Program
Full Program | Thursday | Friday | Saturday | All Sessions | Posters | Talks
SESSION 12: Complexity and many-body problemsChair: (Andrew Landahl (Sandia National Laboratories)) | |
| 1:30pm-2:15pm | Shelby Kimmel, Middlebury College Quantum vs. classical proofs | Abstract. QMA is the quantum generalization of the complexity class NP. QMA contains important and physically relevant problems, such as whether a local Hamiltonian admits a low energy ground state. In QMA, the goal is to verify a proof using a quantum verifier, where the proof is given as a quantum state. It is an open question whether the complexity class loses power if the proof is restricted to be a classical bit-string rather than a quantum state. I will describe work with Bill Fefferman in which we find a class of permutation-oracle-based problems where a quantum proof can be used for verification, but any classical proof is insufficient. This builds off of work by Aaronson and Kuperberg, who first described such a separation using oracles derived from Haar random states. |
| 2:15pm-2:45pm | Isaac Kim, Stanford University Robust entanglement renormalization on a noisy quantum computer | Abstract. A method to study strongly interacting quantum many-body systems at and away from criticality is proposed. The method is based on a MERA-like tensor network that can be efficiently and reliably contracted on a noisy quantum computer using a number of qubits that is much smaller than the system size. We prove that the outcome of the contraction is stable to noise and that the estimated energy upper bounds the ground state energy. The stability, which we numerically substantiate, follows from the positivity of operator scaling dimensions under renormalization group flow. The variational upper bound follows from a particular assignment of physical qubits to different locations of the tensor network plus the assumption that the noise model is local. We postulate a scaling law for how well the tensor network can approximate ground states of lattice regulated conformal field theories in d spatial dimensions and provide evidence for the postulate. Under this postulate, a \(O(log^d(1/\delta))\)-qubit quantum computer can prepare a valid quantum-mechanical state with energy density \(\delta\) above the ground state. In the presence of noise, \(\delta=O(\epsilon log^{d+1}(1/\epsilon))\) can be achieved, where \(ϵ\) is the noise strength. |
- Home
- SQuInT
- Past SQuInT Meetings
- Lodging and Transportation
- Hotel Floor Maps (.pdf)
- Registration
- Submit Your Abstract
- Program
- Instructions for Presenters
SQuInT Chief Organizer
Akimasa Miyake, Assistant Professor
amiyake@unm.edu
SQuInT Co-Organizer
Mark M. Wilde, Assistant Professor LSU
mwilde@phys.lsu.edu
SQuInT Administrator
Gloria Cordova
gjcordo1@unm.edu
505 277-1850
SQuInT Founder
Ivan Deutsch, Regents' Professor
ideutsch@unm.edu
