Strongly Universal Hamiltonian Simulators
summary
Claim: any Hamiltonian whose time evolution a polynomial-size quantum circuit approximates gets encoded as the low-energy sector of a simple simulator with only polynomial overhead. Construction maps that circuit via phase-estimation plus energy-penalty into a spatially sparse circuit, then uses a Kitaev-style circuit-to-Hamiltonian embedding and a non-perturbative degree-reduction to produce either a 2D spin lattice (semi-translational) or a 1D chain of eight-dimensional particles that reproduces spectra and local observables.
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chapters (13)
- 0:00Introduction
- 0:22Analog Simulation
- 3:04Universal Simulations
- 23:08Summary
- 24:14Open Questions
- 26:12Efficient Mapping
- 29:46Constant Strength Degree Reduction
- 32:25No Fast Forward Theorem
- 32:50Fast Forward Theorem
- 33:29No Squashable Theorem
- 38:19Locality
- 39:53Random Commission
- 41:24Universal Digital Analog Machine
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