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arXiv:quant-ph/9608029 · International Journal of Modern Physics B

Design of Gates for Quantum Computation: The NOT Gate

Dima Mozyrsky, Vladimir Privman, Steven P. Hotaling

Published Jul 20, 1997• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1142/s0217979297001143

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The MIT Press eBooks•Mar 19, 2019•2 citations
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.
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.
There are well-known protocols for performing controlled NOT (CNOT) quantum logic with qubits coupled by particular high-symmetry (Ising or Heisenberg) interactions. However, many architectures being considered for quantum computation involve qubits or qubits and resonators coupled by more complicated and less symmetric interactions. Here we consider a widely applicable model of weakly but otherwise arbitrarily coupled two-level systems, and use quantum gate design techniques to derive a simple and intuitive CNOT construction. Useful variations and extensions of the solution are given for common special cases.
Abstract Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different designs, where the logical outputs are encoded either at fixed energy and spatial positioning of the quantum states, or at different energies. We use these results to construct quantum Boolean adders involving a minimal number of quantum states with the two designs. We also establish a matrix algebra giving an analogy between classical Boolean logic gates and quantum ones, and assess the possibilities of both designs for more complex gates.
Quantum computing, which is the most famed topic in this era, a combination of quantum mechanics from the 1900s and the computing point of view, takes a huge place in the quantum realm. Starting from the foundation of abacus since 2700–2300 BC, we humans have always been trying to compute in different ways, and the most modern way of doing it comes with the binary system. Bit is the smallest unit of a binary system and can be in two states, either 0 or 1. On the contrary, quantum computing deals with the “quantum bit” or “qubit”; possible outcomes from the qubits are neither 0 nor 1. It will always be a combination of 0 and 1, which is based on the superposition principle from quantum physics. In this chapter, details of quantum logic gates are discussed for the circuit design perspective, which will be achievable for future realization of quantum computers. Architecture and corresponding formation of basic quantum circuits are discussed, along with the methods of quantum computing. How the technique differs from conventional approaches is also highlighted. The work may be directed toward future hardware realization of quantum information processing.
Abstract Currently, there is an ongoing “race” to build the first practically useful quantum computer that provides substantial speed-ups for certain problems compared to conventional computers. In addition to the development of such devices, this also requires the development of automated tools and methods that provide assistance in the simulation and design of corresponding applications. Otherwise, a situation might be reached where we have powerful quantum computers but hardly any proper means to actually use them. This work provides an overview of corresponding solutions for the task of quantum circuit simulation, the task of quantum circuit design, as well as corresponding mapping tasks. The covered solutions utilise expertise on efficient data structures and algorithms gained in the design of conventional circuits and systems over the last decades. While the respective descriptions are kept brief and mainly convey the general ideas, references to further readings are provided for a more detailed treatment.