21 research outputs found
One-Dimensional Lazy Quantum walk in Ternary System
Quantum walks play an important role for developing quantum algorithms and
quantum simulations. Here we present one dimensional three-state quantum
walk(lazy quantum walk) and show its equivalence for circuit realization in
ternary quantum logic for the first of its kind. Using an appropriate logical
mapping of the position space on which a walker evolves onto the multi-qutrit
states, we present efficient quantum circuits considering the nearest neighbour
position space for the implementation of lazy quantum walks in one-dimensional
position space in ternary quantum system. We also address scalability in terms
of -qutrit ternary system with example circuits for a three qutrit state
space.Comment: 13 pages, 12 figures, and 10 table
Multiple-Valued Quantum Logic Synthesis
This paper asks the question: is logic synthesis for quantum computers a practical research subject?
We would like to assume that any two quantum wires can interact, but we are limited by the realization constraints. Structure of atomic bonds in the molecule determines neighborhoods in the circuit. This is similar to restricted routing in FPGA layout - link between logic and layout synthesis known from CMOS design now appears in quantum. Below we are interested only in the so-called “permutation circuits” - their unitary quantum matrices are permutation matrices