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Extended Clifford circuits straddle the boundary between classical and quantum computational power. Whether such circuits are efficiently classically simulable seems to depend delicately on the ingredients of the circuits. While some combinations of ingredients lead to efficiently classically simulable circuits, other combinations, which might just be slightly different, lead to circuits which are likely not. We extend the results of Jozsa and Van den Nest [Quantum Inf. Comput. 14, 633 (2014)] by studying various further extensions of Clifford circuits. First, we consider how the classical simulation complexity changes when we allow for more general measurements. Second, we investigate different notions of what it means to "classically simulate" a quantum circuit. Third, we consider the class of conjugated Clifford circuits, where one conjugates every qubit in a Clifford circuit by the same single-qubit gate. Our results provide more examples where seemingly modest changes to the ingredients of Clifford circuits lead to "large" changes in the classical simulation complexities of the circuits, and also include new examples of extended Clifford circuits that are potential candidates for "quantum supremacy". Based on Quantum Inf. Comput. 17, 0262 (2017) and proceedings of CCC’18 pp.21:1–21:25 (2018) (joint work with Adam Bouland and Joseph F. Fitzsimons).

A century ago, Emmy Noether published an article, "Invariante Variationsprobleme", which contained 2 theorems on symmetries and conservation laws in the Gottingen Nachrichten. How original, how modern, how influential were her results? Did they shed light on the question of energy conservation that had arisen in the general theory of relativity? I shall comment on the curious transmission of her theorems and the later recognition of their wide applicability in very numerous fields of physics.

A single layer graphene hides many body effects in the dense viscous 
fluid of p-pi electrons, Bilayer graphene, with AA and AB registry, on 
the other hand, exposes some of them. A twisted bilayer springs more 
surprises. We discuss recently seen superconductivity in twisted bilayer 
graphene. Resonating valence bond (RVB) physics contained in the dense 
electron fluid in graphene is invoked [1]. RVB fails to produce 
superconductivity in neutral graphene, as carrier are absent at the 
Fermi level. In a twisted bilayer, interlayer tunneling adds equal 
number of electron and hole carriers in Moire superlattice of dominant 
AA registry. These carriers use RVB pairing and develop charge -2e and 
+2e Cooper pair correlations, in spite of Coulomb repulsions. Resulting 
Moire lattice of Cooper pair puddles form a Josephson lattice. Coulomb 
blockade makes it a Bosonic Mott insulator. Gate voltage dopes the Bose 
Mott insulator and interesting consequences follow.

[1] G. Baskaran, arXiv:1804.00627

Systems of strongly interacting particles can give rise to topological phases beyond non-interacting limit.  Although unique features of strongly interacting topological phases, such as fractionalization of quantum degrees of freedom, have important applications in quantum information processing, these topological phases are still far from experimental realizations. In this talk, by presenting constructions of two strongly interacting topological phases, I will argue the key mechanism of their realizations is to add interactions near topological phase transitions.  I will first introduce a model of interacting Majorana fermions that describes a superconducting phase with Fibonacci topological order. Then I will show that a correlated fluid of electrons and holes, dubbed fractional excitonic insulator phase, can exhibit a fractional quantum Hall effect at zero magnetic field. I will present physical evidence and conjecture that this phase can be realized in a higher angular momentum excitonic paired system in the presence of interactions.   

In quantum theory, the no-information-without-disturbance and no-free-information principles express that those observables that do not disturb the measurement of another observable and those that can be measured jointly with any other observable must be trivial, i.e., coin tossing observables. We show that in the framework of general probabilistic theories these principles do not hold in general. In this way, we obtain characterizations of the probabilistic theories where these principles hold and we show that the two principles are not equivalent.  

Axion-like particles are a broad class of dark matter candidates which are expected to behave as a coherent, classical field with a weak coupling to photons. Research into the detectability of these particles with laser interferometers has recently revealed a number of promising experimental designs. Inspired by these ideas, we propose the Axion Detection with Birefringent Cavities (ADBC) experiment, a new axion interferometry concept using a cavity that exhibits birefringence between its two, linearly-polarized laser eigenmodes. This experimental concept overcomes several limitations of the designs currently in the literature, and can be practically realized in the form of a simple bowtie cavity with tunable mirror angles. Our design thereby increases the sensitivity to the axion-photon coupling over a wide range of axion masses.

Cosmological vacuum energy does not remain constant for the same reason that a uniform electric field cannot persist indefinitely in the presence of quantum fluctuations. The decay rate of the Bunch-Davies state of QFT in de Sitter space due to particle creation is calculated in real time by the same method as that for an electric field, giving Schwinger’s result.  In both the electric field and de Sitter cases the particles created are verified to be real, in that they persist in the final asymptotic region if the background field is switched off. The energy density of the particles decreases the vacuum energy and the Hubble expansion rate.

The sensitivity to infrared physics of this decay rate requires that gravitational backreaction be taken into account on the horizon scale. A Linear Response analysis shows the relevance of the scalar degree of freedom of the conformal anomaly to de Sitter instability, backreaction and screening of vacuum energy. The conformalon scalar gives rise to cosmological horizon modes that can generate the primordial density fluctuations observed in the CMB anisotropy, and lead to dynamical, spacetime dependent dark energy. Possible observational tests of the conformal quantum origin of primordial density fluctuations is suggested by the prediction of equality of scalar and tensor weights spectral indices, and the bispectral shape function of non-Gaussian correlations in the CMB.

Finding a quantum phase transition between two even well-studied phases of matter can be a hard problem. Free probability theory suggests a new method which can give an answer if the Hamiltonians of two phases satisfy certain conditions. In the latter case, the spectral gap behavior can be calculated without solving the full Hamiltonian but using probabilistic estimation instead. As an example, I will consider generic artificial topological systems created by a periodic drive, including Floquet Majorana modes, and show how FPT can be used to predict and characterize disorder-driven phase transitions.

See also: Phys. Rev. Lett. 121, 126803