Tensor Factorized Hamiltonian Downfolding

This talk presents a new variant of post-Hartree-Fock Hamiltonian downfolding-based quantum chemistry methods with optimized scaling for high-cost simulations like coupled cluster (CC), full configuration interaction (FCI), and multi-reference CI (MRCI) on classical and quantum hardware. This improves the applicability of these calculations to practical use cases. High-accuracy quantum chemistry calculations, such as CC, involve memory and timeintensive tensor operations, which are the primary bottlenecks in determining the properties of many-electron systems. The complexity of these operations scales exponentially with the system size. We aim to find properties of chemical systems by optimizing this scaling through mathematical transformations on the Hamiltonian and the state space. By defining a bi-partition of the many-body Hilbert space into electronoccupied and electron-unoccupied blocks for a given orbital, we perform a downfolding transformation that decouples the electron-occupied block from its complement. We factorize high-rank electronic integrals and cluster amplitude tensors into low-rank tensor factors of a downfolding transformation, mapping the full many-body Hamiltonian into a smaller dimensional block-Hamiltonians. This reduces the computational complexity of solving the residual equations for Hamiltonian downfolding from O(N7) for CCSD(T) and O(N9) - O(N10) for CI and MRCI to O(N3). This operations can be implemented as a family of tensor networks solely made from two-rank tensors. Additionally, we create block-encoding quantum circuits of the tensor networks, generating circuits of O(N2) depth with O(logN) qubits. We demonstrate super-quadratic speedups of expensive quantum chemistry algorithms on both classical and quantum computers.

Speaker:

Anirban Mukherjee is a technopreneur for quantum chemistry at TCS, where his patented tensor-factorized downfolding and GPU-QPU algorithms slash high-level quantum-chemical runtimes. A former Ames National Lab postdoc (quantum Gutzwiller embedding) and IISER Kolkata PhD (holographic unitary RG), he holds nine patents, publishes in Physical Review and Communications Physics, and spearheads quantum-accelerated drug-development pilots for Big Pharma.