Watrous complexity theory

What is the computational complexity theory?
Computational complexity theory is a mathematical research area in which the goal is to quantify the resources required to solve computational problems.
It is concerned with algorithms, which are computational methods for solving problems..
A quantum proof is a quantum state that plays the role of a witness or certificate to a quan- tum computer that runs a verification procedure.
The quantum complexity class QMA is defined by this notion: it includes all decision problems whose yes-instances are efficiently verifiable by means of quantum proofs.
Classical Complexity Classes
P stands for “polynomial time” and it represents the set of all problems that can be solved in a reasonable amount of time by a classical computer.
The complexity of quantum states has become a key quantity of interest across various subfields of physics, from quantum computing to the theory of black holes.
The evolution of generic quantum systems can be modelled by considering a collection of qubits subjected to sequences of random unitary gates.
The concept of complexity has its origins in quantum information science, an area developed within the framework of quantum mechanics.
The general idea behind complexity is to quantify how difficult it is to reach a certain quantum state starting from another one.

Apr 21, 2008Abstract: This article surveys quantum computational complexity, with a focus on three fundamental notions: polynomial-time quantum

Apr 21, 2008Quantum Computational Complexity. Authors:John Watrous. Download a PDF of the paper titled Quantum Computational Complexity, by John Watrous.

Apr 21, 2008This article surveys quantum computational complexity, with a focus on three fundamental notions: polynomial-time quantum computations, the

Does quantum query complexity still have enticing and fundamental open problems?

o er 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 tradeo s for collision and element distinctness, to polynomial degree versus quantum query complexity for partial functions, to the Unitary Synthesis Problem and more

What is quantum computational complexity?

This article surveys quantum computational complexity, with a focus on three fundamental notions: polynomial-time quantum computations, the efficient verification of quantum proofs, and quantum interactive proof systems

Properties of quantum complexity classes based on these notions, such as BQP, QMA, and QIP, are presented

Who is John Watrous?

John Watrous is a professor in the School of Computer Science and a faculty member of the Institute for Quantum Computing at the University of Waterloo

He received his PhD in 1998 from the University of Wisconsin – Madison

In computational complexity theory, the class IP is the class of problems solvable by an interactive proof system.
It is equal to the class PSPACE.
The result was established in a series of papers: the first by Lund, Karloff, Fortnow, and Nisan showed that co-NP had multiple prover interactive proofs; and the second, by Shamir, employed their technique to establish that IP=PSPACE.
The result is a famous example where the proof does not relativize.

Watrous complexity theory

What is the computational complexity theory?

Does quantum query complexity still have enticing and fundamental open problems?

What is quantum computational complexity?

Who is John Watrous?