RAC1 Journal Club/Seminar SeriesExport this event to calendar

Friday, June 1, 2018 — 11:45 AM EDT

The number theory of quantum information

Jon YardJon Yard, IQC

Abstract: Quantum-mechanical amplitudes and unitaries are typically expressed over the complex numbers. Because there is a continuum of complex numbers, classical computations of quantum systems generally utilize finite-precision approximations by rational numbers. However, many of the irrational numbers arising in quantum information theory are algebraic, i.e. roots of polynomials with rational coefficients. As with rational numbers, algebraic numbers can be exactly represented and manipulated, enabling precise numerical computations without round-off errors. In this talk, I will give a gentle introduction to the theory of algebraic numbers, focusing on two applications to quantum information: optimal compilation over fault-tolerant quantum gate sets and the exact construction of optimal symmetric quantum measurements. The mathematical depth encountered at this crossroads of quantum mechanics and number theory is at least as compelling as the applications themselves.

Location 
RAC - Research Advancement Centre
2009

,
Canada

S M T W T F S
26
27
28
29
30
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
1
2
3
4
5
6
  1. 2021 (45)
    1. November (2)
    2. October (5)
    3. September (3)
    4. August (4)
    5. July (4)
    6. June (5)
    7. May (3)
    8. April (4)
    9. March (5)
    10. February (4)
    11. January (6)
  2. 2020 (31)
    1. December (2)
    2. November (5)
    3. October (4)
    4. September (3)
    5. August (2)
    6. June (4)
    7. April (1)
    8. March (3)
    9. February (5)
    10. January (2)
  3. 2019 (139)
  4. 2018 (142)
  5. 2017 (131)
  6. 2016 (88)
  7. 2015 (82)
  8. 2014 (94)
  9. 2013 (91)
  10. 2012 (122)
  11. 2011 (117)
  12. 2010 (41)
  13. 2009 (4)
  14. 2008 (1)
  15. 2005 (1)
  16. 2004 (3)