Publications

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• Introduction to quantum error correction and fault tolerance

  Steven M. Girvin

  SciPost Phys. Lect. Notes 70 (2023) · published 12 June 2023 | Toggle abstract · pdf

  These lecture notes from the 2019 Les Houches Summer School on "Quantum Information Machines" are intended to provide an introduction to classical and quantum error correction with bits and qubits, and with continuous variable systems (harmonic oscillators). The focus on the latter will be on practical examples that can be realized today or in the near future with a modular architecture based on superconducting electrical circuits and microwave photons. The goal and vision is "hardware-efficient" quantum error correction that does not require exponentially large hardware overhead in order to achieve practical and useful levels of fault tolerance and circuit depth.

  2 citations

• Quantum to classical mapping of the two-dimensional toric code in an external field

  Sydney R. Timmerman, Zvonimir Z. Bandic, Roger G. Melko

  SciPost Phys. Lect. Notes 57 (2022) · published 20 July 2022 | Toggle abstract · pdf

  Kitaev's toric code Hamiltonian in dimension D=2 has been extensively studied for its topological properties, including its quantum error correction capabilities. While the Hamiltonian is quantum, it lies within the class of models that admits a D+1 dimensional classical representation. In these notes, we provide details of a Suzuki-Trotter expansion of the partition function of the toric code Hamiltonian in the presence of an external magnetic field. By coupling additional degrees of freedom in the form of a matter field that can subsequently be gauged away, we explicitly derive a classical Hamiltonian on a cubic lattice which takes the form of a non-isotropic 3D Ising gauge theory.

  2 citations

• From classical to quantum regime of topological surface states via defect engineering

  Maryam Salehi, Xiong Yao, Seongshik Oh

  SciPost Phys. Lect. Notes 58 (2022) · published 21 July 2022 | Toggle abstract · pdf

  Since the notion of topological insulator (TI) was envisioned in late 2000s, topology has become a new paradigm in condensed matter physics. Realization of topology as a generic property of materials has led to numerous predictions of topological effects. Although most of the classical topological effects, directly resulting from the presence of the spin-momentum-locked topological surface states (TSS), were experimentally confirmed soon after the theoretical prediction of TIs, many topological quantum effects remained elusive for a long while. It turns out that native defects, particularly interfacial defects, have been the main culprit behind this impasse. Even after quantum regime is achieved for the bulk states, TSS still tends to remain in the classical regime due to high density of interfacial defects, which frequently donate mobile carriers due to the very nature of the topologically-protected surface states. However, with several defect engineering schemes that suppress these effects, a series of topological quantum effects have emerged including quantum anomalous Hall effect, quantum Hall effect, quantized Faraday/Kerr rotations, topological quantum phase transitions, axion insulating state, zeroth-Landau level state, etc. Here, we review how these defect engineering schemes have allowed topological surface states to pull out of the murky classical regime and reveal their elusive quantum signatures, over the past decade.

  1 citation

• A somewhat random walk through nuclear and particle physics

  Thomas D. Cohen, Nicholas R. Poniatowski

  SciPost Phys. Lect. Notes 34 (2021) · published 20 September 2021 | Toggle abstract · pdf

  These notes are an outgrowth of an advanced undergraduate course taught at the University of Maryland, College Park. They are intended as an introduction to various aspects of particle and nuclear physics with an emphasis on the role of symmetry. The basic philosophy is to introduce many of the fundamental ideas in nuclear and particle physics using relatively sophisticated mathematical tools -- but to do so in as a simplified a context to explain the underlying ideas. Thus, for example, the Higgs mechanism is discussed in terms of an Abelian Higgs model. The emphasis is largely, but not entirely theoretical in orientation. The goal is for readers to develop an understanding of many of the underlying issues in a relatively sophisticated way.

  1 citation

• Lectures on bulk reconstruction

  Nirmalya Kajuri

  SciPost Phys. Lect. Notes 22 (2021) · published 2 February 2021 | Toggle abstract · pdf

  If the AdS/CFT conjecture holds, every question about bulk physics can be answered by the boundary CFT. But we still don't know how to translate all the questions about bulk physics to questions about the boundary CFT. Completing this bulk-boundary dictionary is the aim of the bulk reconstruction program, which we review in these lectures. We cover the HKLL construction, bulk reconstruction in AdS/Rindler, mirror operator construction of Papadodimas and Raju and the Marolf-Wall paradox. These notes are based on lectures given at ST4 2018.

  1 citation

• A brief introduction to extended gravity and connections to dark energy: Illustrated with scalar field examples

  Clare Burrage

  SciPost Phys. Lect. Notes 41 (2022) · published 15 March 2022 | Toggle abstract · pdf

  These lecture notes provide a brief introduction to extensions of gravity and their connections to dark energy. Due to time and space limitations this is not a comprehensive review of the field. Instead, I aim to introduce key concepts and ideas in this area through a series of examples based on scalar field extensions of gravity and models of dark energy.

  1 citation

• Methods and conversations in (post)modern thermodynamics

  Francesco Avanzini, Massimo Bilancioni, Vasco Cavina, Sara Dal Cengio, Massimiliano Esposito, Gianmaria Falasco, Danilo Forastiere, Nahuel Freitas, Alberto Garilli, Pedro E. Harunari, Vivien Lecomte, Alexandre Lazarescu, Shesha G. Marehalli Srinivas, Charles Moslonka, Izaak Neri, Emanuele Penocchio, William D. Piñeros, Matteo Polettini, Adarsh Raghu, Paul Raux, Ken Sekimoto, Ariane Soret

  SciPost Phys. Lect. Notes 80 (2024) · published 20 March 2024 | Toggle abstract · pdf

  Lecture notes after the doctoral school (Post)Modern Thermodynamics held at the University of Luxembourg, December 2022, 5-7, covering and advancing continuous-time Markov chains, network theory, stochastic thermodynamics, large deviations, deterministic and stochastic chemical reaction networks, metastability, martingales, quantum thermodynamics, and foundational issues.

  1 citation

• Covariant canonical formulations of classical field theories

  Francois Gieres

  SciPost Phys. Lect. Notes 77 (2023) · published 5 December 2023 | Toggle abstract · pdf

  We review in simple terms the covariant approaches to the canonical formulation of classical relativistic field theories (in particular gauge field theories and general relativity) and we discuss the relationships between these approaches as well as the relation with the standard (non-covariant) Hamiltonian formulation. Particular attention is paid to conservation laws (notably related to geometric symmetries) within the different approaches. Moreover, for each of these approaches, the impact of space-time boundaries is also addressed. To make the text accessible to a wider audience, we have included an outline of Poisson and symplectic geometry for both classical mechanics and field theory.

  1 citation

• Quantum enhanced metrology in the search for fundamental physical phenomena

  Konrad W. Lehnert

  SciPost Phys. Lect. Notes 40 (2022) · published 11 March 2022 | Toggle abstract · pdf

  These notes summarize lectures given at the 2019 Les Houches summer school on Quantum Information Machines. They describe and review an application of quantum metrology concepts to searches for ultralight dark matter. In particular, for ultralight dark matter that couples as a weak classical force to a laboratory harmonic oscillator, quantum squeezing benefits experiments in which the mass of the dark matter particle is unknown. This benefit is present even if the oscillatory dark matter signal is much more coherent than the harmonic oscillator that it couples to, as is the case for microwave frequency searches for dark matter axion particles.

  1 citation

• Four lectures on Euler integrals

  Saiei-Jaeyeong Matsubara-Heo, Sebastian Mizera, Simon Telen

  SciPost Phys. Lect. Notes 75 (2023) · published 26 October 2023 | Toggle abstract · pdf

  These lecture notes provide a self-contained introduction to Euler integrals, which are frequently encountered in applications. In particle physics, they arise as Feynman integrals or string amplitudes. Our four selected topics demonstrate the diverse mathematical techniques involved in the study of Euler integrals, including polyhedral geometry, very affine varieties, differential equations, and computational algebra.

  1 citation