CoogeeÕ14

Sydney Quantum Information Theory Workshop

Robin Blume-Kohout

(Sandia, USA)

Implications of analog simulation for computation and complexity

Analog quantum simulation -- the kind of simulation you do in optical lattices, without error correction -- may or may not actually work.  Oddly enough, everybody knows whether or not it will work... but half of us know that it will, and half know it won't!  Both possible answers have interesting implications for computational complexity.  In addition to discussing these implications, I'll use analog simulation as inspiration to try and answer the question "What kind of algorithms could run usefully on a small quantum computer?"

REFERENCES (warning -- these are pretty diverse, tangential to the talk, and in no particular order):

C. Zalka, "Efficient Simulation of Quantum Systems by Quantum Computers", <http://arxiv.org/abs/quant-ph/9603026v2>

J. Cirac and P. Zoller, "Goals and opportunities in quantum simulation", Nature Physics (2012) <http://www.nature.com/nphys/journal/v8/n4/full/nphys2275.html>

K. Brown et al, "Limitations of Quantum Simulation Examined by Simulating a Pairing Hamiltonian Using Nuclear Magnetic Resonance", PRL (2006) <http://prl.aps.org/abstract/PRL/v97/i5/e050504>

C. Clark et al, "Resource Requirements for Fault-Tolerant Quantum Simulation: The Transverse Ising Model Ground State", PRA (2009) <http://arxiv.org/abs/0810.5626>

Kliesch et al, "Dissipative Quantum Church-Turing Theorem", PRL (2011) <http://prl.aps.org/abstract/PRL/v107/i12/e120501>

F. Verstraete et al, "Quantum computation, quantum state engineering, and quantum phase transitions driven by dissipation", Nature Physics (2009) <http://arxiv.org/abs/0803.1447>

F. Le Gall, "Exponential Separation of Quantum and Classical Online Space Complexity", Theory of Computing Systems (2009) <http://arxiv.org/abs/quant-ph/0606066>

Gavin Brennen

(Macquarie, Australia)

Investigations of topological entanglement entropy in 3D Walker-Wang models

Andrew Doherty

(Sydney, Australia)

Really real quantum mechanics

There has been recent work on the foundations of quantum mechanics that attempts understand quantum mechancis better by deriving it from reasonable axioms. Typically it is imagined that a sensible physical theory should have the correct mathematical structure to describe the probabilities of measurement outcomes, and satisfy more physical assumptions such as the possibility of performing tomography with local measurements. Real quantum mechanics as it is usually posited fails the latter requirement. I will describe a version of real quantum mechanics which does have local tomography and satisfies a de Finetti theorem. It is a useful foil theory for axiomatic derivations of quantum mechanics but is also interesting in its own right since it has many of the properties of quantum mechanics that relate to Heisenberg uncertainty but has only very limited entanglement.

If time allows I will discuss other general probabilistic theories that also satisfy local tomography and possess a de Finetti theorem but are not subsets of quantum mechanics. These may also be useful foil theories for future work in quantum foundations.

David Jennings

(Imperial College London, UK)

QI directions for relativistic and non-relativistic fields

I will outline some very recent work that tries to extend ideas and techniques from quantum information theory to quantum field systems. Depending on time available, I describe a line of work that constructs quantum field states that are efficiently contractible in two and three dimensions. I will then ask whether relativistic quantum field systems might admit a broader class of information-theoretic protocols than found in non-relativistic QM.

References:

1. R. Clifton, H. Halvorson, J. Bub. Found. of Phys. 33 (11) 1561) (2003)

2. F. Verstraete, J. Cirac, Phys. Rev. Lett. 104 190405 (2010)

2. D. Jennings, J. Haegeman, T. Osborne, F. Verstraete, arxiv:1212.3833 (2012)

Shelby Kimmel

(MIT, USA)

Problems with Multiple Oracles

I will describe problems where multiple oracles, potentially with different costs, are given as resources. As a sample problem, I will consider searching with multiple classical or quantum oracles, and describe algorithms and lower bounds for this problem.

Some background reading:

Brassard et al. '00, "Quantum Amplitude Amplification and Estimation" http://arxiv.org/abs/quant-ph/0005055

Montanaro '09, "Quantum Search With Advice" http://arxiv.org/abs/0908.3066

Cerf et al. '00 "Nested Quantum Search and Structured Problems"  http://pra.aps.org/abstract/PRA/v61/i3/e032303

Ambainis '06, "Quantum Search With Variable Times" http://arxiv.org/abs/quant-ph/0609168

Enrique Rico Ortega

(Strasbourg, France)

Tensor networks for Lattice Gauge Theories and Atomic Quantum Simulation

We show that gauge invariant quantum link models, Abelian and non-Abelian, can be exactly described in terms of tensor networks states. Quantum link models represent an ideal bridge between high-energy to cold atom physics, as they can be used in cold-atoms in optical lattices to study lattice gauge theories. In this framework, we characterize the phase diagram of a (1+1)-d quantum link version of the Schwinger model in an external classical background electric field: the quantum phase transition from a charge and parity ordered phase with non-zero electric flux to a disordered one with a net zero electric flux configuration is described by the Ising universality class.

References.-

1) arXiv:1312.3127: Tensor networks for Lattice Gauge Theories and Atomic Quantum Simulation. E. Rico, T. Pichler, M. Dalmonte, P. Zoller, S. Montangero.

2) Phys. Rev. Lett. 111, 110504 (2013): Superconducting Circuits for Quantum Simulation of Dynamical Gauge Fields. D. Marcos, P. Rabl, E. Rico, P. Zoller.

3) Phys. Rev. Lett. 110, 125303 (2013): Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories. D. Banerjee, M.Bšgli, M. Dalmonte, E. Rico, P. Stebler, U.-J. Wiese, P. Zoller.

4) Phys. Rev. Lett. 109, 175302 (2012): Atomic Quantum Simulation of Dynamical Gauge Fields coupled to Fermionic Matter: From String Breaking to Evolution after a Quench. D. Banerjee, M. Dalmonte, M. MŸller, E. Rico, P. Stebler, U.-J. Wiese, P. Zoller.

Tobias Osborne

(Hannover, Germany)

Quantum Yang-Mills theory:  an overview of a program

In this talk a description of the ground state of lattice gauge theory in terms of a tensor network state is pursued. We work with pure gauge theory in the hamiltonian formalism on the lattice and study the locally gauge invariant sector of Hilbert space. A toolkit to describe states in this sector, exploiting parallel transport operations and block-spin averaging operations, to construct hierarchical tensor networks for pure gauge theory on the lattice is described. An ansatz for the ground state of pure Yang-Mills theory will then be introduced. The continuum limit of the ground-state ansatz is also discussed, and is connected to the removal of the lattice regulator. This talk is intended as a high-level overview of an ongoing programme.

Background reading:

1. J. Kogut and L. Susskind, Phys. Rev. D 11, 395 (1975)

2. E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, J. Math. Phys. 43, 4452 (2002)

3. C. Beny and T. J. Osborne, arXiv:1310.3188

Giandomenico Palumbo

(University of Leeds, UK)

Non-Abelian anyons from a Hubbard-like model

It was recently shown by the authors [Phys. Rev. Lett. {\bf 110}, 211603 (2013)] that the $(2+1)$-dimensional U(1) symmetric Thirring model, and its bosonised description by Maxwell-Chern-Simons theory, faithfully describes the low energy behaviour of a tight-binding model of spinless fermions. It is also known that Yang-Mills-Chern-Simons theory can emerge from the SU(2) symmetric Thirring model, albeit it can only support Abelian anyons. Here, we provide a simple tight binding model of spin-$1/2$ fermions that gives rise to such a Thirring model. First, we identify the regime that simulates the SU(2) Yang-Mills theory. Then, we suitably extend this model so that it can support non-Abelian Ising anyons. This is achieved by introducing an additional two-dimensional degree of freedom in the lattice fermions and modifying the Thirring interactions, while preserving the SU(2) symmetry of the model.

Background papers:

G. Palumbo and J.K. Pachos, arXiv:1311.2871

M. Freedman, M. Larsen and Z. Wang, Comm. Math. Phys. 228, 177 (2002).

C. Nayak, S. H. Simon, A. Stern, M. Freedman and S. Das Sarma, Rev. Mod. Phys. 80, 1083 (2008).

David Poulin

(Sherbrooke, Canada)

Fault-tolerant quantum computing with a reasonable overhead: Simplified quantum compiling with complex gate distillation

I will present a scheme to compile complex quantum gates that uses significantly fewer resources than existing schemes. In standard fault-tolerant protocols, a magic state is distilled from noisy resources, and copies of this magic state are then assembled to produced complex gates using the Solovay-Kitaev theorem or variants thereof. In our approach, we instead directly distill magic states associated to complex gates from noisy resources, leading to a reduction of the compiling overhead of several orders of magnitude. Joint work with my student Guillaume Duclos-Cianci.

Background material:

http://arxiv.org/abs/1204.4221

http://arxiv.org/abs/quant-ph/0403025

http://arxiv.org/abs/1212.6964

Jiannis Pachos

(University of Leeds, UK)

To be announced

Robert Raussendorf

(UBC, Canada)

Contextuality in measurement-based quantum computation

We show, under natural assumptions for qubit systems, that measurement-based quantum computations (MBQCs) which compute a nonlinear Boolean function with a high probability are contextual. The class of contextual MBQCs includes an example which is of practical interest and has a superpolynomial speedup over the best-known classical algorithm, namely, the quantum algorithm that solves the Òdiscrete logÓ problem.

Based on: R. Raussendorf, PHYSICAL REVIEW A 88, 022322 (2013)

Background:

N. D. Mermin, Rev. Mod. Phys. 65, 803 (1993).

J. Anders and D. E. Browne, Phys. Rev. Lett. 102, 050502 (2009).

Terry Rudolph

(Imperial College London, UK)

An assorted bunch of small open questions Terry is stuck on

The talk will be about the title.

Guifre Vidal

(Perimeter Institute, Canada)

On the shape of entanglement

Over the last ten years, the study of the entanglement in extended quantum many-body systems has lead to very fruitful insights into the structure of many-body wave-functions. For instance, we have learned that the entanglement entropy of a region scales as a boundary law (possibly, with a multiplicative logarithmic correction). This has been crucial for the development of tensor network states to efficiently simulate these systems. From the scaling of entanglement entropy, it is also possible to extract universal properties such as the central charge or a CFT at quantum criticality or the total quantum dimension of an emergent anyon model in a topologically ordered phase. In this talk I will discuss ways of attaching a real-space shape to the entanglement of a region. [In collaboration with Yangang Chen]

Related research:

G. Vidal, J. I. Latorre, E. Rico, A. Kitaev,

Entanglement in quantum critical phenomena

Phys. Rev. Lett. 90:227902, 2003, arXiv:quant-ph/0211074

J. I. Latorre, E. Rico, G. Vidal,

Ground state entanglement in quantum spin chains,

QIC 4 (2004) 48-92, arXiv:quant-ph/0304098