Chapter 24 Non-Hamiltonian Systems as Quantum Computers

Abstract

Publisher Summary This chapter describes the non-Hamiltonian systems as quantum computers. Understanding the dynamics of non-Hamiltonian systems is important for studying quantum noise processes, quantum error correction, decoherence effects in quantum computations, and performing the simulations of open and non-Hamiltonian quantum systems. The usual model of a quantum computer is generalized to a model in which a state is a density operator and gates are general superoperators (quantum operations), not necessarily unitary. The pure state of n two-level closed quantum systems is an element of 2 n -dimensional Hilbert space and it allows considering a quantum computer model with two-valued logic. In a general case, the mixed state (density operator) of n two-level quantum systems is an element of 4 n -dimensional operator Hilbert space (Liouville space). It allows using a quantum computer model with four-valued logic. The gates of this model are general superoperators (quantum operations), which act on general n -ququat state. A ququat is a quantum state in a four-dimensional (operator) Hilbert space. Unitary two-valued logic gates and quantum operations for an n qubit non-Hamiltonian system are considered as four-valued logic gates acting on n -ququat. The chapter discusses universality for general quantum four-valued logic gates acting on ququats.