Improving the Performance of Deep Quantum Optimization Algorithms with Continuous Gate Sets

Nathan Lacroix,Andreas Wallraff,Christoph Hellings,Agustin Di Paolo,Christian Kraglund Andersen,Sebastian Krinner,Stefania Lazar,Graham J Norris,Alexandre Blais,Mihai Gabureac,Ants Remm,Christopher Eichler,Johannes Heinsoo

doi:10.1103/prxquantum.1.020304

Abstract

Variational quantum algorithms are believed to be promising for solving computationally hard problems and are often comprised of repeated layers of quantum gates. An example thereof is the quantum approximate optimization algorithm (QAOA), an approach to solve combinatorial optimization problems on noisy intermediate-scale quantum (NISQ) systems. Gaining computational power from QAOA critically relies on the mitigation of errors during the execution of the algorithm, which for coherence-limited operations is achievable by reducing the gate count. Here, we demonstrate an improvement of up to a factor of 3 in algorithmic performance as measured by the success probability, by implementing a continuous hardware-efficient gate set using superconducting quantum circuits. This gate set allows us to perform the phase separation step in QAOA with a single physical gate for each pair of qubits instead of decomposing it into two C$Z$-gates and single-qubit gates. With this reduced number of physical gates, which scales with the number of layers employed in the algorithm, we experimentally investigate the circuit-depth-dependent performance of QAOA applied to exact-cover problem instances mapped onto three and seven qubits, using up to a total of 399 operations and up to 9 layers. Our results demonstrate that the use of continuous gate sets may be a key component in extending the impact of near-term quantum computers.

Highlights

Quantum computers have the potential to outperform classical computers on a range of computational problems such as prime factoring [1] and quantum chemistry [2]
We demonstrate an improvement of up to a factor of 3 in algorithmic performance for the quantum approximate optimization algorithm (QAOA) as measured by the success probability, by implementing a continuous hardware-efficient gate set using superconducting quantum circuits. This gate set allows us to perform the phase separation step in QAOA with a single physical gate for each pair of qubits instead of decomposing it into two CZ gates and single-qubit gates. With this reduced number of physical gates, which scales with the number of layers employed in the algorithm, we experimentally investigate the circuit-depth-dependent performance of QAOA applied to exact-cover problem instances mapped onto three and seven qubits, using up to a total of 399 operations and up to nine layers
We show that controlled arbitrary phase gates (CZφ gates) enable a significant reduction of the number of physical gates required to implement QAOA circuits of any depth on quantum hardware

Summary

INTRODUCTION

Quantum computers have the potential to outperform classical computers on a range of computational problems such as prime factoring [1] and quantum chemistry [2]. We demonstrate with two concrete examples that the reduction in gate-sequence duration outweighs errors that are potentially introduced by implementing the continuous gate set, such as errors originating from the required interpolation of parameters. Taking advantage of this gain in performance, we investigate the tradeoff between experimental noise, which favors shallow circuits, and increasing the number of layers, which is needed to solve complex problem instances

IMPLEMENTATION

PERFORMANCE OF QAOA

Findings

DISCUSSION