2,537 research outputs found
Optimal Quantum Circuits for Nearest-Neighbor Architectures
We show that the depth of quantum circuits in the realistic architecture
where a classical controller determines which local interactions to apply on
the kD grid Z^k where k >= 2 is the same (up to a constant factor) as in the
standard model where arbitrary interactions are allowed. This allows
minimum-depth circuits (up to a constant factor) for the nearest-neighbor
architecture to be obtained from minimum-depth circuits in the standard
abstract model. Our work therefore justifies the standard assumption that
interactions can be performed between arbitrary pairs of qubits. In particular,
our results imply that Shor's algorithm, controlled operations and fanouts can
be implemented in constant depth, polynomial size and polynomial width in this
architecture.
We also present optimal non-adaptive quantum circuits for controlled
operations and fanouts on a kD grid. These circuits have depth Theta(n^(1 /
k)), size Theta(n) and width Theta(n). Our lower bound also applies to a more
general class of operations.Comment: 24 pages, 6 figures. v1 introduces all the results. v2 and v3 make
minor improvements to the presentation and add additional reference
On the Effect of Quantum Interaction Distance on Quantum Addition Circuits
We investigate the theoretical limits of the effect of the quantum
interaction distance on the speed of exact quantum addition circuits. For this
study, we exploit graph embedding for quantum circuit analysis. We study a
logical mapping of qubits and gates of any -depth quantum adder
circuit for two -qubit registers onto a practical architecture, which limits
interaction distance to the nearest neighbors only and supports only one- and
two-qubit logical gates. Unfortunately, on the chosen -dimensional practical
architecture, we prove that the depth lower bound of any exact quantum addition
circuits is no longer , but . This
result, the first application of graph embedding to quantum circuits and
devices, provides a new tool for compiler development, emphasizes the impact of
quantum computer architecture on performance, and acts as a cautionary note
when evaluating the time performance of quantum algorithms.Comment: accepted for ACM Journal on Emerging Technologies in Computing
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