Error message
- Deprecated function: TYPO3\PharStreamWrapper\Manager::initialize(): Implicitly marking parameter $resolver as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
- Deprecated function: TYPO3\PharStreamWrapper\Manager::initialize(): Implicitly marking parameter $collection as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
- Deprecated function: TYPO3\PharStreamWrapper\Manager::__construct(): Implicitly marking parameter $resolver as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
- Deprecated function: TYPO3\PharStreamWrapper\Manager::__construct(): Implicitly marking parameter $collection as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
- Deprecated function: UpdateQuery::expression(): Implicitly marking parameter $arguments as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: MergeQuery::expression(): Implicitly marking parameter $arguments as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQueryInterface::getArguments(): Implicitly marking parameter $queryPlaceholder as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQueryInterface::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQueryExtender::getArguments(): Implicitly marking parameter $queryPlaceholder as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQueryExtender::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQuery::getArguments(): Implicitly marking parameter $queryPlaceholder as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQuery::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
The class of problems that can be efficiently solved by quantum
computers is called
BQP,
for "bounded error, quantum, polynomial time". Quantum computers only
run randomized algorithms, so BQP on quantum computers
is the counterpart of
BPP
on classical computers. It is defined as the set of problems solvable
with a polynomial-time algorithm, whose probability of error is bounded
away from one half. A quantum computer is said to "solve" a problem if,
for every instance, its answer will be right with high probability. If
that solution runs in polynomial time, then that problem is in
BQP.
BQP is suspected to be disjoint from
NP-complete
and a strict superset of
P,
but that is not known. Both
integer
factorization and
discrete
log are in BQP. Both of these problems are
NP problems suspected to be outside
BPP, and hence outside P. Both are
suspected to not be
NP-complete.
There is a common misconception that quantum computers can solve
NP-complete problems in polynomial time. That is not known to be true,
and is generally suspected to be false.
An operator for a quantum computer can be thought of as changing a
vector by multiplying it with a particular matrix. Multiplication by a
matrix is a
linear
operation. It has been shown that if a quantum computer could be
designed with nonlinear operators, then it could solve
NP-complete problems in polynomial time. It could even do so for
#P-complete
problems. It is not yet known whether such a machine is possible.
Although quantum computers are sometimes faster than classical
computers, ones of the types described above can't solve any problems
that classical computers can't solve, given enough time and memory
(albeit possibly an amount that could never practically be brought to
bear). A
Turing
machine can simulate these quantum computers, so such a quantum
computer could never solve an
undecidable
problem like the
halting
problem. The existence of "standard" quantum computers does not
disprove the
Church-Turing
thesis.
Category:Handbook
of Quantum Information
Last modified:
Monday, October 26, 2015 - 17:56
