Random Functions ◽  
Collision Problem ◽  
Bounded Error ◽  
Quantum Query

The problem of distinguishing between a random function and a random permutation on a domain of size $N$ is important in theoretical cryptography, where the security of many primitives depend on the problem's hardness. We study the quantum query complexity of this problem, and show that any quantum algorithm that solves this problem with bounded error must make $\Omega(N^{1/5}/\polylog N)$ queries to the input function. Our lower bound proof uses a combination of the Collision Problem lower bound and Ambainis's adversary theorem.

An improved quantum algorithm for support matrix machines

2021 ◽  
Vol 20 (7) ◽  
Author(s):  
Yanbing Zhang ◽  
Tingting Song ◽  
Zhihao Wu
Keyword(s):  
Quantum Algorithm ◽  
Support Matrix

scholarly journals Asset–liability modelling in the quantum era

2021 ◽  
Vol 26 ◽  
Author(s):  
T. Berry ◽  
J. Sharpe
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computer ◽  
Quantum Algorithm ◽  
Capital Requirements ◽  
Quantum Computers ◽  
Investment Management ◽  
Asset Liability Management ◽  
Liability Management ◽  
Insight Into ◽  
Current Practices

Abstract This paper introduces and demonstrates the use of quantum computers for asset–liability management (ALM). A summary of historical and current practices in ALM used by actuaries is given showing how the challenges have previously been met. We give an insight into what ALM may be like in the immediate future demonstrating how quantum computers can be used for ALM. A quantum algorithm for optimising ALM calculations is presented and tested using a quantum computer. We conclude that the discovery of the strange world of quantum mechanics has the potential to create investment management efficiencies. This in turn may lead to lower capital requirements for shareholders and lower premiums and higher insured retirement incomes for policyholders.

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