Announcements

Course Description

This class is a joint Harvard-MIT graduate course on topics of recent interest in quantum complexity theory, especially focusing on the area of Hamiltonian complexity.

Course Information

Instructors: Anurag Anshu (anuraganshu at fas dot harvard dot edu), Anand Natarajan (anandn at mit dot edu).

Teaching fellows/assistants: Yeongwoo Hwang, Tina Zhang

Space-time coördinates: Class meetings may be split between MIT and Harvard based on student demand, TBD. Recordings will be made available for those who cannot make class meeting times.

MIT: Tuesdays & Thursdays 11:00 a.m. to 12:30 p.m., 36-153, Harvard: TBD

Our first class meeting will be Thursday 9/4 at MIT!

Piazza: Available here.

Lecture schedule and readings

Date Topic Readings
9/4 QMA basics  
9/9 QMA in PP, Feynman-Kitaev construction and the Local Hamiltonian problem  
9/11 Feynman-Kitaev construction, QMA- and BQP-complete problems  
9/16 Perturbation theory and physical Hamiltonains  
9/18 Quantum Gibbs state basics  
9/23 The Bose-Hubbard and SYK models  
9/25 Subclasses of QMA: StoqMA and QCMA  
9/30 Oracle separations between QMA and QCMA  
10/2 Tractable instances of LH: product states and matrix product states  
10/7 The Guided LH problem and quantum algorithms  
10/9 Hardness of approximation for Hamiltonians and quantum PCP  
10/14 Quantum PCP: proofs and nonlocal games  
10/16 Monogamy of entanglement and the Brandão-Harrow theorem  
10/21 Quantum gap amplificaiton and the detectabilty lemma  
10/23 DL and decay of correlations  
10/25 DL and area laws  
10/30 Area laws in frustrated systems  
11/4 Complexity of state and unitary synthesis  
11/6 Unitary synthesis and Hamiltonian simulation  
11/11 No class (Veterans’ Day)  
11/13 Quantum Gibbs sampling and detailed balance  
11/18 Hamiltonian learning  
11/20 Variational quantum algorithms  
11/25 Group problems in QMA  
11/27 No class (Thanksgiving)  
12/3 Topological data analysis  
12/5 Final project presentations