Title: Quantum Algorithm for Simulating the Wave Equation
Authors: Pedro C.S. Costa (CBPF), Stephen Jordan (NIST/Maryland), Aaron Ostrander (Maryland)
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 for state preparation relative to general purpose linear differential equation algorithms. We also consider using Hamiltonian simulation for Klein-Gordon equations and Maxwell’s equations.
Title: Reversing the thermodynamic arrow of time using quantum correlations
Authors: Kaonan Micadei, John P. S. Peterson, Alexandre M. Souza, Roberto S. Sarthour, Ivan S. Oliveira, Gabriel T. Landi, Tiago B. Batalhão, Roberto M. Serra, Eric Lutz
Abstract: The second law permits the prediction of the direction of natural processes, thus defining a thermodynamic arrow of time. However, standard thermodynamics presupposes the absence of initial correlations between interacting systems. We here experimentally demonstrate the reversal of the arrow of time for two initially quantum correlated spins-1/2, prepared in local thermal states at different temperatures, employing a Nuclear Magnetic Resonance setup. We observe a spontaneous heat flow from the cold to the hot system. This process is enabled by a trade off between correlations and entropy that we quantify with information-theoretical quantities.
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.
Title: Vestiges of quantum oscillations in the open evolution of semiclassical states
Author: Alfredo M. Ozorio de Almeida (qig@CBPF)
Abstract: A single wave component of a quantum particle can in principle be detected by the way that it interferes with itself, that is, through the local wave function correlation. The interpretation as the expectation of a local translation operator allows this measure of quantum wavyness to be followed through the process of decoherence in open quantum systems. This is here assumed to be Markovian, determined by Lindblad operators that are linear in position and momentum. The limitation of small averaging windows and even smaller correlation lengths simplifies the semiclassical theory for the evolving local correlation. Its spectrum has a peak for each classical momentum, subjected to Gaussian broadening with decoherence. These spectral lines can be clearly resolved even after the Wigner function has become positive: The correlations located far from caustics seem to be the last vestige of quantum oscillations.
In this new article we used our NMR quantum computer (only two qubits…), in collaboration with Frederico Brito (USP-SC), to simulate in a digital-analog way a quantum annealing process. We currently hold (as far as I know…) the record of Trotter steps (235) and gates (more than 2000) in a quantum simulation. Moreover, we were able to relate the quality of the computation with the amount of entanglement it generated. But don’t let this trick you: more entanglement does seem to relate with better computation quality, but it does not necessarily imply better-than-classical computation! See the plot and description below, and click here for the full article.
Computation Reliabilty. Experimental results for mean
(time-average) success and fidelity (top panel) and maximum and mean
entanglement (bottom panel), as a function of the applied magnetic
field gradient. Classical algorithm is assumed to not suffer any kind
of noise, as it is implemented in a classical computer.
Title: Reliability of digitized quantum annealing and the decay of entanglement
Authors: John P. S. Peterson (CBPF), Roberto S. Sarthour (CBPF), Alexandre M. Souza (CBPF), Ivan S. Oliveira (CBPF), Frederico Brito (USP-SC), Fernando de Melo (CBPF)
Abstract: We performed a banged-digital-analog simulation of a quantum annealing protocol in a two-qubit Nuclear Magnetic Resonance (NMR) quantum computer. Our experimental simulation employed up to 235 Trotter steps, with more than 2000 gates (pulses), and we obtained a protocol success above 80%. Given the exquisite control of the NMR quantum computer, we performed the simulation with different noise levels. We thus analyzed the reliability of the quantum annealing process, and related it to the level of entanglement produced during the protocol. Although the presence of entanglement is not a sufficient signature for a better-than-classical simulation, the level of entanglement achieved relates to the fidelity of the protocol.
Our NMR “quantum computer” is once again used to probe the foundations of quantum thermodynamics. The qig@CBPF, in collaboration with the quantum information group from the UFABC, were now able to create a quantum Maxwell’s Demon! See the details below, and check the full article here.
Title: Experimental rectification of entropy production by a Maxwell’s Demon in a quantum system
Authors: P. A. Camati, J. P. S. Peterson, T. B. Batalhão, K. Micadei, A. M. Souza, R. S. Sarthour, I. S. Oliveira, R. M. Serra
Abstract: Maxwell’s demon explores the role of information in physical processes. Employing information about microscopic degrees of freedom, this “intelligent observer” is capable of compensating entropy production (or extracting work), apparently challenging the second law of thermodynamics. In a modern standpoint, it is regarded as a feedback control mechanism and the limits of thermodynamics are recast incorporating information-to-energy conversion. We derive a trade-off relation between information-theoretic quantities empowering the design of an efficient Maxwell’s demon in a quantum system. The demon is experimentally implemented as a spin-1/2 quantum memory that acquires information, and employs it to control the dynamics of another spin-1/2 system, through a natural interaction. Noise and imperfections in this protocol are investigated by the assessment of its effectiveness. This realization provides experimental evidence that the irreversibility on a non-equilibrium dynamics can be mitigated by assessing microscopic information and applying a feed-forward strategy at the quantum scale.
Peter A. Bouvrie, aka Alex, a postdoc from the qig@CBPF, has recently published a PRA in collaboration with the quantum information group from UFRJ, and colleagues from Mexico e Argentina — a Latin America collaboration! See the details below, and read the article here
Title: Multipartite concurrence for identical-fermion systems
Authors: A. P. Majtey, P. A. Bouvrie, A. Valdés-Hernández, and A. R. Plastino
Abstract: We study the problem of detecting multipartite entanglement among indistinguishable fermionic particles. A multipartite concurrence for pure states of N identical fermions, each one having a d-dimensional single-particle Hilbert space, is introduced. Such an entanglement measure, in particular, is optimized for maximally entangled states of three identical fermions that play a role analogous to the usual (qubit) Greenberger-Horne-Zeilinger state. In addition, it is shown that the fermionic multipartite concurrence can be expressed as the mean value of an observable, provided two copies of the composite state are available.