# Online: Seminar, Elizabeth Crosson (University of New Mexico), The Sign Problem and its Relation to the Spectral Gap of Quantum Many-Body Systems #### calendar\_today Date and Time **June 9, 2020** 10:00AM - 10:00AM EDT #### pin\_drop Location **Zoom** ![Elizabeth Crosson](/sites/g/files/omnuum6611/files/styles/hwp_1_1__720x720_scale/public/mathpicture/files/crosson.jpg?itok=lypTzV3Z) **Location:** Zoom [https://harvard.zoom.us/j/779283357 ](https://harvard.zoom.us/j/779283357%C2%A0) **Time:** Tuesday, June 9, 2020, 10:00 AM (Eastern US), 16:00 (Central Europe), 22:00 (China) **Title:** The Sign Problem and its Relation to the Spectral Gap of Quantum Many-Body Systems **Abstract:** The partition function of a quantum system without a sign problem can be represented by a path integral in which every amplitude is efficiently computable and nonnegative, which is a substantial simplification from the interference of complex amplitudes in the general quantum case. In quantum computing the presence of a sign problem has been recast as a virtue, because it helps to increase the complexity of the quantum system beyond the range of classical simulation. This is particularly important for quantum adiabatic algorithms based on ground states, where the run time depends on the scaling of the spectral gap above the ground state. This motivates us to study the relation of the sign problem to the spectral gap, using methods such as random matrix theory and spectral graph theory. The latter relates the discrete geometry of ground states (in a world where vertices are basis elements and edges are Hamiltonian matrix elements) to the level spacings in the low energy spectrum using the higher-order signed Cheeger inequalities. This talk will include analytical results from 1703.10133 and 2004.07681. **Additional Ways to Join** Join by telephone (use any number to dial in) +1 929 436 2866 +1 312 626 6799 +1 669 900 6833 +1 253 215 8782 +1 301 715 8592 +1 346 248 7799 +41 43 210 70 42 +41 43 210 71 08 +41 22 591 00 05 +41 22 591 01 56 +41 31 528 09 88 +31 20 794 6520 +31 20 794 7345 +31 20 241 0288 +31 20 794 0854 +31 20 794 6519 +65 3165 1065 +65 3158 7288 +33 1 7095 0350 +33 7 5678 4048 +33 1 7037 2246 +33 1 7037 9729 +33 1 7095 0103 +49 30 5679 5800 +49 695 050 2596 +49 69 7104 9922 +45 32 72 80 11 +45 89 88 37 88 +45 32 70 12 06 +45 32 71 31 57 +45 32 72 80 10 400 669 9381 China Toll-free 400 616 8835 China Toll-free 0 800 561 252 Switzerland Toll-free 0 800 002 622 Switzerland Toll-free 0 800 220 0040 Netherlands Toll-free 0 800 022 1954 Netherlands Toll-free 800 852 6054 Singapore Toll-free 800 101 3814 Singapore Toll-free 0 805 082 588 France Toll-free 0 800 940 415 France Toll-free 0 800 1800 150 Germany Toll-free 0 800 000 6954 Germany Toll-free 80 82 02 88 Denmark Toll-free 80 71 12 51 Denmark Toll-free International numbers available: [https://harvar](https://harvard.zoom.us/u/aclg6kOggb)[d.zoom.us/u/aclg6kOggb](https://harvard.zoom.us/u/aclg6kOggb) One tap mobile: +19294362866,,779283357# US (New York) Join by SIP conference room system Meeting ID: 779 283 357 <779283357@zoomcrc.com> **Attachments:** --- Attachments- [ picture\_as\_pdf Flyer ](/sites/g/files/omnuum6611/files/mathpicture/files/crosson_seminar_june_9_2002.pdf) --- Share on:- [ Facebook ](#) - [ Twitter ](#) - [ Linkedin ](#) Save: [ Add to calendar calendar\_today ](https://mathpicture.fas.harvard.edu/node/1510212/event-feed.ics) Copy link link