Tensor-based quantum phase difference estimation for large-scale demonstration

Quantum Phase Estimation (QPE) is a central quantum algorithm, but real device demonstrations of QPE are limited to only a few system qubits due to their high operational cost. We developed a QPE algorithm for large-scale quantum chemistry demonstrations. Our algorithm uses a Quantum Phase Difference Estimation (QPDE) scheme and tensor-network-based unitary compression for state preparation of a superposition state and time-evolution gates. Alongside its efficient implementation, the algorithm exponentially reduces depolarization noise. We calculated energy gaps for one-dimensional Hubbard models on IBM superconducting devices using circuits with up to 32 system qubits (plus one ancilla), achieving an order of magnitude increase over previous QPE demonstrations. This was realized at the 7242 controlled-Z gate level of standard transpilation, using the Q-CTRL error suppression module. Additionally, we propose a technique for molecular executions employing spatial orbital localization and index sorting, verified by 13-qubit (17-qubit) hexatriene (octatetraene) simulations. As QPDE addresses the same objectives as QPE, our algorithm thereby marks a significant advancement in quantum computing on real devices.