Scientific Series

Raussendorf introduced a powerful model of fault tolerant measurement based quantum computation, which can be understood as a layering (or “foliation”) of a multiplicity of Kitaev’s toric code.  I will discuss our generalisation of Raussendorf’s construction to an arbitrary CSS code.  We call this a Foliated Quantum Code.  Decoding this foliated construction is not necessarily straightforward, so I will discuss an example in which we foliate a family of finite-rate quantum turbo codes, and present the results of numerical simulations of the decoder performance.

If I have time, I will discuss some ongoing work (with Gavin Brennan) on relational time applied to topological quantum field theories, in particular, how anyonic systems with essentially trivial dynamics can still exhibit correlations that track “time".

Improving the broadband quantum sensitivity of an advanced gravitational wave detector is one of the key steps for future updating of  gravitational wave detectors. Reduction of the broadband quantum noise needs squeezed light with frequency dependent squeezing angle. Current designs for generating frequency dependent squeezed light are based on an ultra-high finesse filter cavity, therefore optical loss will serious contaminate the squeezed light. To circumvent this problem, we  propose an new method for generating a frequency dependent squeezing of quantum noise field quadrature by engineering the quantum entangled field pairs which are filtered through the interferometer arm cavity.  This new method may have the potential to beat the quantum noise by 7dB in recent future.

Strongly interacting quantum systems driven out of equilibrium represent a fascinating field where several questions of fundamental importance remains to be addressed [1].

These range from the dynamics of high-dimensional interacting models to the thermalization properties of quantum gases in continuous space.

In this Seminar I will review our recent contributions to some of the dynamical quantum problems which have been traditionally inaccessible to accurate many-body techniques.

I will first focus on the main methodological developments we devised in the past years.

In particular, I will describe the time-dependent Variational Monte Carlo method [2,3] and two notable classes of variational quantum states : the time-dependent Jastrow-Feenberg expansion, and the most recently introduced Neural-network Quantum States [4]. These states can achieve high (and controllable) accuracy both in one and higher dimensions.

Then, I will discuss specific applications to the problem of information spreading in both short- and long-ranged interacting quantum systems [3,5]. Finally, I will also discuss recent applications to thermalization properties of Lieb-Liniger quantum gases [6].

In this talk, I will outline the current state of the art in the study of the reality of the quantum state.  The main theme will be that, although you cannot derive the reality of the quantum state in an ontological model without additional assumptions, you can place constraints on the amount of overlap between probability measures that begin to make psi-epistemic theories look implausible.  These overlap bounds come from noncontextuality inequalities, and there are two types in the literature: those based on Cabello-Severini-Winter type inequalities and those based on Yu-Oh type inequalities.  The latter type of overlap bound was not originally derived from noncontextuality, but thinking of them this way yields a new proof of the Yu-Oh inequality and gives rise to family of related inequalities.  I will also explain why I think that most papers on ovelap bounds (including my own) have adopted sub-optimal measures, introduce better ones, and explain how this affects the choice of the best experimental protocol for demonstrating overlap bounds.  

The ideas of no-signalling, nonlocality, Bell inequalities, and quantum correlations can all be understood as implications of a presumed causal structure. In particular, the causal structure of the Bell scenario implies the Bell inequalities whenever the shared resource is presumed to act like a classical hidden random variable. If the shared resource in the scenario is a quantum system, however, then the quantum causal structure can give rise to a larger set of correlations, including probability distributions which violate Bell inequalities up to Tsirelson's bound. It is hard to generically distinguish between the classical and quantum correlations, though, because the standard method for computing Bell inequalities cannot be generalized to general causal scenarios. We therefore introduce a method (the "Inflation DAG" technique) to heuristically constrain the set of correlations compatible with a given classical causal structure, and we demonstrate how it may be used to derive explicit inequalities in terms of probabilities. We also discuss deriving physics-independent constraints, i.e. non-trivial inequalities which are nevertheless satisfied even by all quantum correlations, thereby quantifying some absolute limits as to what the universe allows.

[Unpublished results of E.W., Rob Spekkens, Tobias Fritz]

In this talk I will go over the recent paper by Daniela Frauchiger and Renato Renner, "Single-world interpretations of quantum theory cannot be self-consistent" (arXiv:1604.07422).

The paper introduces an extended Wigner's friend thought experiment, which makes use of Hardy's paradox to show that agents will necessarily reach contradictory conclusions - unless they take into account that they themselves may be in a superposition, and that their subjective experience of observing an outcome is not the whole story.

Frauchiger and Renner then put this experiment in context within a general framework to analyse physical theories. This leads to a theorem saying that a theory cannot be simultaneously (1) compliant with quantum theory, including at the macroscopic level, (2) single-world, and (3) self-consistent across different agents.

In this talk I will (1) describe the experiment and its immediate consequences, (2) quickly review how different interpretations react to it, (3) explain the framework and theorem in more detail.


 

Certain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all of these zeros, the well can be split into multiple adjacent infinite square wells without affecting the wavefunction. While the average energy of the state was unchanged, this splitting effects a change of the energy eigenbasis of the state to a basis that does not commute with the original, and a subsequent measurement of the energy now reveals a completely different spectrum, which we call the interference energy spectrum of the state. Numerical simulations were used to verify that a barrier can be rapidly raised at a zero of the wavefunction without significantly affecting it. The concept of state inherent energy spectra is further explored as it relates to quantum state time evolution, probability theory, and weak value measurements. Of particular interest, this procedure can result in measurable energies that are greater than the energy of the highest mode in the original superposition, raising questions about the conservation of energy akin to those that have been raised in the study of superoscillations.

Tensor networks have been very successful for approximating quantum states that would otherwise require exponentially many parameters.

I will discuss how a similar compression can be achieved in models used to machine learn data, such as sets of images, by representing the fitting parameters as a tensor network. The resulting model achieves state-of-the-art performance on standard classification tasks. I will discuss implications for machine learning research, exploring which insights from physics could be imported into this field.

Most physicists take it for granted that the experimental violation of Bell's inequality provides evidence that it is not possible to completely describe the state of a physical system in terms of purely local information when this system is entangled with some other system. We disagree. Provided we redefine appropriately what is the information-theoretic state of a quantum system, it becomes possible to recover the whole from the description of its parts. This is in sharp contrast with the standard formalism of quantum mechanics in which the density matrix provides all there is to say about the state of a system. According to our formalism, there is no need to invoke supernatural nonlocality in order to explain everything standard quantum mechanics tells us that we can observe. We show, however, that this is inconsistent with the usual belief held among Everettians that the universal wavefunction can be taken as the complete representation of reality. Inspired by Plato and Kant, we introduce and contrast the notions of noumenal and phenomenal states of physical systems: the former corresponds to the complete but unknowable state of the system and the latter to what can be perceived about it with the help of arbitrary technology. We exhibit an explicit epimorphism from the former to the latter, which explains the relationship between all that there is and all that can be apprehended. Joint work with Paul Raymond-Robichaud

For a spin 1/2 (a qubit), Hamiltonian evolution is equivalent to an elliptic rotation of the (Bloch) spin vector in 3D space. In contrast, measurement alters the state norm, so may not be described as such a rotation. Nevertheless, extending the 3D spin vector to a 4D "spacetime" representation allows weak measurements to be interpreted as hyperbolic (boost) rotations. The combined Hamiltonian and measurement dynamics in continuous weak measurement trajectories are then equivalent to (stochastic) Lorentz transformations. Notably, in superconducting circuit QED implementations, the choice between which type of stochastic rotation occurs may be made long after the qubit and measurement field interact.