scholarly journals The quantum query complexity of elliptic PDE

2006 ◽  
Vol 22 (5) ◽  
pp. 691-725 ◽  
Author(s):  
Stefan Heinrich
Keyword(s):  
Query Complexity ◽  
Elliptic Pde ◽  
Quantum Query Complexity ◽  
Quantum Query

scholarly journals Exact quantum algorithms have advantage for almost all Boolean functions

2015 ◽  
pp. 435-452
Author(s):  
Andris Ambainis ◽  
Jozef Gruska ◽  
Shenggen Zheng
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Query Complexity ◽  
Exact Quantum ◽  
Quantum Query Complexity ◽  
Almost All ◽  
Quantum Query

It has been proved that almost all n-bit Boolean functions have exact classical query complexity n. However, the situation seemed to be very different when we deal with exact quantum query complexity. In this paper, we prove that almost all n-bit Boolean functions can be computed by an exact quantum algorithm with less than n queries. More exactly, we prove that ANDn is the only n-bit Boolean function, up to isomorphism, that requires n queries.

Open Problems Related to Quantum Query Complexity

2021 ◽  
Vol 2 (4) ◽  
pp. 1-9
Author(s):  
Scott Aaronson
Keyword(s):  
Synthesis Problem ◽  
Query Complexity ◽  
Partial Functions ◽  
Open Problems ◽  
Polynomial Degree ◽  
Quantum Query Complexity ◽  
Time Space ◽  
Quantum Query

I offer a case that quantum query complexity still has loads of enticing and fundamental open problems—from relativized QMA versus QCMA and BQP versus IP , to time/space tradeoffs for collision and element distinctness, to polynomial degree versus quantum query complexity for partial functions, to the Unitary Synthesis Problem and more.

Quantum Query Complexity for Some Graph Problems

2004 ◽  
pp. 140-150 ◽  
Author(s):  
Aija Berzina ◽  
Andrej Dubrovsky ◽  
Rusins Freivalds ◽  
Lelde Lace ◽  
Oksana Scegulnaja
Keyword(s):  
Query Complexity ◽  
Graph Problems ◽  
Quantum Query Complexity ◽  
Quantum Query

scholarly journals Improving Quantum Query Complexity of Boolean Matrix Multiplication Using Graph Collision

Algorithmica ◽  
2015 ◽  
Vol 76 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Stacey Jeffery ◽  
Robin Kothari ◽  
François Le Gall ◽  
Frédéric Magniez
Keyword(s):  
Matrix Multiplication ◽  
Boolean Matrix ◽  
Query Complexity ◽  
Quantum Query Complexity ◽  
Boolean Matrix Multiplication ◽  
Quantum Query

scholarly journals The quantum query complexity of AC0

2012 ◽  
Vol 12 (7&8) ◽  
pp. 670-676
Author(s):  
Paul Beame ◽  
Widad Machmouchi
Keyword(s):  
Lower Bound ◽  
Quantum Algorithm ◽  
Input Function ◽  
Query Complexity ◽  
Quantum Query Complexity ◽  
Quantum Query

We show that any quantum algorithm deciding whether an input function $f$ from $[n]$ to $[n]$ is 2-to-1 or almost 2-to-1 requires $\Theta(n)$ queries to $f$. The same lower bound holds for determining whether or not a function $f$ from $[2n-2]$ to $[n]$ is surjective. These results yield a nearly linear $\Omega(n/\log n)$ lower bound on the quantum query complexity of $\cl{AC}^0$. The best previous lower bound known for any $\cl{AC^0}$ function was the $\Omega ((n/\log n)^{2/3})$ bound given by Aaronson and Shi's $\Omega(n^{2/3})$ lower bound for the element distinctness problem.

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