Scientific Series

Query complexity is a common tool for comparing quantum and classical computation, and it has produced many examples of how quantum algorithms differ from classical ones. Here we investigate in detail the role that oracles play for the advantage of quantum algorithms. We do so by using a simulation framework, Quantum Simulation Logic (QSL), to construct oracles and algorithms that solve some problems with the same success probability and number of queries as the quantum algorithms. The framework can be simulated using only classical resources at a constant overhead as compared to the quantum resources used in quantum computation. Our results clarify the assumptions made and the conditions needed when using quantum oracles. Using the same assumptions on oracles within the simulation framework we show that for some specific algorithms, such as the Deutsch-Jozsa and Simon’s algorithms, there simply is no advantage in terms of query complexity. This does not detract from the fact that quantum query complexity provides examples of how a quantum computer can be expected to behave, which in turn has proved useful for finding new quantum algorithms outside of the oracle paradigm, where the most prominent example is Shor’s algorithm for integer factorization.

Julia is a modern programming language that is (so they say) as easy to use as Python and as fast as Fortran, combined with the expressive power of Lisp. I will introduce the language via examples taken from linear algebra, differential equations, and scientific visualization.

In QFT, the renormalization group is usually formulated in Euclidean signature. I will discuss time-dependent probes of the RG, in Lorentzian signature, and derive new dynamical constraints that govern the spread of local operators. Through a chain of Wick rotations and dualities, the same methods lead to new sum rules for inflationary correlators, which relate observable quantities like the inflationary speed of sound to properties of the UV.

I will discuss the problem of an observer's S-matrix in de Sitter space, i.e. the mapping between fields on the initial and final horizons of a de Sitter static patch. I will show how the S-matrix of free massless fields can be packaged in a spinor-helicity language. This involves “cheating” the static patch’s painfully low symmetry, by relating each horizon separately to global, de Sitter-invariant data.

I will then discuss the important special case of higher-spin gravity in de Sitter, and argue that higher-spin symmetry prevents any corrections to the free S-matrix, except in the “soft" sector of zero frequencies.

Bell inequalities are important tools in contrasting classical and quantum behaviors. To date, most Bell inequalities are linear combinations of statistical correlations between remote parties. Nevertheless, finding the classical and quantum mechanical (Tsirelson) bounds for a given Bell inequality in a general scenario is a difficult task which rarely leads to closed-form solutions. Here we introduce a new class of Bell inequalities based on products of correlators that alleviate these issues. Each such Bell inequality is associated with a non-cooperative coordination game. In the simplest case, Alice and Bob, each  having two random variables, attempt to maximize the area of a rectangle and the rectangle’s area is represented by a certain parameter. This parameter, which is a function of the correlations between their random variables, is shown to be a Bell parameter, i.e. the achievable bound using only classical correlations is strictly smaller than the achievable bound using non-local quantum correlations We continue by generalizing to the case in which Alice and Bob, each having now n random variables, wish to maximize a certain volume in n-dimensional space. We term this parameter a multiplicative Bell parameter and prove its Tsirelson bound. Finally, we investigate the case of local hidden variables and show that for any deterministic strategy of one of the players the Bell parameter is a harmonic function whose maximum approaches the Tsirelson bound as the number of measurement devices increases. Some implications of these results are discussed.

The Hubble constant remains one of the most important parameters in the cosmological model, setting the size and age scales of the Universe. Present uncertainties in the cosmological model including the nature of dark energy, the properties of neutrinos and the scale of departures from flat geometry can be constrained by measurements of the Hubble constant made to higher precision than was possible with the first generations of Hubble Telescope instruments. A streamlined distance ladder constructed from infrared observations of Cepheids and type Ia supernovae with ruthless attention paid to systematics now provide <2% precision and offer the means to do much better. By steadily improving the precision and accuracy of the Hubble constant, we now see evidence for significant deviations from the standard model, referred to as LambdaCDM, and thus the exciting chance, if true, of discovering new fundamental physics such as exotic dark energy, a new relativistic particle, or a small curvature to name a few possibilities. I will review recent and expected progress.

The no-signalling principle, preventing superluminal communication and the consequent logical paradoxes, is typically formulated within the information-theoretic framework in terms of admissible correlations in composite systems. In my talk, I will present its complementary incarnation associated with dynamics of single systems subject to invasive measurements. The `dynamical no-signalling principle' applies to any theory with well defined rules of calculating detection statistics in spacetime. It thus offers a new framework, based on measure theory, for studying ``post-quantum'' theories in spacetime. I will show that, strikingly, the `dynamical no-signalling' principle rules out some of the well know models of quantum wave dynamics.

Topological crystalline states are short-range entangled states jointly protected by onsite and crystalline symmetries. While the non-interacting limit of these states, e.g., the topological crystalline insulators, have been intensively studied in band theory and have been experimentally discovered, the classification and diagnosis of their strongly interacting counterparts are relatively less well understood. Here we present a unified scheme for constructing all topological crystalline states, bosonic and fermionic, free and interacting, from real-space "building blocks" and "connectors". Building blocks are finite-size pieces of lower dimensional topological states protected by onsite symmetries alone, and connectors are "glue" that complete the open edges shared by two or multiple pieces of building blocks. The resulted assemblies are selected against two physical criteria we call the "no-open-edge condition" and the "bubble equivalence", which, respectively, ensure that each selected assembly is gapped in the bulk and cannot be deformed to a product state. The scheme is then applied to obtaining the full classification of bosonic topological crystalline states protected by several onsite symmetry groups and each of the 17 wallpaper groups in two dimensions and 230 space groups in three dimensions. We claim that our real-space recipes give the complete set of topological crystalline states for bosons and fermions, and prove the boson case analytically using a spectral sequence expansion of group cohomology.

If General Relativity emerges from quantum gravity, then general covariance, the gauge invariance of GR, will emerge with it. We can ask, within any approach to the problem of quantum gravity, what is the “precursor” principle or precept that will give rise to — or manifest itself as — general covariance in the large scale semi-classical approximation?
Given how important the understanding of general covariance (or lack of it!) was in the development of GR we might expect that thinking about this question will be similarly important in the development of quantum gravity.
I will explain how general covariance is seen from the perspective of the causal set approach to quantum gravity and describe recent progress in creating a framework for causal set dynamics that is completely covariant and does not refer to any gauge degrees of freedom at all.

In quantum error correcting codes, there is a distinction
between coherent and incoherent noise. Coherent noise can cause the
average infidelity to accumulate quadratically when a fixed channel is
applied many times in succession, rather than linearly as in the case
of incoherent noise. I will present a proof that unitary single qubit
noise in the 2D toric code with minimum weight decoding is mapped to
less coherent logical noise, and as the code size grows, the coherence
of the logical noise channel is suppressed. In the process, I will
describe how to characterize the coherence of noise using either the
growth of infidelity or the relation between the diamond distance from
identity and the average infidelity. I will explain how coherence in
the noise on physical qubits is transformed by error correction in
stabilizer codes. Then, I will sketch the proof that coherence is
suppressed for the 2D toric code. The result holds even when the
single qubit unitary rotation are allowed to have arbitrary directions
and angles, so long as the angles are below a threshold, and even when
the rotations are correlated. Joint work with John Preskill.

We consider supersymmetric $AdS_3\times Y_7$ solutions of type IIB supergravity dual to N=(0,2) SCFTs in d=2, as well as  $AdS_2\times Y_9$ solutions of D=11 supergravity dual to N=2 supersymmetric quantum mechanics, some of which arise as the near horizon limit of supersymmetric, charged black hole solutions in $AdS_4$. The relevant geometry on $Y_{2n+1}$, $n\ge 3$ was first identified in 2005-2007 and around that time infinite classes of explicit examples solutions were also found but, surprisingly, there was little progress in identifying the dual SCFTs. We present new results which change the status quo. For the case of $Y_7$, a variational principle allows one to calculate the central charge of the dual SCFT without knowing the explicit metric. This provides a geometric dual of c-extremization for d=2 N=(0,2) SCFTs analogous to the well known geometric duals of a-maximization of d=4 N=1 SCFTs and F-extremization of d=3 N=2 SCFTs in the context of Sasaki-Einstein geometry.  In the case of $Y_9$ a similar variational principle can be used to obtain properties of the dual N=2 quantum mechanics as well as the entropy of a class of supersymmetric black holes in $AdS_4$ thus providing a geometric dual of $I$-extremization.

Understanding entanglement in QFTs is a challenging topic that involves many aspects. One important probe for this is the modular (or entanglement) Hamiltonian, which is closely related to the Unruh effect. We determine this operator for the chiral fermion at finite temperature on the circle using complex analysis, and show that it exhibits surprising new features. This simple system illustrates how a modular flow can transition from complete locality to complete non-locality as a function of temperature, thus bridging the gap between previously known limits. We also derive the first exact results for the entanglement and relative entropies of this system for the different spin sectors. Based on [1905.05768,1906.02207].