151 research outputs found
Synthesis of Quantum Logic Circuits
We discuss efficient quantum logic circuits which perform two tasks: (i)
implementing generic quantum computations and (ii) initializing quantum
registers. In contrast to conventional computing, the latter task is nontrivial
because the state-space of an n-qubit register is not finite and contains
exponential superpositions of classical bit strings. Our proposed circuits are
asymptotically optimal for respective tasks and improve published results by at
least a factor of two.
The circuits for generic quantum computation constructed by our algorithms
are the most efficient known today in terms of the number of expensive gates
(quantum controlled-NOTs). They are based on an analogue of the Shannon
decomposition of Boolean functions and a new circuit block, quantum
multiplexor, that generalizes several known constructions. A theoretical lower
bound implies that our circuits cannot be improved by more than a factor of
two. We additionally show how to accommodate the severe architectural
limitation of using only nearest-neighbor gates that is representative of
current implementation technologies. This increases the number of gates by
almost an order of magnitude, but preserves the asymptotic optimality of gate
counts.Comment: 18 pages; v5 fixes minor bugs; v4 is a complete rewrite of v3, with
6x more content, a theory of quantum multiplexors and Quantum Shannon
Decomposition. A key result on generic circuit synthesis has been improved to
~23/48*4^n CNOTs for n qubit
Constructive Quantum Shannon Decomposition from Cartan Involutions
The work presented here extends upon the best known universal quantum
circuit, the Quantum Shannon Decomposition proposed in [Vivek V. Shende,
Stephen S. Bullock and Igor Markov, Synthesis of Quantum Logic Circuits, IEEE
Trans. Comput.-Aided Des. Integr. Circuits Syst. 25 (6): 1000-1010 (2006)]. We
obtain the basis of the circuit's design in a pair of Cartan decompositions.
This insight gives a simple constructive algorithm for obtaining the Quantum
Shannon Decomposition of a given unitary matrix in terms of the corresponding
Cartan involutions
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
System
Towards optimization of quantum circuits
Any unitary operation in quantum information processing can be implemented
via a sequence of simpler steps - quantum gates. However, actual implementation
of a quantum gate is always imperfect and takes a finite time. Therefore,
seeking for a short sequence of gates - efficient quantum circuit for a given
operation, is an important task. We contribute to this issue by proposing
optimization of the well-known universal procedure proposed by Barenco et.al
[1]. We also created a computer program which realizes both Barenco's
decomposition and the proposed optimization. Furthermore, our optimization can
be applied to any quantum circuit containing generalized Toffoli gates,
including basic quantum gate circuits.Comment: 10 pages, 11 figures, minor changes+typo
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