From this Friday (20.10) up to the end of the month we have the pleasure to receive Giuseppe Di Molfeta at CBPF. Giuseppe has many contributions to the topic of quantum walks. More specifically he employs quantum walks to simulate all sort of systems: from neutrino oscillations and Dirac equation, all the way up to gravity! The latter is the subject of the talk he will deliver in the Theory Seminar. See the details below, and be sure to be there!
Title: Quantum walking in curved spacetime
Speaker: Giuseppe Di Molfetta (Université Aix-Marseille )
Coordinates: seminar room 6th floor, CBPF. 25.10, 14h30
Abstract:In the framework of Quantum Simulation, a crucial topic for the exploration of physical situations where experiments are currently hard or impossible to setup (e.g. quantum gravity), Quantum Walks (QW) are increasingly recognized as prominent models. A discrete-time QW is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation). We introduce Grouped QWs, a generalization of the usual QWs where (i) the input is allowed a simple prior encoding and (ii) the local unitary coin is allowed to act on larger than usual neighborhoods. In  it was shown that the continuum limit of this class of QWs leads to an entire class of PDEs, encompassing the Hamiltonian form of the massive Dirac equation in (1 + 1) curved spacetime . Therefore a certain QW provides us with a unitary discrete toy model of a test particle in curved spacetime, in spite of the fixed background lattice.
Here we take a step further and discretize the coin operator itself, only allowing, as elementary local unitary operator, the identity (no propagation) or the Pauli X operator (full-speed propagation). This discretization has the practical advantage of allowing easier experimental implementation, as well as of being of interest for studying the quantization of the metric. We prove that we can obtain the Dirac equation in the case of constant background metric. We also thoroughly analyze the non-constant metric case showing how, due to a non-differentiability issue in the discrete model, a new term arises in the differential equation, deviating from the usual Dirac equation.
 P. Arrighi, S. Facchini, M. Forets, Quantum Inf. Process. (2016) 15: 3467
 G. Di Molfetta, F. Debbasch, M. E. Brachet, Phys. Rev. A 88.4 (2013): 042301
Next in our series QM Talks@CBPF is a talk by Pedro C. da Silva, PhD student here at CBPF. In this talk Pedro will show some interesting results he got during his stay in Maryland, collaborating with the group of Prof. Stephen P. Jordan. Be sure to be there! Details follow.
Title: Quantum Algorithm for Simulating the Wave Equation
Speaker: Pedro C. da Silva (CBPF)
Coordinates: room 601C, CBPF. 11.10, 16h00
Abstract: We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of discretized Laplacian operators to allow for improved scaling in truncation errors and improved scaling in state preparation relative to general purpose linear differential equation algorithms. We also consider using Hamiltonian simulation for Klein-Gordon equations and Maxwell’s equations.
We continue our series of seminars with a talk by Daniel S. Tasca (IF-UFF). Daniel and co-authors have recently performed an experiment where they verify that a coarse graining procedure might break the mutual unbiasedness between conjugate variables. That sounds interesting! To know more about the topic, check out Daniel’s article here, and attend to his talk. See you there.
Title: Mutual Unbiasedness in Coarse-grained Continuous Variables
Speaker: Daniel S. Tasca (IF-UFF)
Coordinates: room 601C, CBPF. 27.09, 16h00
Abstract: The notion of mutual unbiasedness for coarse-grained measurements of quantum continuous variable systems is considered. It is shown that while the procedure of “standard” coarse graining breaks the mutual unbiasedness between conjugate variables, this desired feature can be theoretically established and experimentally observed in periodic coarse graining. We illustrate our results in an optics experiment implementing Fraunhofer diffraction through a periodic diffraction grating, finding excellent agreement with the derived theory. Our results are an important step in developing a formal connection between discrete and continuous variable quantum mechanics.
Next week in our QM Talks@CBPF series we’ll have a talk by Víctor Montenegro, from the Pontificia Universidad Catolica de Chile. Victor holds a postdoc position at the PUC-Chile in the group lead by Miguel Orszag — a group which has contributed a lot to the development of the quantum optics area.
Victor is on vacation in Rio, and he was very kind to contact us and to accept to give a talk at CBPF. See the details of the talk below, and be sure to be there!
Title: Macro-mechanical quantum state superposition via spin post-selection in dispersive systems
Speaker: Víctor Montenegro (PUC- Chile)
Coordinates: room 601C, CBPF. 28.06, 16h00
Abstract: Macroscopic quantum superposition states are fundamental to test the classical-quantum boundary and present suitable candidates for quantum technologies. Although the preparation of such states have already been realized, the existing setups commonly consider external driving and resonant interactions, which might limit scalability for quantum computation purposes. Motivated by these, we present a scheme to prepare non-classical states of a macroscopic mechanical object. The protocol comprises a probabilistic qubit (0 and 1 phononic states) superposition, and the generation of mechanical Schroedinger’s cat states. To realize this, we have considered an open spin-mechanical quantum system via conditional displaced interaction Hamiltonian in the dispersive regime without any need for adjusting resonances. Therefore, in comparison with previous works on the matter, our proposal does not rely on any non-linearity, energy exchange nor external pumping —which could be an advantage for scalability purposes. Our probabilistic preparation protocol is uniquely based on two steps. Firstly, we weakly evolve the spin-mechanical system for a time t, allowing us to truncate the oscillator Hilbert space up to a single phonon excitation. Subsequently, we then proceed to post-select the spin system. The latter step aims to prepare (probabilistically) any mechanical qubit superposition. Our results can be understood within the clear connection between the quantum coherence of the mechanics and the amplification of the position and momentum quadratures on average.
Our series of seminars continues this week with Tobias Micklitz (CBPF). Tobias is an expert on many-body problems within condensed matter, especially on issues related to Anderson’s location. Recently, we’ve been discussing some ideas at the interface between condensed matter and quantum information. I’m sure something nice will come out of this interaction.
See the details of the talk below, and be sure to not miss it. See you there!
Title: Disordered Quantum Systems from Anderson- to many-body localization
Speaker: Tobias Micklitz (CBPF)
Coordinates: room 601C, CBPF. 21.06, 16h00
Abstract: Disorder is known to have dramatic effects on single particle-dynamics in low dimensional quantum systems. The absence of diffusion in dimensions smaller than three emerges within a single-particle picture where non-interacting particles, scattering off disorder, interfere with themselves and effectively get localized to a finite region in space. This ‘Anderson localization’ originates from the quantum-mechanical wave-nature of particles and is fundamentally different from classical trapping in deep valleys of a disorder potential. The impact of weak interactions on the single-particle localization problem can be subsumed as a fluctuating bath. The bath induces decoherence and thus suppresses localization. More strikingly, it has been recently proposed that (isolated) disordered quantum systems of interacting particles undergo a finite-temperature phase-transition which can be thought of as a many-body localization transition. The ‘many-body localized’ phase is characterized by the absence of ergodicity and the vanishing of transport coefficients. In the talk I will give a brief introduction into the phenomenon of (quantum) localization in disordered systems emphasizing recent trends, and then discuss a field-theory approach to the many-body localization problem.
Our next seminar from the series QM Talks@CBPF will be given by Fernando Nicácio, aka, Boiúna (or is it the other way around?).
See the details below. See you there!
Title: Determinando propriedades de estados estacionários diretamente
das interações do sistema com o ambiente
Speaker: Fernando Nicácio (UFRJ)
Coordinates: room 601C, CBPF. 07.06, 16h00
Abstract: Considerando estados estacionários de um sistema de variáveis contínuas evoluindo sob uma dinâmica não-unitária, revelamos a conexão entre propriedades e simetrias do sistema com os parâmetros dinâmicos da evolução. Em particular, estabelecemos uma relação entre a equação de Lyapunov para sistemas dinâmicos não-Hamiltonianos e as soluções estacionárias de uma equação mestra de Lindblad independente do tempo para modos bosônicos. Explorando relações de “bona fide”, as quais são utilizadas para caracterizar propriedades quânticas genuínas (emaranhamento, “steerabilidade”, classicalidade), obtemos condições sobre os parâmetros dinâmicos da equação de Lindblad que fazem com que o sistema seja conduzido a um estado estacionário que detém tais propriedades. Desenvolveremos também um método para capturar as simetrias do estado estacionário baseado nas simetrias da equação de Lyapunov. E por fim, apresentamos um método teórico simples para engenharia de reservatórios baseado nos resultados preliminares.
F. Nicacio, M. Paternostro, & A. Ferraro,
Determining stationary-state quantum properties directly from system-environment interactions,
Phys. Rev A 94, 052129 (2016).
Title: Emerging Dynamics Arising From Quantum Mechanics
Authors: Cristhiano Duarte (UFMG), Gabriel Dias Carvalho (CBPF), Nadja K. Bernades (UFMG), Fernando de Melo (CBPF)
Abstract: Physics dares to describe Nature from elementary particles all the way up to cosmological objects like cluster of galaxies and black holes. Although a unified description for all this spectrum of events is desirable, an one-theory-fits-all would be highly impractical. To not get lost in unnecessary details, effective descriptions are mandatory. Here we analyze what are the dynamics that may emerge from a fully quantum description when one does not have access to all the degrees of freedom of a system. More concretely, we describe the properties of the dynamics that arise from Quantum Mechanics if one has only access to a coarse grained description of the system. We obtain that the effective channels are not necessarily of Kraus form, due to correlations between accessible and non-accessible degrees of freedom, and that the distance between two effective states may increase under the action of the effective channel. We expect our framework to be useful for addressing questions such as the thermalization of closed quantum systems, and the description of measurements in quantum mechanics.