Quantum Turing machine

A quantum Turing machine (QTM) or universal quantum computer is an abstract machine used to model the effects of a quantum computer. It provides a simple model that captures all of the power of quantum computation—that is, any quantum algorithm can be expressed formally as a particular quantum Turing machine. However, the computationally equivalent quantum circuit is a more common model.[1][2]: 2 

Quantum Turing machines can be related to classical and probabilistic Turing machines in a framework based on transition matrices. That is, a matrix can be specified whose product with the matrix representing a classical or probabilistic machine provides the quantum probability matrix representing the quantum machine. This was shown by Lance Fortnow.[3]

  1. ^ Andrew Yao (1993). Quantum circuit complexity. 34th Annual Symposium on Foundations of Computer Science. pp. 352–361.
  2. ^ Abel Molina; John Watrous (2018). "Revisiting the simulation of quantum Turing machines by quantum circuits". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 475 (2226). arXiv:1808.01701. doi:10.1098/rspa.2018.0767. PMC 6598068. PMID 31293355.
  3. ^ Fortnow, Lance (2003). "One Complexity Theorist's View of Quantum Computing". Theoretical Computer Science. 292 (3): 597–610. arXiv:quant-ph/0003035. doi:10.1016/S0304-3975(01)00377-2. S2CID 18657540.

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