# Design and execution of quantum circuits using tens of superconducting qubits and thousands of gates for dense Ising optimization problems

**Authors:** Filip B. Maciejewski, Stuart Hadfield, Benjamin Hall, Mark Hodson, Maxime Dupont, Bram Evert, James Sud, M. Sohaib Alam, Zhihui Wang, Stephen Jeffrey, Bhuvanesh Sundar, P. Aaron Lott, Shon Grabbe, Eleanor G. Rieffel, Matthew J. Reagor, Davide Venturelli  
**arXiv:** [2308.12423](https://arxiv.org/abs/2308.12423)  
**Date:** 2023-08-18  
**Summary page:** https://www.summarizepaper.com/en/paper/2308.12423v1/

## Key points

- Authors propose a hardware-efficient ansatz for variational optimization in quantum circuits
- Ansatz derived from existing ones in the literature and parametrizes subsets of all interactions in the Cost Hamiltonian in each layer
- Treating gate orderings as a variational parameter improves performance in experiments
- Experimental runs conducted using compilation-optimized implementation of fully-connected Sherrington-Kirkpatrick Hamiltonians on a 50-qubit linear-chain subsystem of the Rigetti Aspen-M-3 transmon processor
- Average performance at optimized angles and gate orderings increased with circuit depth for best circuit designs tested
- Approach achieved significantly better performance than using random guess oracle for circuits involving up to approximately 5000 two-qubit and 5000 one-qubit native gates
- Hardware-efficient ansatz effectively tackles dense Ising optimization problems
- Findings contribute to more effective utilization of current and future quantum processors for optimization purposes
- Potential applications in solving dense Ising optimization problems using tens of superconducting qubits and thousands of gates

## Summary

The authors of this study propose a hardware-efficient ansatz for variational optimization in quantum circuits. They derive their ansatz from existing ones in the literature and parametrize subsets of all interactions in the Cost Hamiltonian in each layer. Additionally, they treat gate orderings as a variational parameter and find that doing so can significantly improve performance in experiments. To test their approach, the researchers conducted experimental runs using a compilation-optimized implementation of fully-connected Sherrington-Kirkpatrick Hamiltonians on a 50-qubit linear-chain subsystem of the Rigetti Aspen-M-3 transmon processor. Despite the presence of high levels of noise, they observed that the average performance at optimized angles and gate orderings increased with circuit depth (using more parameters) for the best circuit designs tested. Remarkably, the results showed that their approach achieved performance significantly better than using a random guess oracle for circuits involving up to approximately 5000 two-qubit and 5000 one-qubit native gates. This indicates that their hardware-efficient ansatz can effectively tackle dense Ising optimization problems. In addition to presenting their findings, the authors discuss various takeaways from their results that contribute to more effective utilization of current and future quantum processors for optimization purposes. Overall, this study introduces a novel hardware-efficient ansatz for variational optimization in quantum circuits and demonstrates its effectiveness through experimental runs on a real quantum processor. The promising results suggest potential applications in solving dense Ising optimization problems using tens of superconducting qubits and thousands of gates.