quantum Turing machine , QTM (abbreviation)

A theoretical model is the quantum Turing machine, also known as the universal quantum computer.

A quantum Turing machine can efficiently simulate any realistic model of computation.

Any quantum algorithm can be expressed formally as a particular quantum Turing machine.

Quantum Turing machines are not always used for analyzing quantum computation; the quantum circuit is a more common model.

BQP: The complexity class of decision problems that can be solved with 2-sided error on a quantum Turing machine in polynomial time.

Similarly, one may define a quantum complexity class using a quantum model of computation, such as a standard quantum computer or a quantum Turing machine.

A quantum Turing machine (QTM), also a universal quantum computer, is an abstract machine used to model the effect of a quantum computer.

His 1993 paper with his student Ethan Bernstein on quantum complexity theory defined a model of quantum Turing machines which was amenable to complexity based analysis.

Quantum Turing machines can be related to classical and probabilistic Turing machines in a framework based on transition matrices, shown by Lance Fortnow.

Using postselection it seems quantum Turing machines are much more powerful: Scott Aaronson proved PostBQP is equal to PP.

Iriyama, Ohya, and Volovich have developed a model of a Linear Quantum Turing Machine (LQTM).

He pioneered the field of quantum computation by formulating a description for a quantum Turing machine, as well as specifying an algorithm designed to run on a quantum computer.

Topological quantum computers are equivalent in computational power to other standard models of quantum computation, in particular to the quantum circuit model and to the quantum Turing machine model.

However, this language can efficiently solve NP-complete problems, and therefore appears to be strictly stronger than the standard quantum computational models (such as the quantum Turing machine or the quantum circuit model).

Topological quantum computer (computation decomposed into the braiding of anyons in a 2D lattice) The Quantum Turing machine is theoretically important but direct implementation of this model is not pursued.

For example, it is an open question whether all quantum mechanical events are Turing-computable, although it is known that rigorous models such as quantum Turing machines are equivalent to deterministic Turing machines.

A quantum Turing machine with postselection was defined by Scott Aaronson, who showed that the class of polynomial time on such a machine (PostBQP) is equal to the classical complexity class PP.

The above is merely a sketch of a quantum Turing machine, rather than its formal definition, as it leaves vague several important details: for example, how often a measurement is performed; see for example, the difference between a measure-once and a measure-many QFA.

Another feature that is often considered important for a model of quantum cellular automata is that it should be universal for quantum computation (i.e. that it can efficiently simulate quantum Turing machines, some arbitrary quantum circuit or simply all other quantum cellular automata).

The addition of postselection seems to make quantum Turing machines much more powerful: Scott Aaronson proved PostBQP is equal to PP, a class which is believed to be relatively powerful, whereas BQP is not known even to contain the seemingly smaller class NP.

In computational complexity theory, PostBQP is a complexity class consisting of all of the computational problems solvable in polynomial time on a quantum Turing machine with postselection and bounded error (in the sense that the algorithm is correct at least 2/3 of the time on all inputs).