Lifting the Curse of Dimensionality
Lifting the Curse of Dimensionality
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Interested in AVOIDING TRAP, relying on Quantum Oracle
Barren Plateaus, Scaling Complexity, Reduced Readout, Inherent Instability
Avoid NP-Hard; change an N**3 problem into a 3*N problem
Never write down the matrix elements of the Hamiltonian, which avoids NP-Hard entirely
Work in separate dimensions with explicitly correct Hamiltonians
Collective behavior through Eigensolve
Apply true methods like Lanczos, get compression for free
Solve impossibly high-dimensional problems routinely.
Taking a play from the Quantum Dynamics playbook, which can routinely solve in 12 dimensions with HPC
Routinely use PC’s to push physics in 6 dimensions
Bridge the gap from Quantum Dynamics to Quantum Electron Dynamics
Electronic Hamiltonian in reduced dimensions
12-dimensional tensor exactly reduced to a tensor train of 2-dimensional terms
Build interactions in the wink of an eye
Work in operational/separation/compression space
Patented on Quantum Computing
Dream of ’60s Chemistry: Geminals
Published several times since 2019, including JCP, Molecular Physics, and PCCP
Compose various chemistries beyond Fermions.
Told by Steve Barry to keep pushing the envelope
More reliable control of correlation
Beyond the chemistry of state: Solving Time Dependence with additional fields
Quantum Electron Dynamics is within reach
The ringing bell of geminal fields can be solved in QTiP
2nd Quant also fits into the framework
Factor numbers, Feature selection, and various other tasks
Random Hamiltonians
Dreams of the Grid
Dreams of the Grid
Why bother with Matrix Elements?
Pioneering digital Hartree Fock with tens of electrons, I found that writing down every matrix element takes much longer. Whereas writing down the core 'lookup tables' takes almost no time. Why solve the system with matrix elements (slow deployment) instead of focusing on tying together 'lookup tables' directly?
In 2018, I realized it was possible. I designed the Andromeda code around the electronic structure lookup tables, facilitating dimensional separation works written by Beylkin and Mohlenkamp, 2005. This paper shows how to treat dense systems as separated dimensional systems. Now, Quantum Dynamics technology can be used to directly access the quantum electron.
A Texas Tech patent, two Army Research Office STIR grants, and several good papers later, including PCCP on quantum computing, demonstrated that faster quantum dynamics algorithms also work with quantum computers.
The ground state is beside the point!
We are concerned with unbiased approach to excited states, allowing for genuine dimensional reductions.
Our techniques reduce complex systems to crisp matrix elements on a many-state basis; these are matrix elements of physical merit. We have the foundations of future technology now.
Quantum Ready
Quantum Ready
Published 12 electronic degrees of freedom in PCCP for quantum as well as classical hardware
"dont let them say your not doing physics, for you have a mole of matrix elements", comment at ACS meeting
"You have turned a N^3 problem into a 3N problem!" commentary at LANL of early work
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