Development of Advanced Quantum Algorithms

In collaboration with Classiq, this project focused on developing and benchmarking advanced quantum algorithms for the simulation of coupled harmonic oscillator systems. Such systems arise in a wide range of physical models across condensed matter physics, materials science, and molecular dynamics, making them an important testbed for evaluating the potential of quantum computing.

The study builds on top of the study by Google Quantum AI for efficiently simulating networks of coupled oscillators. The algorithm is theoretically capable of delivering exponential speedups over classical approaches for certain problem classes. The project focused on linearly connected oscillator chains, translating the theoretical formulation into practical implementations that can be analyzed and benchmarked on modern quantum software platforms.

Three distinct algorithmic realizations were developed and compared including Sparse state preparation with product-formula simulation, Fully quantum oracle-based simulation using Quantum Singular Value Transformation (QSVT), and a more efficient Hybrid optimized approach combining sparse state preparation with the oracle-based block-encoding pipeline to reduce implementation overhead.

All implementations were developed and benchmarked using the Classiq high-level quantum design platform, enabling detailed analysis of circuit resources, qubit counts, and algorithmic scalability. The work provides practical implementation pathways for advanced Hamiltonian simulation algorithms, clarifying their resource requirements and bringing theoretical proposals for quantum advantage closer to realistic execution on future quantum hardware.

WISER Research Fellows: Viraj Dsouza, Weronika Golletz, Dimitrios Kranas, Bakhao Dioum