Scalable quantum circuit generation for iterative ground state approximation using Majorana Propagation

TL;DR

This paper introduces ADAPT-VMPE, a scalable classical algorithm leveraging Majorana Propagation to efficiently generate quantum circuits for approximating molecular ground states, with proven polynomial complexity and practical applications to large systems.

Contribution

The paper presents ADAPT-VMPE, a novel classical algorithm that uses Majorana Propagation for scalable, polynomial-time quantum circuit generation for ground state approximation.

Findings

Constructed up to 100-qubit ansätze for complex molecules.

Achieved polynomial-time convergence to the ground state.

Provided practical guidelines for efficient ansatz construction.

Abstract

We introduce the Adaptive Derivative-Assembled Pseudo-Trotter ansatz Variational Majorana Propagation Eigensolver (ADAPT-VMPE), a quantum-inspired classical algorithm that exploits Majorana Propagation (MP) to produce circuits for approximating the ground state of molecular Hamiltonians. Equipped with the theoretical guarantees of MP, which provide controllable bounds on the approximation error, ADAPT-VMPE offers an efficient and scalable approach for iterative ansatz construction. A theoretical analysis of the computational complexity demonstrates that it is polynomial in both the number of qubits and the number of iterations. We present an in-depth analysis of circuit construction strategies, analyzing their impact on convergence and provide practical guidance for efficient ansatz generation. Using ADAPT-VMPE, we construct up to 100-qubit ans\"atze for a strongly correlated photosensitizer currently undergoing human clinical trials for cancer treatment. Our results demonstrate that constant overlap with the ground state across system sizes can be reached in polynomial time with polynomially sized circuits.