Circuit-To-Hamiltonian From Tensor Networks and Fault Tolerance
summary
Constructs a clock-free map from any quantum circuit to a local Hamiltonian by turning the circuit’s Choi states into an injective PEPS parent Hamiltonian; the ground state equals a computation plus independent local errors so the rightmost qubits hold a noisy computation with local depolarizing noise per gate. Shows exponential-in-depth energy density still forces an adversarially noisy computation, and 1/poly(depth) combinatorial error gives polylog adversarial noise. Uses quantum fault tolerance to make outputs recoverable and proves contracting these injective tensor networks to additive error is BQP-hard.
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chapters (11)
- 0:00Circuit-to-Hamiltonian mapping intro
- 3:29Robustness in classical/quantum mappings
- 8:38Quantum computation via tensor networks
- 13:23PEPS and parent Hamiltonian
- 17:34Operational interpretation of PEPS
- 22:07Fault tolerance to preserve computation
- 23:31Definitions and robustness theorems
- 26:01Spectral gap implications
- 27:48QMA-completeness with log-local Hamiltonian
- 28:54Quantum PCP and fault tolerance
- 31:58Conclusion and open questions
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