Quantum Simulation

Übungsgruppen

• Gruppe A (Martin Gärttner)
  11 Teilnehmer/innen
  INF 227, 3.404, Do 16:15 - 17:45

Course description

Quantum simulators, special purpose quantum computers, are the first kind of quantum computers that will surpass the capabilities of classical computers in simulating the dynamics of quantum many-body systems. Outstanding problems in condensed matter, quantum chemistry, and high energy physics, such as high temperature superconductivity or quantum magnetism can supposedly described by simple quantum mechanical models like the Hubbard model. However, these models turn out to be exceedingly hard to solve on classical computers because the memory needed to store the quantum state of a system grows exponentially with the number of particles. A solution to this problem would be to use a quantum computer to simulate quantum dynamics, i.e. to have a perfectly controlled quantum systems that we can prepare, time evolve, and measure and thus understand the effects leading to the phenomena mention above. Thanks to rapid technological advances for example in cooling and trapping atoms, ions, and molecules, such devices are now becoming available in the lab. In this seminar we will take a tour from the original problem of quantum complexity formulated by Feynman to the most recent experimental progress that is made in quantum simulation labs around the world, including here in Heidelberg.

 

Literature:

1) Quantum simulation review article by I. M. Georgescu in Review of Modern Physics. (https://arxiv.org/abs/1308.6253)

2) Nature Physics special issue on quantum simulation: Insight issue: April 2012 Volume 8, No 4

 

 

Presentation topics:

 

1)      Simulating Physics with computers (26.10.2017) [Michael Rautenberg]

Guiding questions:

What is Feynman’s line of thought? Why is it not possible to simulate quantum physics problems on classical computers?

What is Lloyd’s idea for implementing a quantum simulator?

What is the difference between an analog and a digital quantum simulator?

Optional: How can the complexity of quantum problems be classified?

Literature:

R. P. Feynman, Int. J. Theor. Phys. 21, 467 (1982). (https://people.eecs.berkeley.edu/~christos/classics/Feynman.pdf)

Universal Quantum Simulators, Seth Lloyd, Science 273, 1073 (1996). (http://science.sciencemag.org/content/273/5278/1073)

Optional: https://arxiv.org/abs/0804.3401 (Mathematical approach to quantum complexity)

 

2)      Classical ways of dealing with quantum complexity (2.11.2017) [Daniel Spitz]

Guiding questions:

Is the experimental size of the Hilbert space necessarily a problem for simulating physical systems? For what types of systems can we make statements about the part of Hilbert space that is explored?

What is the basic idea behind matrix product states and tensor network states in general? (Illustrate with a simple example.)

What systems/problems can be efficiently simulated using MPS? What are their limitations?

Literature:

https://arxiv.org/abs/1306.2164 (Tutorial style intro to MPS)

https://arxiv.org/abs/0907.2796 (A bit more technical but with nice intro explaining some basic ideas and concepts.)

https://arxiv.org/abs/1008.3477 (Classic DMRG review, probably much too technical but chapters 1-4 are very instructive.)

 

3)      Certifying quantum simulators (9.11.2017) [cancelled]

Guiding questions:

What are basic requirements that a quantum simulator should fulfil? What is meant by “quantum supremacy”?

Which are the most common approaches for certifying that a quantum simulator works correctly?

How does the certification scheme proposed in arXiv:1602.00703 work?

Literature:

https://arxiv.org/abs/1203.5813 (General discussion of the potential of quantum simulators, definition of the notion of “quantum supremacy”)

https://arxiv.org/abs/1602.00703v3 (Certifying quantum simulators using local measurements, nice intro, specific type of quantum simulations: Ground state preparation of frustration-free Hamiltonians)

https://arxiv.org/abs/1109.6457 (Discussion of imperfections of quantum simulators.)

 

4)      Adiabatic quantum computing (16.11.2017) [Alexander Gersch]

Guiding questions:

What physical problem is “simulated” by adiabatic computing?

Why are such problems of broader relevance for computer science?

Describe an implementation of a quantum annealer?

Is the d-wave machine a proper quantum annealer?

Literature:

Nature 473, 194–198 (12 May 2011), “Quantum annealing with manufactured spins” (more recent paper of the d-wave collaboration)

Science 294(5516), pp. 472-475 (2001) (https://arxiv.org/abs/quant-ph/0104129). (Original adiabatic quantum computing proposal)

KITP lecture of Wolfgang Lechner: http://online.kitp.ucsb.edu/online/synquant-c16/lechner/ First ~15min are a very nice introduction to the topic.

 

5)      Quantum phase transitions (MI-SF experiment) (23.11.2017) [Aleksandr Mikheev]

Guiding questions:

What is a quantum phase transition?

Can this problem be simulated on a classical computer?

How is an optical lattice implemented experimentally?

Literature:

Nature 415, 39-44 (2002) “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms”

 

6)      Digital quantum simulation of quantum electrodynamics (30.11.2017) [Manuel Rudolph]

Guiding questions:

What is the “hard” physical problem that is simulated?

How is the digital quantum simulation implemented with a chain of trapped ions?

Literature:

Nature 534, 516–519 (2016) (https://arxiv.org/abs/1605.04570) (Proof of principle experiment for using a digital quantum simulator to emulate lattice gauge theories.)

Science 334, 57 (2011) (https://arxiv.org/abs/1109.1512) (Demonstration of digital quantum simulation.)

 

7)      Quantum thermalization through entanglement in an isolated many-body system (7.12.2017) [Sebastian Geier]

Science 353, 794 (2016) (https://arxiv.org/abs/1603.04409)

 

8)      On solving quantum many-body problems by experiment (14.12.2017) [Lara Kuhn]

Nature 545, 323 (2017) (https://arxiv.org/abs/1505.03126)

 

9)      Quantum simulation with linear ion chains (21.12.2017) [Alexander Hesse]

Many-body localization in a quantum simulator with programmable random disorder. Nature Physics 12, 907–911 (2016) (https://arxiv.org/abs/1508.07026)

Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator (https://arxiv.org/abs/1708.01044) 

 

10)   Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms (11.01.2017) [Lauritz Klaus]

Nature 545, 462-466 (2017) (https://arxiv.org/abs/1612.08436)

Guiding questions:

Why is realizing the ground state of the anti-ferromagnetic Hubbard model considered a breakthrough for condensed matter physics?

What other groups realized fermionic quantum gas microscopes with similar results?

 

11)   Microtrap arrays of Rydberg atoms (18.1.2018) [Lena Haaga]

Probing many-body dynamics on a 51-atom quantum simulator (https://arxiv.org/abs/1707.04344)

 

12)   Emergence of a turbulent cascade in a quantum gas (25.1.2018) [Sarah Bartha]

Nature 539, 72 (2016) (https://arxiv.org/abs/1609.01271)

 

13)   Implementing Boson sampling with Photons (1.2.2018) [Dragos Duse]

Experimental Boson Sampling. Nature Photonics 7 540 - 544 (2013) (https://arxiv.org/abs/1212.2240)

Multi-photon boson-sampling machines beating early classical computers (https://arxiv.org/abs/1612.06956)

Recent critical theory paper: No imminent quantum supremacy by boson sampling (https://arxiv.org/abs/1705.00686)

 

Topics 5-13 are concrete physical implementations of a quantum simulator. For each of them it should be clarified what is the physical problem that the experiment tries of simulate and why is it interesting? Is the problem hard classically? How does the experimental implementation work? What has to be done in order to reach a regime that is not accessible to classical simulations?

 

All topics have been assigned. All participants should sign up for the practice group. If you have questions, please contact martin.gaerttner@kip.uni-heidelberg.de