Search Talks

Recent experiments have demonstrated that it is possible to create a synthetic magnetic field for neutral atoms in optical lattices using two-photon (Raman) processes. Motivated by exploring the interplay of such artificial magnetic fields and strong correlations for bosons, we have studied the Bose Hubbard model in the presence of pi-flux per plaquette. Using a variety of techniques, this model is shown to support a remarkable chiral Mott insulator phase on a 2-leg ladder. This state is a fully gapped insulator with staggered loop currents. We discuss physical insights as well experimental signatures of such a state for cold atoms as well as for Josephson junction arrays in a magnetic field.

We used time-of-flight inelastic neutron scattering to measure the excitation spectra from field-polarized states of exotic frustrated magnets. A knowledge of these spin-wave excitations in various directions in reciprocal space allows a robust determination of exchange parameters in suitable model Hamiltonians.  We have taken this approach with two pyrochlores, Er2Ti2O7 and Yb2Ti2O7, whose magnetic properties have until this point been somewhat puzzling.  The model we use is an effective spin-1/2 exchange Hamiltonian that incorporates the full anisotropy allowed by symmetry at the rare earth site.  Er2Ti2O7, an XY anti-ferromagnet on the pyrochlore lattice, is found to reach its unexpected ordered ground state via quantum-order-by-disorder.  Meanwhile, Yb2Ti2O7's effective Hamiltonian reveals the possibility of a Coulombic quantum spin liquid through what we have revealed to be "quantum spin ice" interactions.   I will focus on the experimental side of these collaborative studies.

The quantum spin liquid state is a prime example of an emergent phenomenon. Theory predicts that new particles such as spinons and gauge fields may emerge at low temperatures. However, for many years there have not been any examples in nature. The situation has changed in recent years in that a number of candidate materials have been discovered which may exhibit these exotic phenomena.

Joint work with Earl Campbell (FU-Berlin) and Hussain Anwar (UCL)   Magic state distillation is a key component of some high-threshold schemes for fault-tolerant quantum computation [1], [2]. Proposed by Bravyi and Kitaev [3] (and implicitly by Knill [4]), and improved by Reichardt [4], Magic State Distillation is a method to broaden the vocabulary of a fault-tolerant computational model, from a limited set of gates (e.g. the Clifford group or a sub-group[2])  to full universality, via the preparation of mixed ancilla qubits which may be prepared without fault tolerant protection.    Magic state distillation schemes have a close relation with quantum error correcting codes, since a key step in such protocols [5] is the projection onto a code subspace. Bravyi and Kitaev proposed two protocols; one based upon the 5-qubit code, the second derived from a punctured Reed-Muller code. Reed Muller codes are a very important family of classical linear code. They gained much interest [6] in the early years of quantum error correction theory, since their properties make them well-suited to the formation of quantum codes via the CSS-construction [7]. Punctured Reed-Muller codes (loosely speaking, Reed-Muller codewords with a bit removed) in particular lead to quantum codes with an unusual property, the ability to implement non-Clifford gates transversally [8].    Most work in fault-tolerant quantum computation focuses on qubits, but fault tolerant constructions can be generalised to higher dimensions [9]  - particularly readily for prime dimensions. Recently, we presented the first magic state distillation protocols [10] for non-binary systems, providing explicit protocols for the qutrit case (complementing a recent no-go theorem demonstrating bound states for magic state distillation in higher dimensions [11]). In this talk, I will report on more recent work [12], where the properties of punctured Reed-Muller codes are employed to demonstrate Magic State distillation protocols for all prime dimensions. In my talk, I will give a technical account of this result and present numerical investigations of the performance of such a protocol in the qutrit case. Finally, I will discuss the potential for application of these results to fault-tolerant quantum computation.     This will be a technical talk, and though some concepts of linear codes and quantum codes will be briefly revised, I will assume that listeners are familiar with quantum error correction theory (e.g. the stabilizer formalism and the CSS construction) for qubits.   [1] E. Knill. Fault-tolerant postselected quantum computation: schemes, quant-ph/0402171 [2] R. Raussendorf, J. Harrington and K. Goyal, Topological fault-tolerance in cluster state quantum computation, arXiv:quant-ph/0703143v1 [3] S. Bravyi and A. Kitaev. Universal quantum computation based on a magic states distillation, quant- ph/0403025 [4] B. W. Reichardt, Improved magic states distillation for quantum universality, arXiv:quant-ph/0411036v1 [5] E.T. Campbell and D.E. Browne, On the Structure of Protocols for Magic State Distillation, arXiv:0908.0838
[6] A. Steane, Quantum Reed Muller Codes, arXiv:quant-ph/9608026 [7] Nielsen and Chuang, Quantum Information and Computation, chapter 10 [8] E. Knill, R. Laflamme, and W. Zurek, Threshold accuracy for quantum computation, quant-ph/9610011 [9] D. Gottesman, Fault-Tolerant Quantum Computation with Higher-Dimensional Systems, quant-ph/9802007 [10] H. Anwar, E.T Campbell and D.E. Browne, Qutrit Magic State Distillation, arXiv:1202.2326 [11] V. Veitch, C. Ferrie, J. Emerson, Negative Quasi-Probability Representation is a Necessary Resource for Magic State Distillation, arXiv:1201.1256v3 [12] H. Anwar, E.T Campbell and D.E. Browne, in preparation

Majorana disappeared under mysterious circumstances in 1938 and the particle that bears his name remains elusive to experiments. There is growing interests in realizing the Majorana bound state in the Laboratory because it is expected to possess unusual properties such as non-abelian statistics. I shall discuss various proposals to produce  Majorana bound states and the associated topological superconductors which support them.

It is sometimes pointed out as a curiosity that the state space of quantum theory and actual physical space seem related in a surprising way: not only is space three-dimensional and Euclidean, but so is the Bloch ball which describes quantum two-level systems. In the talk, I report on joint work with Lluis Masanes, where we show how this observation can be turned into a mathematical result: suppose that physics takes place in d spatial dimensions, and that some events happen probabilistically (dropping quantum theory and complex amplitudes altogether). Furthermore, suppose there are systems that in some sense behave as “binary units of direction information”, interacting via some continuous reversible time evolution. We prove that this uniquely determines d=3 and quantum theory, and that it allows observers to infer local spatial geometry from probability measurements.

We review the notion of a quantum state of the universe and its role in fundamental cosmology. Then we discuss recent work which points towards a profound connection, at the level of the quantum state, between (asymptotic) Euclidean AdS spaces and Lorentzian de Sitter spaces. This gives a new framework in which (a mild generalization of) AdS/CFT can be applied to inflationary cosmology.   For the specific case of the Hartle-Hawking no-boundary quantum state the ADS/ de Sitter connection yields a natural proposal for a more precise `dual' formulation of the wave function, in terms of field theories on the future de Sitter boundary that are certain relevant deformations of the CFTs that occur in AdS/CFT.

I will review the construction of lattice theories which maintain one or more exact supersymmetries for non zero lattice spacing concentrating in particular on the case of N=4 super Yang-Mills. Such lattice theories may be studied using Monte Carlo techniques borrowed from lattice QCD and can be used to explore issues in holography. In three dimensions the same constructions can be used to formulate a topological theory of gravity which we argue is equivalent to Witten's Chern Simons theory.

The ground state phase of spin-1/2 J1-J2 antiferromagnetic Heisenberg model on square lattice in the maximally frustrated regime (J2 ~ 0.5J1) has been debated for decades. Here we study this model by using a recently proposed novel numerical method - the cluster update algorithm for tensor product states (TPSs). The ground state energies at finite sizes and in the thermodynamic limit (with finite size scaling) are in good agreement with the state of art exact diagonalization study, and
the energy differences between these two studies are of the order of 0.001 J1 per site. At the largest bond dimension available D (D = 9), we find a paramagnetic ground state without any valence bond solid order in the thermodynamic limit in the range of 0.5 <= J2/J1 <= 0.6, which implies the emergence of a spin-liquid phase. Furthermore, we investigate the topologically ordered nature of such a spin-liquid phase by measuring a nonzero topological entanglement entropy.

There has been some significant recent progress on the long-standing problem of identifying the conditions under which equilibrium statistical mechanics can arise from an exact quantum mechanical treatment of the dynamics. I will give an overview of this progress, describing in particular how random matrix models and the associated concentration of measure phenomena imply that equilibration is generic even for the closed system evolution of pure quantum states. I will then discuss the relevance of these models to clarifying the conditions for quantum-classical correspondence of few-body chaotic systems. In particular, I will show that the Newtonian description of the dynamics of chaotic macroscopic bodies, remarkably, does not emerge from the underlying quantum mechanical description. These results suggest, under reasonable assumptions, that pure quantum states require a statistical interpretation.