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Approximation of the ground state wave function and energy of a quantum system is often achieved using perturbation theory or the variational method. The former approach suffers from the requirement that the Hamiltonian perturbation be small enough for the series to converge while the variational method is only as good as the choice of functions used in the expansion, providing only an approximate ground state whose mean energy is an upper bound to the ground state energy. The method of gradient descent, typically used for optimizing functions over finite dimensions, may be generalized to the infinite-dimensional Hilbert space of a quantum mechanical system to avoid both previous limitations. One may find the ground state of a quantum system by minimizing the energy functional of the wave function of the system via iterative calculation of better approximations using the gradient of the functional. This can be achieved in an infinite-dimensional setting by careful bookkeeping of only the non-zero components of the state vector in the chosen basis of expansion and those matrix elements of the Hamiltonian in that basis required to calculate the next iterative approximation via gradient descent. The sparse nature of the Hamiltonian matrix elements in a chosen basis for many quantum systems ensures that subsequent iterations of the state vector have only a finite number of non-zero components, thereby making the method computationally tractable.

The gradient descent method will be formulated for a quantum system with a time-independent Hamiltonian. The algorithm will be illustrated with a simple quantum system. The impact of symmetry in the choice of initial state vector will be discussed. Limitations of the method and potential improvements (e.g. conjugate gradient) will be considered.

CAP Virtual Congress 2021

Implementing the Gradient Descent Method in an Infinite Dimensional Hilbert Space

time-independent hamiltonian

eigenfunction algorithm

quantum mechanics

gradient descent

**BQIT is a three day annual workshop** aimed at enabling leading UK and international academics and industrial partners to come together; to explore and discuss future ambitions and challenges in the field of **Quantum Information Technologies.** Since our conception in 2014 we have had 230 speakers and panellists who have presented their work and opinions on a range of topics, from quantum theory to innovation in industry.


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The BQIT:21 team welcomes you to the eighth Bristol Quantum Information Technologies workshop! 

Last year was the first time in our workshop's history that we had gone fully virtual. The global circumstances that continue to impact us all professionally and personally have forced BQIT once again to be delivered as an all-virtual workshop for 2021. The access this creates to colleagues across the world who would otherwise be unable to join us, as well as being able to make the workshop free for all attendees due to the lower costs involved in delivering an online workshop, are just a couple of the extraordinary benefits of meeting online. This also means that we can welcome three times as many attendees to BQIT than previous years.   

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Bristol Quantum Information Technologies Workshop

technical paper

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This talk will focus on an overview of Eliashberg theory, a formalism that Jules was very well known for. But I will also discuss some potential shortcomings of this framework, as time permits, from the weak coupling to the strong coupling limit, with polaron physics, and applicability to the hydride and superhydride materials.

Eliashberg Theory and Jules Carbotte

In this work we explore the use of multi-layer graphene (MLG) films grown by chemical vapor deposition for adaptive thermal camouflage. Using different ionic liquids, we tune the opto-electronic properties of MLG (150 – 200 layers) and investigate changes in optical reflectivity and emissivity in the infrared region (IR). We fabricate devices having a metallic back electrode supporting a porous membrane onto which we deposit the MLG. We use both non-stretchable polyethylene (PE), and stretchable polydimethylsiloxane (PDMS) as porous membranes. Using a thermal imaging system, we demonstrate that even when the device temperature is maintained higher than the environment, the MLG emissivity can be electrically controlled such that the device appears indistinguishable from the environment [1]. Moreover, we evaluate the performance of such devices based on flexible textiles towards developing a new material platform for defense applications.

Multilayer Graphene as Adaptive Thermal Camouflage

Supercontinuum generation in optical fiber is the result of an interplay between multiple nonlinear processes. Simulations to reproduce experimental observations are well documented: a differential equation known as the generalized nonlinear Schrödinger equation (GNLSE) is solved to determine the effect of propagation on the spectral and temporal profiles of the slowly-varying amplitude of a laser pulse. For the scalar case, the GNLSE has been shown to yield good results. In a more accurate case, it becomes necessary to take into account the polarization evolution of light as it travels through the fiber, for instance for a fiber with two orthogonal principal axes. This is typically added into the GNLSE to form coupled equations including the birefringence of the fiber and additional nonlinear terms coupling the slowly-varying amplitudes of two polarization components. Upon studying the experimental spectra obtained from a germania-doped photonic crystal fiber, we observe that the polarization state varies significantly across the spectrum, leaving the spectral edges with a greater degree of polarization than the areas near the input pump wavelength. We also observe that the spectral region around the pump maintains a low degree of polarization. These trends lead us to believe that a portion of the energy transfer from input polarization state to an orthogonal output state is proportional to the propagation length, consistent with a linear depolarization contribution that cannot be reproduced using only nonlinear equations. We therefore demonstrate the effect of an additional depolarization term to account for the redistribution of energy between polarization modes. Furthermore, the interaction between linear and nonlinear depolarization mechanisms leads to a more realistic estimate of the polarization maintaining capability of an optical fiber over a broadband spectrum.

Adding a linear contribution to depolarization in simulations of supercontinuum generation

Spectral purity in laser emission is key for several applications such as remote sensing, non-linear optics and laser spectroscopy. However, producing single mode emission at high power in free-space, standing-wave resonators is challenging. Nanostructured laser mirrors can be used to achieve that in compact microchip monolithic laser resonators without using any additional intra-cavity element [1,2]. For instance, using a pair of mirrors displaying a π phase shift between orthogonal polarization states at reflection produces the twisted mode operation, which allows one to eliminate the contrast of the standing wave inside the cavity and makes it possible to eliminate multi-longitudinal mode operation originating from axial spatial hole burning. However, dual-polarization emission remains an issue if there is no mechanism to suppress competing polarization states, and this may give rise to unstable emission, in addition to producing dual frequency emission. In this presentation, we propose a resonator made of anisotropic mirrors displaying both birefringence and diattenuation as a mean to eliminate both spatial hole burning and dual polarization emission. The relative angle of the two mirrors’ principal axes is adjusted such that the laser operates just at the transition between broken and unbroken parity-time symmetric polarization states. At this transition point, the two eigen-polarization states are found to merge to a single state, called an exceptional point, while the counter-propagating waves are orthogonal, and no spatial hole burning takes place [3]. Hence, microchip PT-symmetric states are an attractive option to achieve single mode operation from a miniature microchip laser without the need to introduce any additional intracavity element.

[1] J.-F. Bisson, K. N. Amouzou, Controlling spatial hole burning in lasers using anisotropic laser mirrors J. Opt. Soc. Amer. B 36(12), 3322-
3332, (2019).
[2] J.-F. Bisson, K. N. Amouzou, Elimination of spatial hole burning in solid-state lasers using nanostructured thin films Appl. Opt. 59(5), A83-
A91, (2020).
[3] J.-F. Bisson, Y. C. Nonguierma, Single-mode lasers using parity-time-symmetric polarization eigenstates, Phys. Rev. A, 102, 043522, (2020).

Eliminating dual-polarization laser emission and spatial hole burning by using parity-time-symmetric eigenstates

A programmable quantum simulator can simulate models of quantum many-body systems that may otherwise be impossible to be modeled with conventional computers. Simulation of such many-body quantum systems may further advance our understanding of exotic quantum materials, fundamental forces of nature, molecules for drug discovery, etc. Laser-cooled and trapped atomic ions serve as an ideal platform for the simulation of interacting quantum spin models. In this talk, we describe the development of a large-scale quantum simulator based on a multi-segmented blade electrode ion trap capable of trapping a large (>50) chain of Ytterbium ions in a near uniformly spaced configuration. A high numerical aperture (NA) holographic optical addressing system will be used for aberration-corrected addressing of the trapped ions with minimal ‘crosstalk error’ [1]. This would usher the capability to engineer dynamic many-body Hamiltonians with control over the individual ion-spins and the interactions between them. A high NA imaging system would allow us to detect the spin states of individual ions simultaneously with high precision, including the capability to perform partial measurements without necessarily decohering rest of the system. The trap will be housed inside an XHV vacuum system to keep the ions free from background collisions. Optimal vacuum system engineering has allowed us to design a vacuum vessel with simulated pressures of at least one order of magnitude lower than current room temperature trapped ion quantum simulators.
[1] C.-Y. Shih, S. Motlakunta, N. Kotibhaskar, M.Sajjan, R. Hablützel, R. Islam npj Quantum Information (in press, 2021)

Towards a large scale fully programable trapped ion quantum simulator

We examine the thermodynamics of a new class of asymptotically AdS black holes with non-constant curvature event horizons in Gauss-Bonnet Lovelock gravity, with the cosmological constant acting as thermodynamic pressure. We find that non-trivial curvature on the horizon can significantly affect their thermodynamic behaviour. We observe novel triple points in 6 dimensions between large and small uncharged black holes and thermal AdS. For charged black holes we find a continuous set of triple points whose range depends on the parameters in the horizon geometry. We also find new generalizations of massless and negative mass solutions previously observed in Einstein gravity.

Thermodynamics of Exotic Gauss-Bonnet Black Holes

Trapped ions are a leading platform for noisy intermediate-scale quantum (NISQ) computing with high gate fidelities, long coherence times, and natural long range ion-ion interactions. QuantumION is a project which aims to scale trapped ion quantum computing to 16 Ba+ qubits while providing an open-access resource to the whole research community. High fidelity control over each ion is crucial to scalability and direct access to the hardware level is needed to make a useful community resource. This talk presents the synthesis of these two concepts exemplified by the individual addressing scheme at the heart of QuantumION. A femtosecond laser direct write (FLDW) waveguide is used to split a single laser source into 16 path-length matched and fibre coupled beams. Intensity, phase, and frequency can be controlled independently with commercial fibre AOMs. The fibre tip of each beam is imaged onto a chain of ions aided by a micro-machined array of lenses to provide individual control over 16 ions with projected $10^{-4}$ overall crosstalk. This scheme could also allow operation at multiple wavelengths opening the door to individual state readout of the ion chain with the same beam path.


*We acknowledge support from TQT (CFREF) and the University of Waterloo.

An individual optical addressing scheme for trapped Ba+ ions in an open-access quantum information processor

Understanding and controlling the properties of 2D materials to our advantage can be contemplated with the development of experimental tools to probe and manipulate electrons and their interactions at the atomic scale. In this talk, I will present scanning tunnelling microscopy and spectroscopy experiments aimed at: elucidating the nature of atomic-scale defects in 2D materials [1], visualizing moiré patterns between crystals with different symmetries [2] and imaging surface and edge states in a magnetic topological system. Moreover, I will discuss how we leverage our expertise in probing and engineering electronic states at surfaces of 2D materials to further the development of graphene-based gas sensors [3] and gated quantum dot circuits based on 2D semiconductors [4]. 

REFERENCES

[1] Plumadore et al., PRB, (2020) 
[2] Plumadore et al., Journal of Applied Physics, (2020)
[3] Rautela et al., ACS Applied Materials & Interfaces (2020) 
[4] Boddison-Chouinard, Appl. Phys. Lett., (2019)

Quantum materials at the atomic scale

In this talk I will discuss how one may view four-dimensional de Sitter space as a coherent Glauber-Sudarshan state in string theory. I will also discuss why a de Sitter space cannot exist as a vacuum state in string theory.

de Sitter space in string landscape

Bell nonlocality describes a manifestation of quantum mechanics that cannot be explained by any local hidden variable model. Its origin lies in the nature of quantum entanglement, although understanding the precise relationship between nonlocality and entanglement has been a notorious open problem. In this talk, I will describe a resolution to this problem by developing a dynamical framework in which quantum Bell nonlocality emerges as special form of entanglement, and both are unified as resources under local operations and classical communication (LOCC). The framework is built on the notion of quantum processes, which are abstract quantum channels mapping elements between fixed intervals in space and time. Entanglement is then identified as a quantum process that cannot be generated by LOCC while Bell nonlocality is the subset of these processes that have an instantaneous input- output delay time. LOCC pre-processing is a natural set of free operations in this theory, thereby enabling all entangled states to activate some form of Bell nonlocality.

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Eliashberg Theory and Jules Carbotte

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