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Electronic Colloquium on Computational Complexity

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Reports tagged with BQP:
TR10-170 | 11th November 2010
Scott Aaronson, Alex Arkhipov

The Computational Complexity of Linear Optics

We give new evidence that quantum computers -- moreover, rudimentary quantum computers built entirely out of linear-optical elements -- cannot be efficiently simulated by classical computers. In particular, we define a
model of computation in which identical photons are generated, sent through a linear-optical network, then nonadaptively measured to count ... more >>>

TR11-008 | 27th January 2011
Scott Aaronson, Andrew Drucker

Advice Coins for Classical and Quantum Computation

We study the power of classical and quantum algorithms equipped with nonuniform advice, in the form of a coin whose bias encodes useful information. This question takes on particular importance in the quantum case, due to a surprising result that we prove: a quantum finite automaton with just two states ... more >>>

TR11-103 | 31st July 2011
Yang Li


We initiate the study of the relationship between two complexity classes, BQP
(Bounded-Error Quantum Polynomial-Time) and PPAD (Polynomial Parity Argument,
Directed). We first give a conjecture that PPAD is contained in BQP, and show
a necessary and sufficient condition for the conjecture to hold. Then we prove
that the conjecture ... more >>>

TR13-147 | 25th October 2013
Adam Bouland, Scott Aaronson

Any Beamsplitter Generates Universal Quantum Linear Optics

Revisions: 3

In 1994, Reck et al. showed how to realize any linear-optical unitary transformation using a product of beamsplitters and phaseshifters. Here we show that any single beamsplitter that nontrivially mixes two modes, also densely generates the set of m by m unitary transformations (or orthogonal transformations, in the real case) ... more >>>

TR14-181 | 19th December 2014
Scott Aaronson, Adam Bouland, Joseph Fitzsimons, Mitchell Lee

The space "just above" BQP

We explore the space "just above" BQP by defining a complexity class PDQP (Product Dynamical Quantum Polynomial time) which is larger than BQP but does not contain NP relative to an oracle. The class is defined by imagining that quantum computers can perform measurements that do not collapse the ... more >>>

TR18-107 | 31st May 2018
Ran Raz, Avishay Tal

Oracle Separation of BQP and PH

We present a distribution $D$ over inputs in $\{-1,1\}^{2N}$, such that:
(1) There exists a quantum algorithm that makes one (quantum) query to the input, and runs in time $O(\log N)$, that distinguishes between $D$ and the uniform distribution with advantage $\Omega(1/\log N)$.
(2) No Boolean circuit of $\mathrm{quasipoly}(N)$ ... more >>>

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