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We study approximate quantum low-density parity-check (QLDPC) codes, which are approximate quantum error-correcting codes specified as the ground space of a frustration-free local Hamiltonian, whose terms do not necessarily commute. Such codes generalize stabilizer QLDPC codes, which are exact quantum error-correcting codes with sparse, low-weight stabilizer generators (i.e. each stabilizer generator acts on a few qubits, and each qubit participates in a few stabilizer generators). Our investigation is motivated by an important question in Hamiltonian complexity and quantum coding theory: do stabilizer QLDPC codes with constant rate, linear distance, and constant-weight stabilizers exist? We show that obtaining such optimal scaling of parameters (modulo polylogarithmic corrections) is possible if we go beyond stabilizer codes: we prove the existence of a family of [[N,k,d,ε]] approximate QLDPC codes that encode k = Ω(N/polylog N) into N physical qubits with distance d = Ω(N/polylog N) and approximation infidelity ε = 1/polylog N. We prove the existence of an efficient encoding map, and we show that arbitrary Pauli errors can be locally detected by circuits of polylogarithmic depth. Finally, we show that the spectral gap of the code Hamiltonian is Ω(N^(-3.09)) (up to polylog(N) factors) by analyzing a spacetime circuit-to-Hamiltonian construction for a bitonic sorting network architecture that is spatially local in polylog(N) spatial dimensions. (Joint work with Elizabeth Crosson, Chinmay Nirkhe, and Henry Yuen, arXiv:1811.00277)

Einstein is well known for his rejection of quantum mechanics in the form it emerged from the work of Heisenberg, Born and Schrodinger in 1926. Much less appreciated are the many seminal contributions he made to quantum theory prior to his final scientific verdict: that the theory was at best incomplete. In this talk I present an overview of Einstein’s many conceptual breakthroughs and place them in historical context. I argue that Einstein, much more than Planck, introduced the concept of quantization of energy in atomic mechanics. Einstein proposed the photon, the first force-carrying particle discovered for a fundamental interaction, and put forward the notion of wave-particle duality, based on sound statistical arguments 14 years before De Broglie’s work. He was the first to recognize the intrinsic randomness in atomic processes, and introduced the notion of transition probabilities, embodied in the A and B coefficients for atomic emission and absorption. He also preceded Born in suggesting the interpretation of wave fields as probability densities for particles, photons, in the case of the electromagnetic field. Finally, stimulated by Bose, he introduced the notion of indistinguishable particles in the quantum sense and derived the condensed phase of bosons, which is one of the fundamental states of matter at low temperatures. His work on quantum statistics in turn directly stimulated Schrodinger towards his discovery of the wave equation of quantum mechanics. It was only due to his rejection of the final theory that he is not generally recognized as the most central figure in this historic achievement of human civilization.   

Recently, a new family of correlated honeycomb materials with strong spin-orbit coupling have been promising candidates to realize the Kitaev spin liquid. In particular, a half-integer quantized thermal Hall conductivity was reported in alpha-RuCl3 under the magnetic field. Using a generic nearest neighbour spin model with bond-dependent interactions, I will present numerical evidence of an extended regime of quantum spin liquids. I will also discuss how to achieve a chiral spin liquid near ferromagnetic Kitaev interaction in the presence of the magnetic field leading to the quantized thermal Hall conductivity.

We derive Born’s rule and the density-operator formalism for quantum systems with Hilbert spaces of finite dimension. Our extension of Gleason’s theorem only relies upon the consistent assignment of probabilities to the outcomes of projective measurements and their classical mixtures. This assumption is significantly weaker than those required for existing Gleason-type theorems valid in dimension two.

This talk is about a new type of string theory with a non-relativistic conformal field theory on the world-sheet, as well as a non-relativistic target space geometry. Starting with the relativistic Polyakov action with a fixed momentum along a non-compact null-isometry, we can take a scaling limit that gives the non-relativistic string, including an interesting intermediate step. This can in particular be applied to a string on AdS5 x S5. In this case the scaling limit realizes a limit of AdS/CFT that on the field theory side gives a quantum mechanical theory known as Spin Matrix theory. We review that Spin Matrix theory is a finite-N version of nearest neighbor spin chains, from which one can find a long-wavelength semi-classical description using sigma-model such as the Landau-Lifshitz sigma-model. Hence, we can show that both sides of the AdS/CFT gives, in this limit, equivalent non-relativistic sigma-models that we are able to write down in a fully covariant manner, and show that it has a non-relativistic local symmetry that realizes the Galilean Conformal Algebra (GCA). This suggests that one has a holographic duality between the quantum mechanical theory of Spin Matrix theory, and the non-relativistic string. This could provide a more tractable holographic duality in which one can study the emergence of non-relativistic strings, geometry and gravity.

We present the complete history of structure formation in a simple dissipative dark-sector model. The model has only two particles: a dark electron and a dark photon. Dark-electron perturbations grow from primordial overdensities, become non-linear, and form dense, dark galaxies. We show that asymmetric dark stars and black holes form within the Milky Way from the collapse of dark electrons. These exotic compact objects may be detected and their properties measured at new high-precision astronomical observatories, giving insight into the particle nature of the dark sector without the requirement of non-gravitational interactions with the visible sector.

Fundamental physics traditionally views the dynamical laws governing the world as time reversal invariant. The evident arrow of time of nature is then held to be an accident, emerging as we coarse grain and originating in the improbable choice of initial conditions. The main pillar which supports this time-symmetric lifestyle is the fluctuation-dissipation theorem, which connects purely time-symmetric microscopic equations to the emergence of a macroscopic arrow of thermodynamics. I will describe arguments from statistical physics claiming that existing proofs of this theorem are faulty and do not demonstrate the emergence of an arrow from time-symmetric laws. I will argue that, as a result of this assumption of time symmetry, we cosmologists stand to pay an unreasonable price concerning what we’re expected to explain. I argue for instead to turn this picture around and propose a fundamental theory of cosmology and quantum gravity which is fundamentally time asymmetric and based on time-irreversible laws. I will describe a new class of models of quantum space-time, energetic causal sets, in which space-time itself, as well as aspects of quantum theory, emerge under natural conditions. The framework is based on arXiv:1307.6167 and subsequent papers in collaboration with Lee Smolin.

Strominger-Yau-Zaslow explained mirror symmetry via duality between tori.  There have been a lot of recent developments in the SYZ program, focusing on the non-equivariant setting.  In this talk, I explain an equivariant construction and apply it to toric Calabi-Yau manifolds.  It has a close relation to the equivariant open GW invariants found by Aganagic-Klemm-Vafa and studied by Katz-Liu, Graber-Zaslow and many others.

2D CFTs have an infinite set of commuting conserved charges, known as the quantum KdV charges. There is a generalised Gibbs ensemble for these theories where we turn on chemical potentials for these charges. I will describe some partial results on calculating this partition function, both in the limit of large charges and perturbatively in the chemical potentials. 

The partition function of three-dimensional N=2 SCFTs on circle bundles of closed Riemann surfaces \Sigma_g was recently computed via supersymmetric localization. In this talk I will describe supergravity solutions having as conformal boundary such circle bundle. These configurations are solutions to N=2 minimal gauged supergravity in 4d and pertain to the class of AdS-Taub-NUT and AdS-Taub-Bolt preserving 1/4 of the supersymmetries. I will discuss the conditions for the uplift of these solutions to M-theory and I provide the expression for the on-shell action of the Bolt solutions, computed via holographic renormalization. I will show that, when the uplift condition is satisfied, the Bolt free energy matches with the large N limit of the partition function of the corresponding dual field theory. I will finally comment on possible subtleties that arise in our framework when a given boundary geometry admits multiple bulk fillings.

What is the black hole in quantum mechanics? We examine this problem in a self-consistent manner. First, we analyze time evolution of a 4D spherically symmetric collapsing matter including the back reaction of particle creation that occurs in the time-dependent spacetime. As a result, a compact high-density star with no horizon or singularity is formed and eventually evaporates. This is a quantum black hole. We can construct a self-consistent solution of the semi-classical Einstein equation showing this structure. In fact, we construct the metric, evaluate the expectation values of the energy momentum tensor, and prove the self-consistency under some assumptions. Large pressure appears in the angular direction to support this black hole, which is consistent with 4D Weyl anomaly. When the black hole is formed adiabatically in the heat bath, integrating the entropy density over the interior volume reproduces the area law. 

One of the central problems in the study of quantum resource theories is to provide a given resource with an operational meaning, characterizing physical tasks relevant to information processing in which the resource can give an explicit advantage over all resourceless states. We show that this can always be accomplished for all convex resource theories. We establish in particular that any resource state enables an advantage in a channel discrimination task, allowing for a strictly greater success probability than any state without the given resource. Furthermore, we find that the generalized robustness measure serves as an exact quantifier for the maximal advantage enabled by the given resource state in a class of subchannel discrimination problems, providing a universal operational interpretation to this fundamental resource quantifier. 

Next, we significantly extend the above consideration beyond "quantum" resource theories of "states"; we establish an operational characterization of general convex resource theories --- describing the resource content of not only states, but also measurements and channels, both within quantum mechanics and in general probabilistic theories (GPTs) --- in the context of state and channel discrimination. We find that discrimination tasks provide a unified operational description for quantification and manipulation of resources by showing that the family of robustness measures can be understood as the maximum advantage provided by any physical resource in several different discrimination tasks, as well as establishing that such discrimination problems can fully characterize the allowed transformations within the given resource theory. Our results establish a fundamental connection between the operational tasks of discrimination and core concepts of resource theories --- the geometric quantification of resources and resource manipulation --- valid for all physical theories beyond quantum mechanics with no additional assumptions about the structure of the GPT required.

References: 

[1] Ryuji Takagi, Bartosz Regula, Kaifeng Bu, Zi-Wen Liu, and Gerardo Adesso, "Operational Advantage of Quantum Resources in Subchannel Discrimination", Phys. Rev. Lett. 122.140402 (2019)

[2] Ryuji Takagi and Bartosz Regula, "General resource theories in quantum mechanics and beyond: operational characterization via discrimination tasks", arXiv: 1901.08127