Convergence of Digitized-Counterdiabatic QAOA: circuit depth versus free parameters

Abstract

Recently, Digitized-Counterdiabatic (CD) Quantum Approximate Optimization Algorithm (QAOA) has been proposed to make QAOA converge to the solution of an optimization problem in fewer steps, inspired by Trotterized counterdiabatic driving in continuous-time quantum annealing. In this paper, we critically revisit this approach by focusing on the paradigmatic weighted and unweighted one-dimensional MaxCut problem. We study two variants of QAOA with first and second-order CD corrections. Our results show that, indeed, higher order CD corrections allow for a quicker convergence to the exact solution of the problem at hand by increasing the complexity of the variational cost function. Remarkably, however, the total number of free parameters needed to achieve this result is independent of the particular QAOA variant analyzed.

References in corpus (46)

• Variational Quantum Algorithms
• Ising formulations of many NP problems
• Quantum Annealing in the Transverse Ising Model
• Noisy intermediate-scale quantum (NISQ) algorithms
• Adiabatic Quantum Computing
• From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
• Theory of Quantum Annealing of an Ising Spin Glass
• Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices
• Quantum Approximate Optimization Algorithm for MaxCut: A Fermionic View
• Obstacles to State Preparation and Variational Optimization from Symmetry Protection
• Warm-starting quantum optimization
• Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
• Floquet-engineering counterdiabatic protocols in quantum many-body systems
• Generalized Jordan-Wigner Transformations
• Reachability Deficits in Quantum Approximate Optimization
• Efficient computation of the Zassenhaus formula
• Digitized-counterdiabatic quantum approximate optimization algorithm
• Counterdiabaticity and the quantum approximate optimization algorithm
• Grover Mixers for QAOA: Shifting Complexity from Mixer Design to State Preparation
• Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware
• On the Universality of the Quantum Approximate Optimization Algorithm
• Reinforcement Learning for Many-Body Ground-State Preparation Inspired by Counterdiabatic Driving
• Counterdiabatic Optimised Local Driving
• Reinforcement Learning assisted Quantum Optimization
• Digitized-Counterdiabatic Quantum Algorithm for Protein Folding
• Avoiding barren plateaus via transferability of smooth solutions in Hamiltonian Variational Ansatz
• Classical symmetries and the Quantum Approximate Optimization Algorithm
• Reverse quantum annealing of the $p$-spin model with relaxation
• Counterdiabatic driving in the quantum annealing of the $p$-spin model: a variational approach
• Portfolio Optimization with Digitized-Counterdiabatic Quantum Algorithms
• Improving quantum annealing of the ferromagnetic $p$-spin model through pausing
• Constrained mixers for the quantum approximate optimization algorithm
• Quantum optimization via four-body Rydberg gates
• Quantum Approximate Optimization Algorithm with Adaptive Bias Fields
• A dissipative environment may improve the quantum annealing performances of the ferromagnetic p-spin model
• Optimal quantum annealing: A variational shortcut to adiabaticity approach
• Quantum Computational Phase Transition in Combinatorial Problems
• Performance and limitations of the QAOA at constant levels on large sparse hypergraphs and spin glass models
• Explicit Baker-Campbell-Hausdorff formulae for some specific Lie algebras
• A native measurement-based QAOA algorithm, applied to the MAX K-CUT problem
• Shortcuts to Quantum Approximate Optimization Algorithm
• Standard quantum annealing outperforms adiabatic reverse annealing with decoherence
• Fermionic Quantum Approximate Optimization Algorithm
• Counterdiabatic Reverse Annealing
• Automatic Depth Optimization for Quantum Approximate Optimization Algorithm
• Deep learning optimal quantum annealing schedules for random Ising models

Cited by in corpus (6)

• Barren Plateaus in Variational Quantum Computing
• Shortcuts to adiabaticity: theoretical framework, relations between different methods, and versatile approximations
• Counterdiabatic optimized driving in quantum phase sensitive models
• Efficient DCQO Algorithm within the Impulse Regime for Portfolio Optimization
• Noise Effects on Diabatic Quantum Annealing Protocols
• Nonadiabatic Self-Healing of Trotter Errors in Digitized Counterdiabatic Dynamics