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 Scribe notes
9/4 QMA basics L0, L1
9/9 QMA in PP, Feynman-Kitaev construction and the Local Hamiltonian problem L2
9/11 Feynman-Kitaev construction, QMA- and BQP-complete problems L3
9/16 Perturbation theory and physical Hamiltonains L4
9/18 Quantum Gibbs state basics L5
9/23 The Bose-Hubbard and SYK models L6
9/25 Subclasses of QMA: StoqMA and QCMA L7
9/30 Oracle separations between QMA and QCMA L8
10/2 Tractable instances of LH: product states and matrix product states L9
10/7 The Guided LH problem and quantum algorithms L10
10/9 Hardness of approximation for Hamiltonians and quantum PCP L11
10/14 Quantum PCP: proofs and nonlocal games L12
10/16 Monogamy of entanglement and the Brandão-Harrow theorem L13
10/21 Quantum gap amplificaiton and the detectabilty lemma L14
10/23 DL and decay of correlations  
10/25 DL and area laws L16
10/30 Area laws in frustrated systems  
11/4 Renormalization group and algorithms for 1D systems L18
11/6 Gibbs sampling  
11/11 No class (Veterans’ Day)  
11/13 Hamiltonian learning L20
11/18 State synthesis L21
11/20 Unitary synthesis  
11/25 Consistency of local density matrices L23
11/27 No class (Thanksgiving)  
12/2 Class cancelled  
12/4 Guest lecture: Hamiltonian DQI L24
12/9 Final project presentations