Author: mskotiniotis

While the ZX and ZW calculi have been effective as graphical reasoning tools for finite-dimensional quantum computation, the possibilities for continuous-variable quantum computation (CVQC) in infinite-dimensional Hilbert space are only beginning to be explored. In this work, we formulate a graphical language for CVQC. Each diagram is an undirected graph made of two types of spiders: the Z spider from the ZX calculus defined on the reals, and the newly introduced Fock spider defined on the natural numbers. The Z and X spiders represent functions in position and momentum space respectively, while the Fock spider represents functions in the discrete Fock basis. In addition to the Fourier transform between Z and X, and the Hermite transform between Z and Fock, we present exciting new graphical rules capturing heftier CVQC interactions.
We ensure this calculus is complete for all of Gaussian CVQC interpreted in infinite-dimensional Hilbert space, by translating the completeness in affine Lagrangian relations by Booth, Carette, and Comfort. Applying our calculus for quantum error correction, we derive graphical representations of the Gottesman-Kitaev-Preskill (GKP) code encoder, syndrome measurement, and magic state distillation of Hadamard eigenstates. Finally, we elucidate Gaussian boson sampling by providing a fully graphical proof that its circuit samples submatrix hafnians.

https://arxiv.org/abs/2406.02905

Google Meet Link: https://meet.google.com/csb-snng-bmu

The ZX calculus is a graphical language that provides an intuitive and elegant way to reason about quantum computing, rigorously backed by 300 research papers (cf. zxcalculus.com/publications). In this talk, we will introduce this calculus’s fundamental concepts and techniques. After introducing the basics and time permitting, we will overview diagrammatic reasoning of several quantum applications such as Quantum Teleportation, the Quantum Approximate Optimization Algorithm, Measurement-Based Quantum Computing, and quantum computing for chemistry and condensed matter applications.

Date: 14 February 2025

Time: 11:00 am

Location:
Computational Physics Laboratory, Department of Electromagnetism and Condensed Mater.

Google Meets Link: https://meet.google.com/csb-snng-bmu

Magic state distillation is a key subroutine in many leading schemes for achieving a fault tolerant quantum computer. However, despite significant recent progress, the overhead of state-of-the-art protocols for magic distillation is still eyewatering. This poses the natural question: can we do better, even in principle?

In this talk I’ll introduce the basics of majorization theory – an abstract mathematical toolset with a wide range of applications spanning economics [*] and quantum theory alike. I’ll discuss some recent work where we apply the machinery of majorization to quasiprobability representations of magic states to obtain entropic constraints on the achievable overhead of magic distillation. These constraints give rise to fundamental trade-off relations on the code parameters appearing in practical distillation protocols. From a more foundational perspective, in this picture the processing of magic states under stabilizer circuits (a universal model for quantum computing) can be viewed as akin to classical statistical mechanics with the appearance of negative entropies. In this context, we find that negative entropy is equivalent to Wigner negativity, and thus constitutes a necessary ingredient for quantum computational speed-up.

[*] https://en.wikipedia.org/wiki/Gini_coefficient

Google meets link
https://meet.google.com/csb-snng-bmu

Magic state distillation is a key subroutine in many leading schemes for achieving a fault tolerant quantum computer. However, despite significant recent progress, the overhead of state-of-the-art protocols for magic distillation is still eyewatering. This poses the natural question: can we do better, even in principle?

In this talk I’ll introduce the basics of majorization theory – an abstract mathematical toolset with a wide range of applications spanning economics [*] and quantum theory alike. I’ll discuss some recent work where we apply the machinery of majorization to quasiprobability representations of magic states to obtain entropic constraints on the achievable overhead of magic distillation. These constraints give rise to fundamental trade-off relations on the code parameters appearing in practical distillation protocols. From a more foundational perspective, in this picture the processing of magic states under stabilizer circuits (a universal model for quantum computing) can be viewed as akin to classical statistical mechanics with the appearance of negative entropies. In this context, we find that negative entropy is equivalent to Wigner negativity, and thus constitutes a necessary ingredient for quantum computational speed-up.

[*] https://en.wikipedia.org/wiki/Gini_coefficient

Google Meets Link
https://meet.google.com/csb-snng-bmu

Contextuality can be seen as a purely non-classical phenomenon in physical systems, its quantum realizations being of special interest. We have been presencing an ongrowing attention to it in the recent years, from a proper experimental verification that led to a Nobel Prize to its roles on the foundational aspects of quantum theory and on the exploration of quantum versions of communication and computation schemes. In this seminar I am going to give an introduction to the phenomenon, in the traditional approach, and talk about its characterization and some of the associated challenges and applications, as well as connections to other areas, including quantum computing.

Google Meet link to the seminar

Seminarios QuThCo
Viernes, 26 de abril · 11:00am – 12:00pm
Zona horaria: Europe/Madrid
Información para unirse con Google Meet
https://meet.google.com/pfu-awyh-hmz

In open quantum dynamics, the structure of the environment determines the way a system loses its coherence. In this seminar, we show how to use a Bayesian learning protocol to infer properties of the environment from experimental data. Specifically, we estimate a set of scalar parameters of the spectral density of the bath that interacts with a quantum dot via exciton-phonon interaction in the weak coupling regime, using simulated data. We will compare offline and online protocols and their performance.
For those without a background in the topic, we will review concepts on the theory of open quantum systems, quantum metrology, quantum process tomography, and parameter estimation.

Google Meet Link

meet.google.com/pfu-awyh-hmz

The quantum marginal problem investigates the compatibility of the eigenvalues of the local and global states of a multipartite quantum system. It is a fundamental problem in quantum information for which the solution is only known for simple cases. We investigate a simpler question of the same flavour: Given the purities of the local states of a multipartite system, what is the maximum purity the global state can achieve? We derive a new inequality that holds for bipartite systems of arbitrary dimensions and gives a complete solution for two qubits. Together with previous findings, this result gives rise to a new representation of the quantum state space – the Bloch ball – of two qubits. We show that this 3-dimensional visualization has various interesting properties regarding geometry and argue why it indeed captures many relevant properties of the full, high-dimensional, state space. Finally we extend this solution to three-qubit states, where we derive tight inequalities on the two- and three-body correlations compatible with a pure state.

You can also follow the seminar online at https://meet.google.com/pfu-awyh-hmz

Quantum thermodynamics arises when extending the ideas from classical thermodynamics to the microscopic, i.e., quantum, regime. In this course, we will address the fundamentals of the theory focusing on the laws of quantum thermodynamics. We will also present the main practical applications of this theory, such as quantum thermal machines and batteries, and point out the main conceptual issues when dealing with quantities such as heat, work, or entropy.
Please note: This is a graduate-level course. Attendees are expected to have a minimum understanding of thermodynamics and quantum theory. While familiarity with Master Equation techniques is advisable (see Ref. [1]), a general overview will be provided at the beginning of the course.

Structure:
1. Introduction and historical motivation
2. Previous key concepts
3. Laws of Quantum Thermodynamics
4. Entropy production, Quantum Information and Thermodynamics 5. Applications: Quantum thermal engines and batteries

[1] D. Manzano, A short introduction to the Lindblad master equation, AIP Advances 10, 025106 (2020). (https://arxiv.org/abs/1906.04478)
[2] P. Strasberg, Quantum Stochastic Thermodynamics: Foundations and Selected Applications. Oxford University Press (2022)
[3] S. Deffner and S. Campbell, Quantum Thermodynamics: An introduction to the thermodynamics of quantum information, Morgan & Claypool Publishers (2019). (https://arxiv.org/abs/1907.01596)
[4] F. Binder et al. (eds.), Thermodynamics in the quantum regime. Springer (2018)
[5] S. Vinjanampathy and J. Anders, Quantum Thermodynamics, Contemporary Physics, 57, 545 (2016) (https://arxiv.org/abs/1508.06099)
[6] G. Landi and M. Paternostro, Irreversible entropy production, from quantum to classical, Rev. Mod. Phys. 93, 035008 (2021) (https://arxiv.org/abs/2009.07668)
[7] S. Bhattacharjee and A. Dutta, Quantum thermal machines and batteries, Eur. Phys. J. B 94, 239 (2021) (https://arxiv.org/abs/2008.07889)
[8] N. Myers, O. Abah and S. Deffner, Quantum thermodynamic devices: from theoretical proposals to experimental reality, AVS Quantum Sci. 4, 027101 (2022) (https://arxiv.org/abs/2201.01740)

Link to google meet https://meet.google.com/mmj-wgez-dee

Fault-tolerant quantum computers promise the capability of performing certain tasks much faster than their classical counterparts. Quantum computations are usually described using quantum circuits, a picture inspired by the circuit model of classical computation. In this seminar, I will discuss a different universal model of quantum computation known as Pauli-based computation [1], which has no classical analog. To that end, I will start by introducing all of the concepts and definitions needed for the understanding of this presentation. Then, I will describe Pauli-based computation and convey an informal and intuitive (visual) proof of its universality. Finally, I will discuss recently published results [2] illustrating how this model can be used as a tool for performing circuit compilation and hybrid quantum-classical computation. 

[1] Sergey Bravyi, Graeme Smith, and John A. Smolin. “Trading Classical and Quantum
Computational Resources”. Phys. Rev. X 6,021043 (2016).
[2] Filipa C. R. Peres and Ernesto F. Galvão, Quantum circuit compilation and hybrid computation using Pauli-based computation, Quantum 7, 1126 (2023).

Google Meets link

https://meet.google.com/cxd-httw-rud?pli=1

The theory of open quantum system is one of the most essential tools for the development of quantum technologies. Furthermore, the Lindblad (or Gorini-Kossakowski-Sudarshan-Lindblad) Master Equation plays a key role as it is the most general generator of Markovian dynamics in quantum systems. In this presentation, we present this equation together with its derivation from microscopic principles. The presentation tries to be as self-contained and straightforward as possible to be useful to readers with no previous knowledge of this field. Undergrad, master, and PhD students are encouraged to assist.

Reference: https://pubs.aip.org/aip/adv/article/10/2/025106/1021638/A-short-introduction-to-the-Lindblad-master

Google Meet Link

https://meet.google.com/imv-oxks-bkk