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arXiv:1707.06356 · New Journal of Physics

Use of global interactions in efficient quantum circuit constructions

Dmitri Maslov, Yunseong Nam

Published Dec 21, 2017• 53 citations
arXivHTMLPDF

Abstract

In this paper we study the ways to use a global entangling operator to efficiently implement circuitry common to a selection of important quantum algorithms. In particular, we focus on the circuits composed with global Ising entangling gates and arbitrary addressable single-qubit gates. We show that under various circumstances the use of global operations can substantially improve the entangling gate count.

DOI
10.1088/1367-2630/aaa398

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In this paper we study the ways to use a global entangling operator to efficiently implement circuitry common to a selection of important quantum algorithms. In particular, we focus on the circuits composed with global Ising entangling gates and arbitrary addressable single-qubit gates. We show that under various circumstances the use of global operations can substantially improve the entangling gate count.
Abstract There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and two-qubit CNOT gates. A CNOT gate is however not always the natural multi-qubit interaction that can be implemented on a given physical quantum computer, necessitating a compilation step that transforms these CNOT gates to the native gate set. An especially interesting case where compilation is necessary is for ion trap quantum computers, where the natural entangling operation can act on more than two qubits and can even act globally on all qubits at once. This calls for an entirely different approach to constructing efficient circuits. In this paper we study the problem of converting a given circuit that uses two-qubit gates to one that uses global gates. Our three main contributions are as follows. First, we find an efficient algorithm for transforming an arbitrary circuit consisting of Clifford gates and arbitrary phase gates into a circuit consisting of single-qubit gates and a number of global interactions proportional to the number of non-Clifford phases present in the original circuit. Second, we find a general strategy to transform a global gate that targets all qubits into one that targets only a subset of the qubits. This approach scales linearly with the number of qubits that are not targeted, in contrast to the exponential scaling reported in (Maslov and Nam 2018 New J. Phys. 20 033018). Third, we improve on the number of global gates required to synthesise an arbitrary n-qubit Clifford circuit from the 12n − 18 reported in (Maslov and Nam 2018 New J. Phys. 20 033018) to 6n − 8.
We consider quantum circuits composed of single-qubit operations and global entangling gates generated by Ising-type Hamiltonians. It is shown that such circuits can implement a large class of unitary operators commonly used in quantum algorithms at a very low cost-using a constant or effectively constant number of global entangling gates. Specifically, we report constant-cost implementations of Clifford operations with and without ancillae, constant-cost implementation of the multiply-controlled gates with linearly many ancillae, and an O(log^{*}(n)) cost implementation of the n-controlled single-target gates using logarithmically many ancillae. This shows a significant asymptotic advantage of circuits enabled by the global entangling gates.
We present improved circuits for the Toffoli gate and the control-swap (Fredkin) gate using three and four global two-qubit gates, respectively. This is a nearly double speedup compared to the conventional circuits, which require five (for Toffoli) and seven (for Fredkin) local two-qubit gates. We apply the same approach to construct the conditional four-qubit phase gate by seven global two-qubit gates. We also present construction of the Toffoli and Fredkin gates with five global gates in systems with nearest-neighbor interactions. Our constructions do not employ ancilla qubits or ancilla internal states and are particularly well suited for ion qubits and for circuit QED systems, where the entangling operations can be implemented by global addressing.
Abstract Compiling quantum circuits to account for hardware restrictions is an essential part of the quantum computing stack. Circuit compilation allows us to adapt algorithm descriptions into a sequence of operations supported by real quantum hardware, and has the potential to significantly improve their performance when optimisation techniques are added to the process. One such optimisation technique is reducing the number of quantum gates that are needed to execute a circuit. For instance, methods for reducing the number of non-Clifford gates or CNOT gates from a circuit are an extensive research area that has gathered significant interest over the years. For certain hardware platforms such as trapped-ion quantum computers, we can leverage some of their special properties to further reduce the cost of executing a quantum circuit in them. In this work we use global interactions, such as the Global Mølmer–Sørensen (MS) gate present in trapped-ion hardware, to optimise and synthesise quantum circuits. We design and implement an algorithm that is able to compile an arbitrary quantum circuit into another circuit that uses global gates as the entangling operation, while optimising the number of global interactions needed. The algorithm is based on the ZX -calculus and uses a specialised circuit extraction routine that groups entangling gates into Global MS gates. We benchmark the algorithm in a variety of circuits, and show how it improves their performance under state-of-the-art hardware considerations in comparison to a naive algorithm and the Qiskit optimiser.
In conventional circuit-based quantum computing architectures, the standard gate set includes arbitrary single-qubit rotations and two-qubit entangling gates. This choice is not always aligned with the native operations available in certain hardware, where the natural entangling gates are not restricted to two qubits but can act on multiple, or even all, qubits simultaneously. However, leveraging the capabilities of global quantum operations for algorithm implementations is highly challenging, as directly compiling local gate sequences into global gates usually gives rise to a quantum circuit that is more complex than the original one. Here, we circumvent this difficulty using a variational approach. Specifically, we study parameterized circuit ansatze composed of a finite number of global gates and layers of single-qubit unitaries. We demonstrate the expressibility of these ansatze and apply them to the problem of ground state preparation for the Heisenberg model and the toric code Hamiltonian, highlighting their potential for offering practical advantages.
We investigate quantum circuits built from arbitrary single-qubit operations combined with programmable all-to-all multiqubit entangling gates that are native to, among other systems, trapped-ion quantum computing platforms. We report a constant-cost of no more than 6 application of such Clifford entangling multiqubit gates to realize any sequence of Clifford operations of any length, without ancillae. Furthermore, we show that any sequence of CNOT gates of any length, can be replaced with 5 applications of such Clifford entangling multiqubit gates, without ancillae. We investigate the required qubit drive power that is associated with these implementations. Our work introduces a practical and computationally efficient algorithm to realize these compilations.