Tensor-based quantum phase difference estimation for large-scale
  demonstration
We develop an energy calculation algorithm leveraging quantum phase
difference estimation (QPDE) scheme and a tensor-network-based unitary
compression method in the preparation of superposition states and
time-evolution gates. Alongside its efficient implementation, this algorithm
reduces depolarization noise affections exponentially. We demonstrated energy
gap calculations for one-dimensional Hubbard models on IBM superconducting
devices using circuits up to 32-system (plus one-ancilla) qubits, a five-fold
increase over previous QPE demonstrations, at the 7242 controlled-Z gate level
of standard transpilation, utilizing a Q-CTRL error suppression module.
Additionally, we propose a technique towards molecular executions using spatial
orbital localization and index sorting, verified by a 13- (17-)qubit hexatriene
(octatetraene) simulation. Since QPDE can handle the same objectives as QPE,
our algorithm represents a leap forward in quantum computing on real devices.
Shu Kanno Kenji Sugisaki Hajime Nakamura Hiroshi Yamauchi Rei Sakuma Takao Kobayashi Qi Gao Naoki Yamamoto