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IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

Exact Reordering of Circuit Lines for Nearest Neighbor Quantum Architectures

Robert Wille, Aaron Lye, Rolf Drechsler

Published Nov 26, 2014• 98 citations
Publisher

Abstract

Research in the domain of quantum computation is mainly driven by their promising applications e.g., for factorization or database search. At the same time, physical developments for this emerging technology constantly lead to new constraints to be addressed by logic designers. The limited interaction distance between qubits, the elementary information storage in quantum circuits, is one of the most common restrictions, leading to the fact that, for many quantum architectures, computations can only be performed on adjacent (i.e., nearest neighbor) qubits. Motivated by that, optimization of quantum circuits with respect to this restriction has become an intensely considered research topic. In this paper, we briefly review existing approaches that have been proposed in the past for this purpose. We particularly consider that almost all existing solutions are of heuristic nature, i.e., do not guarantee an optimal solution. In order to address this, exact alternatives are introduced which make use of the deductive power of constraint solvers. By this, we are able to perform a qualitative evaluation of the performance of existing (heuristic) solutions for linear nearest neighbor quantum circuit optimization.

DOI
10.1109/tcad.2014.2356463

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Research in the domain of quantum computation is mainly driven by their promising applications e.g., for factorization or database search. At the same time, physical developments for this emerging technology constantly lead to new constraints to be addressed by logic designers. The limited interaction distance between qubits, the elementary information storage in quantum circuits, is one of the most common restrictions, leading to the fact that, for many quantum architectures, computations can only be performed on adjacent (i.e., nearest neighbor) qubits. Motivated by that, optimization of quantum circuits with respect to this restriction has become an intensely considered research topic. In this paper, we briefly review existing approaches that have been proposed in the past for this purpose. We particularly consider that almost all existing solutions are of heuristic nature, i.e., do not guarantee an optimal solution. In order to address this, exact alternatives are introduced which make use of the deductive power of constraint solvers. By this, we are able to perform a qualitative evaluation of the performance of existing (heuristic) solutions for linear nearest neighbor quantum circuit optimization.
Motivated by the promises of significant speed-ups for certain problems, quantum computing received significant attention in the past. While much progress has been made in the development of synthesis methods for quantum circuits, new physical developments constantly lead to new constraints to be addressed. The limited interaction distance between the respective qubits (i.e. nearest neighbor optimization) has already been considered intensely. But with the emerge of multi-dimensional quantum architectures, new physical requirements came up for which only a few automatic synthesis solutions exist yet all of them of heuristic nature. In this work, we propose an exact scheme for nearest neighbor optimization in multi-dimensional quantum circuits. Although the complexity of the problem is a serious obstacle, our experimental evaluation shows that the proposed solution is sufficient to allow for a qualitative evaluation of the respective optimization steps. Besides that, this enabled an exact comparison to heuristical results for the first time.
Motivated by its promising applications e.g. for database search or factorization, significant progress has been made in the development of automated design methods for quantum circuits. But in order to keep up with recent physical developments in this domain, new technological constraints have to be considered. Limited interaction distance between gate qubits is one of the most common of these constraints. This led to the development of several strategies aiming at making a given quantum circuit nearest neighbor-compliant by inserting SWAP gates into the existing structure. Usually these strategies are of heuristic nature. In this work, we present an exact approach that enables nearest neighbor-compliance by inserting a minimal number of SWAP gates. Experiments demonstrate the applicability of the approach which enabled a comparison of results obtained by heuristic methods to the actual optimum.
Abstract In quantum computing hardware, physical limitations are defining the connectivity of qubits, with Linear Nearest Neighbor being a convenient ordering for quantum mapping. To make quantum circuit Linear Nearest Neighbor-compatible, significant overhead (given by the so-called Nearest Neighbor Cost) may be caused by a set of additional gates necessary to make qubit lines of each gate of the circuit adjacent. In this work, the problem of quantum circuit optimization for Linear Nearest Neighbor architecture according to Nearest Neighbor Cost is treated by global qubit lines reordering. Such a reordering may be obtained as a result of graph partitioning heuristics. In this paper, we perform recursive graph partitioning on a quantum annealing hardware, thus making use of quantum optimizer to optimize a quantum circuit, to the best of our knowledge, for the first time. Extensive numerical experiments are performed for several circuits from various quantum circuit libraries, which demonstrate perspectives of the proposed approach.
Real quantum computing technologies have different restrictions and constraints which need to be considered during circuit synthesis. In certain technologies, only physically adjacent qubits can interact. It is common to use a pair of SWAP gates to bring the control and target qubits of any quantum gate to adjacent lines and maintain correct circuit functionality. This paper introduces a new method to synthesize linear nearest neighbor quantum circuit on the base of the analysis of quantum state in circuit. For all 3-qubit quantum circuit, experimental results shows that our algorithm can reduce the quantum cost by approximately 30% on average compared with one recent proposed method.
Synthesis and optimization of quantum circuits have received significant attention from researchers in recent years. Developments in the physical realization of qubits in quantum computing have led to new physical constraints to be addressed. One of the most important constraints that is considered by many researchers is the nearest neighbor constraint which limits the interaction distance between qubits for quantum gate operations. Various works have been reported in the literature that deal with nearest neighbor compliance in multi-dimensional (mostly 1D and 2D) qubit arrangements. This is normally achieved by inserting SWAP gates in the gate netlist to bring the interacting qubits closer together. The main objective function to minimize here is the number of SWAP gates. The present paper proposes an efficient qubit placement strategy in a three-dimensional (3D) grid that considers not only qubit interactions but also the relative positions of the gates in the circuit. Experimental evaluation on a number of benchmark circuits show that the proposed method reduces the number of SWAP gates by 16.2% to 47.0% on the average as compared to recently published works.
This paper is concerned with the physical design of quantum logic circuits. More precisely, it addresses the problem of minimizing the number of required qubit reorderings (achieved by inserting explicit SWAP gates) when mapping a quantum circuit into a linear nearest neighbor quantum archi-tecture. First, an interaction graph that captures the interaction distances among various qubits in the quantum circuit is constructed. The interaction graph is utilized to partition the quantum circuit into a set of subcircuits such that the number of required qubit reoderings within each subcircuit is provably no more than a given threshold. Next, a Minimum Linear Arrangement problem for each subcircuit is formulated and solved to achieve the minimum number of internal qubit reorderings and determine the subcircuit input and output qubit orderings. Finally, a bubble sort algorithm is repeatedly employed to minimize the number of qubit reorderings that are required between the consecutive subcircuits. Experiments done on various quantum Fourier transform circuits as well as various reversible logic circuits demonstrate the effectiveness of the proposed approach.