Campus Event Calendar
Event Entry
What and Who
Hamiltonian simulation theory: from near-term quantum computing to quantum gravity
Tony Cubitt
University College London
INF Distinguished Lecture Series
AG 1, AG 2, AG 3, INET, AG 4, AG 5, D6, SWS, RG1, MMCI
AG Audience
English
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Date, Time and Location
Thursday, 28 July 2022
16:00
45 Minutes
E1 4
024
Saarbrücken
Abstract
"Analogue" Hamiltonian simulation involves engineering a Hamiltonian of interest
in the laboratory and studying its properties experimentally. Large-scale
Hamiltonian simulation experiments have been carried out in optical lattices,
ion traps and other systems for two decades. This is often touted as the most
promising near-term application of quantum computing technology, as it is argued
it does not require a scalable, fault-tolerant quantum computer.
Despite this, the theoretical basis for Hamiltonian simulation is surprisingly
sparse. Even a precise definition of what it means to simulate a Hamiltonian was
lacking. In my talk, I will explain how we put analogue Hamiltonian simulation
on a rigorous theoretical footing, by drawing on techniques from Hamiltonian
complexity theory in computer science, and Jordan and C* algebra results in
mathematics.
I will then explain how this proved to be far more fruitful than a mere
mathematical tidying-up exercise. It led to the discovery of universal quantum
Hamiltonians [Science, 351:6 278, p.1180 (2016); Proc. Natl. Acad. Sci. 115:38
p.9497, (2018); J. Stat. Phys. 176:1 p228\u2013261 (2019);
[[[01]https://link.springer.com/article/10.1007/s00023-021-01111-7][Annales
Henri Poincar?, 23 p.223 (2021)], later shown to have a deep connection back to
quantum complexity theory [PRX Quantum 3:010308 (2022)]. The theory has also
found applications in developing new and more efficient fermionic encodings for
quantum computing [Phys. Rev. B 104:035118 (2021)], leading to dramatic
reductions in the resource requirements for Hamiltonian simulation on near-term
quantum computers [Nature Commun. 12:1, 4929 (2021)]. It has even found
applications in quantum gravity, leading to the first toy models of AdS/CFT to
encompass energy scales, dynamics, and (toy models of) black hole formation [J.
High Energy Phys. 2019:17 (2019); J. High Energy Phys. 2022:52 (2022)].
in the laboratory and studying its properties experimentally. Large-scale
Hamiltonian simulation experiments have been carried out in optical lattices,
ion traps and other systems for two decades. This is often touted as the most
promising near-term application of quantum computing technology, as it is argued
it does not require a scalable, fault-tolerant quantum computer.
Despite this, the theoretical basis for Hamiltonian simulation is surprisingly
sparse. Even a precise definition of what it means to simulate a Hamiltonian was
lacking. In my talk, I will explain how we put analogue Hamiltonian simulation
on a rigorous theoretical footing, by drawing on techniques from Hamiltonian
complexity theory in computer science, and Jordan and C* algebra results in
mathematics.
I will then explain how this proved to be far more fruitful than a mere
mathematical tidying-up exercise. It led to the discovery of universal quantum
Hamiltonians [Science, 351:6 278, p.1180 (2016); Proc. Natl. Acad. Sci. 115:38
p.9497, (2018); J. Stat. Phys. 176:1 p228\u2013261 (2019);
[[[01]https://link.springer.com/article/10.1007/s00023-021-01111-7][Annales
Henri Poincar?, 23 p.223 (2021)], later shown to have a deep connection back to
quantum complexity theory [PRX Quantum 3:010308 (2022)]. The theory has also
found applications in developing new and more efficient fermionic encodings for
quantum computing [Phys. Rev. B 104:035118 (2021)], leading to dramatic
reductions in the resource requirements for Hamiltonian simulation on near-term
quantum computers [Nature Commun. 12:1, 4929 (2021)]. It has even found
applications in quantum gravity, leading to the first toy models of AdS/CFT to
encompass energy scales, dynamics, and (toy models of) black hole formation [J.
High Energy Phys. 2019:17 (2019); J. High Energy Phys. 2022:52 (2022)].
Contact
Christina Fries
+49 681 9325 5722
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Christina Fries, 07/18/2022 10:55 -- Created document.