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Design of gates for quantum computation: the NOT gate

Mozyrsky, D, Privman, V, Hotaling, S P

Published Aug 17, 1996• 4 citations
OpenAlex

Abstract

We consider interactions needed to operate the quantum-mechanical NOT gate in the conventional formulation when the evolution is in time only and also in the case of spatially separated Input and Output two-state systems. Explicit expressions for the Hamiltonian are derived for the interaction which is time-independent for the duration of the gate operation. We develop a general approach which can be used to obtain Hamiltonians of this sort for quantum computer gates. We also discuss extensions to the case of time-dependent interactions.

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We consider interactions needed to operate the quantum-mechanical NOT gate in the conventional formulation when the evolution is in time only and also in the case of spatially separated Input and Output two-state systems. Explicit expressions for the Hamiltonian are derived for the interaction which is time-independent for the duration of the gate operation. We develop a general approach which can be used to obtain Hamiltonians of this sort for quantum computer gates. We also discuss extensions to the case of time-dependent interactions.
We offer an alternative to the conventional network formulation of quantum computing. We advance the analog approach to quantum logic gate/circuit construction. As an illustration, we consider the spatially extended NOT gate as the first step in the development of this approach. We derive an explicit form of the interaction Hamiltonian corresponding to this gate and analyze its properties. We also discuss general extensions to the case of certain time-dependent interactions which may be useful for practical realization of quantum logic gates.
Quantum information and quantum computation are emerging research areas based on the properties of quantum resources, such as superposition and entanglement. In the quantum gate array version, the use of convenient and proper gates is essential. While these gates adopt theoretically convenient forms to reproduce computational algorithms, their design and feasibility depend on specific quantum systems and physical resources used in their setup. These gates should be based on systems driven by physical interactions ruled by a quantum Hamiltonian. Then, the gate design is restricted to the properties and the limitations imposed by the interactions and the physical elements involved. This work shows how anisotropic Heisenberg-Ising interactions, written in a non-local basis, allow the reproduction of quantum computer operations based on unitary processes. We show that gates can be generated by a pulse sequence of driven magnetic fields. This fact states alternative techniques in quantum gate design for magnetic systems. A brief final discussion around associated fault tolerant extensions to the current work is included.