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Quantum Science and Technology

Optimisation and synthesis of quantum circuits with global gates

Alejandro Villoria, Henning Basold, Alfons Laarman

Published Dec 22, 2025• 2 citations
Publisher

Abstract

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.

DOI
10.1088/2058-9565/ae3029

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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.
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.
As quantum computing scales up, circuits relying on sequential two-qubit gates face severe challenges from excessive depth and decoherence. In trapped-ion systems, global entangling gates offer a highly parallel alternative but are hindered by complex numerical optimization. We propose an efficient numerical framework for piecewise-constant amplitude-modulated global gates. Based on the Mølmer-Sørensen protocol, we utilize null-space projection for linear constraints of spin-motion coupling and tangent-space gradient descent to minimize laser power, while achieving high-order robustness against frequency drifts. At the application level, we identify a structural correspondence between hardware-native global interactions and Pauli strings in Hamiltonian simulation and propose an efficient compilation scheme. By reducing common physical models to fundamental X X interactions and formulating interaction graph partitioning as a Set Cover problem, we leverage global gates to significantly optimize the compilation process. Explicit pulse-level benchmarks further show that, for the tested weighted interaction graphs, the reduction in entangling-gate count can translate into a substantial reduction in total entangling duration. These results demonstrate that integrating hardware-native operations with tailored compilation strategies can substantially reduce circuit overhead, providing a practical roadmap for the codesign of near-term quantum simulators.
Quantum circuit synthesis describes the process of converting arbitrary unitary operations into a gate sequence of a fixed universal gate set, usually defined by the operations native to a given hardware platform. Most current synthesis algorithms are designed to synthesize towards a set of single qubit rotations and an additional entangling two qubit gate, such as CX, CZ, or the Molmer Sorensen gate. However, with the emergence of neutral atom based hardware and their native support for gates with more than two qubits, synthesis approaches tailored to these new gate sets become necessary. In this work, we present an approach to synthesize multi controlled phase gates using ZX calculus. By representing quantum circuits as graph like ZX diagrams, one can utilize the distinct graph structure of diagonal gates to identify multi controlled phase gates inherently present in some quantum circuits even if none were explicitly defined in the original circuit. We evaluate the approach on a wide range of benchmark circuits and compare them to the standard Qiskit synthesis regarding its circuit execution time for neutral atom based hardware with native support of multi controlled gates. Our results show possible advantages for current state of the art hardware and represent the first exact synthesis algorithm supporting arbitrary sized multi controlled phase gates.
Quantum circuit synthesis and compilation are critical components in the quantum computing stack, both for contemporary quantum systems, where efficient use of limited resources is essential, as well as for large-scale fault-tolerant platforms, where computation time can be minimized. The specific characteristics of the quantum hardware determine which circuit designs and optimizations are feasible. We present a phase-gadget based method for compilation of quantum circuits using programmable multiqubit entangling gates, that are native, among others, to trapped-ions quantum computers. We use phase-gadgets in order to generically reduce circuit depths and efficiently implement them with few, high-fidelity, multiqubit gates. We test our methods on a large set of benchmark circuits and demonstrate generic circuit depth reduction and implementation error reduction.
The increasing capabilities of quantum computing hardware and the challenge of realizing deep quantum circuits require fully automated and efficient tools for compiling quantum circuits. To express arbitrary circuits in a sequence of native gates specific to the quantum computer architecture, it is necessary to make algorithms portable across the landscape of quantum hardware providers. In this work, we present a compiler capable of transforming and optimizing a quantum circuit targeting a shuttling-based trapped-ion quantum processor. It consists of custom algorithms set on top of the quantum circuit framework Pytket. The performance was evaluated for a wide range of quantum circuits and the results show that the gate counts can be reduced by factors up to 5.1 compared to standard Pytket and up to 2.2 compared to standard Qiskit compilation.
State-of-the-art noisy-intermediate-scale quantum processors are currently implemented across a variety of hardware platforms, each with their own distinct gatesets. As such, circuit compilation should not only be aware of but also deeply connect to the native gateset and noise properties of each. Trapped-ion processors are one such platform that provides a gateset that can be continuously parameterized across both one- and two-qubit gates. Here we use the Quantum Scientific Computing Open User Testbed to study noise-aware compilations focused on continuously parameterized two-qubit Z Z gates (based on the Mølmer-Sørensen interaction) using , a quantum software platform for hardware-aware circuit compiler optimizations. We discuss the realization of Z Z gates with arbitrary angle on the all-to-all connected trapped-ion system. Then we discuss a variety of different compiler optimizations that innately target these Z Z gates and their noise properties. These optimizations include moving from a restricted maximally entangling gateset to a continuously parameterized one, swap mirroring to further reduce the total entangling angle of the operations, focusing the heaviest Z Z angle participation on the best-performing gate pairs, and circuit approximation to remove the least impactful Z Z gates. We demonstrate these compilation approaches on the hardware with randomized quantum volume circuits, observing the potential to realize a larger quantum volume as a result of these optimizations. Using differing yet complementary analysis techniques, we observe the distinct improvements in system performance provided by these noise-aware compilations and study the role of stochastic and coherent error channels for each compilation choice.