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Achieving high-fidelity control of many-body dynamics

arXiv link here

Authors: J.H.M. Jensen, F.S. Møller (TU Wien), J.J. Sørensen, J.F. Sherson

We apply recent state-of-the-art optimal control techniques to a challenging many-body problem: driving the superfluid-Mott insulator transition in an optical lattice. At system sizes well beyond the reach of exact diagonalization approaches, and thus requiring a matrix product state ansatz, we obtain fidelities in the range 0.99-0.9999 and beyond with associated quantum speed limit estimates. Whereas previous efforts yielded lower fidelity solutions with smooth, monotonic controls, we efficiently identify a rich hierarchy of bang-bang-like solutions. These facilitate the non-adiabatic quantum interference pathways using sequential tunneling and phase-imprinting dynamics necessary for high fidelity. Mapping out the optimal solutions at various process durations, we observe a characteristic, exponential dependence for the fidelity across several orders of magnitude. Overall, we achieve these results by utilizing the counter-intuitive fact that appropriate dynamical approximations lead to a more precise and significantly cheaper implementation of optimal control than a full dynamical solution. In discussing the technique's generality, this demonstration may pave the way for fulfilling the comprehensive demands for efficient high-fidelity control in very high-dimensional systems which has hitherto not been feasible.

Approximate Dynamics Lead to More Optimal Control: Efficient Exact Derivatives

arXiv link here

Authors: J.H.M. Jensen, F.S. Møller (TU Wien), J.J. Sørensen, J.F. Sherson

Accurate derivatives are important for efficiently locally traversing and converging in quantum optimization landscapes. By deriving analytically exact control derivatives (gradient and Hessian), it is shown here that the feasibility of meeting this central accuracy requirement critically depends on the choice of propagation scheme and problem representation. Even when exact propagation is sufficiently cheap it is, perhaps surprisingly, much more efficient to optimize the (appropriately) approximate propagators: in a certain sense, approximations in the dynamics are traded off for significant complexity reductions in the exact derivative calculations. Importantly, past the initial analytical considerations, only standard numerical techniques are explicitly required with straightforward application to realistic systems. These results are numerically verified for two concrete problems of increasing Hilbert space dimensionality. The best schemes obtain unit fidelity to machine precision, whereas the results for other schemes are separated consistently by orders of magnitude in computation time and in worst case 10 orders of magnitude in achievable fidelity. Since these gaps continually increase with system size and complexity, this methodology unlocks efficient optimization of many-body dynamics operating in the unprecedented high-fidelity regime which will be published separately.

Quantum Composer: A programmable quantum visualization and simulation tool for education and research

Accepted in the American Journal of Physics.

arXiv link here.

Authors: Shaeema Z. Ahmed*, Jesper H.M. Jensen*, Carrie A. Weidner*, Jens Jakob Sørensen, Marcel Murdrich, Jacob F. Sherson

*indicates co-first-authorship

Making quantum mechanical equations and concepts come to life through interactive simulation and visualization are commonplace for augmenting learning and teaching. However, graphical visualizations nearly always exhibit a set of hard-coded functionalities while corresponding text-based codes offer a higher degree of flexibility at the expense of steep learning curves or time investments. We introduce Quantum Composer, which allows the user to build, expand, or explore quantum mechanical simulations by interacting with graphically connectable nodes, each corresponding to a physical concept, mathematical operation, visualization, etc. Abstracting away numerical and programming details while at the same time retaining accessibility, emphasis on understanding, and rapid feedback mechanisms, we illustrate through a series of examples its open-ended applicability in both introductory and advanced quantum mechanics courses, student projects, and for visual exploration within research environments.

Investigating student use of a flexible tool for simulating and visualizing quantum mechanics

Published in the 2020 Physics Education Research Conference (PERC) Proceedings 31 August 2020.

Authors: Carrie A. Weidner*, Shaeema Z. Ahmed*, Jesper H.M. Jensen, Jacob F. Sherson and Heather J. Lewandowski (JILA/CU Boulder)

* indicates co-first-authorship

As education researchers gain a broader understanding of how students learn quantum mechanics, new pedagogical and technical resources are being developed to facilitate student learning. To further research-based knowledge of student learning of quantum mechanics, we present a study on the use of Quantum Composer, a flexible, flow-based tool for the exploration and simulation of quantum mechanical systems in one dimension. To explore Composer's impact on students' knowledge of quantum mechanics, we carried out think-aloud interviews where students worked through an exercise exploring the statics and time-dynamics of quantum states in single and double harmonic well potentials. Student Outcomes are then cross-coded with their observed Interactions with Composer. We find that defined Outcomes of Recollection, Reinforcement and Discovery happen most often when students are using the Composer tools that allow them to visualize quantum states, simulate their time dynamics, and change parameters repeatedly in order to understand how systems are represented in both the static and dynamic cases.

Hessian-based optimization of constrained quantum control

arXiv link here

Authors: Mogens Dalgaard, Felix Motzoi, Jesper Hasseriis Mohr Jensen, Jacob F. Sherson

Efficient optimization of quantum systems is a necessity for reaching fault tolerant thresholds. A standard tool for optimizing simulated quantum dynamics is the gradient-based GRAPE algorithm,which has been successfully applied in a wide range of different branches of quantum physics. In this work, we derive and implement exact 2nd order analytical derivatives of the coherent dynamics and find improvements compared to the standard of optimizing with the approximate 2nd order BFGS. We demonstrate performance improvements for both the best and average errors of constrained unitary gate synthesis on a circuit-QED system over a broad range of different gate durations.

Spatial tomography of individual atoms in a quantum gas microscope

Accepted to Physical Review A.

arXiv link here

Authors: Ottó Elíasson*, Jens S. Laustsen*, Robert Heck, Romain Müller, Jan J. Arlt, Carrie A. Weidner, and Jacob F. Sherson

*denotes co-first-authorship

We demonstrate a method to determine the position of single atoms in a three-dimensional optical lattice. Atoms are sparsely loaded from a far-off-resonant optical tweezer into a few vertical planes of a cubic optical lattice positioned near a high-resolution microscope objective. In a single real-ization of the experiment, we pin the atoms in deep lattices and then acquire multiple fluorescence images with single-site resolution. The objective is translated between images, bringing different lattice planes of the lattice into focus. The applicability of our method is assessed using simulated fluorescence images, where the atomic filling fraction in the lattice is varied. This opens up the possibility of extending the domain of quantum simulation using quantum gas microscopes from two to three dimension.

Crowdsourcing human common sense for quantum control

submitted to Physical Review Research

arXiv link here

Authors: J.H.M. Jensen, M. Gajdacz, S.Z. Ahmed, J.H. Czarkowski, C. Weidner, J. Rafner, J.J. Sørensen, K. Mølmer, J.F. Sherson

Citizen science methodologies have over the past decade been applied with great success to help solve highly complex numerical challenges. Here, we take early steps in the quantum physics arena by introducing a citizen science game, Quantum Moves 2, and compare the performance of different optimization methods across three different quantum optimal control problems of varying difficulty. Inside the game, players can apply a gradient-based algorithm (running locally on their device) to optimize their solutions and we find that these results perform roughly on par with the best of the tested standard optimization methods performed on a computer cluster. In addition, cluster-optimized player seeds was the only method to exhibit roughly optimal performance across all three challenges. This highlights the potential for crowdsourcing the solution of future quantum research problems.

Optimization of pulses with low bandwidth for improved excitation of multiple-quantum coherences in NMR of quadrupolar nuclei

Published in The Journal Of Chemical Physics 3 February 2020.

arXiv link here

Authors: J.J. Sørensen, J.S. Nyemann (QMMG, iNano AU), F. Motzoi (QMMG, FZ Jülich), J.F. Sherson, T. Vosegaard (iNano AU)

We discuss the commonly encountered problem when optimizing nuclear magnetic resonance (NMR) pulses using optimal control that the otherwise very precise NMR theory does not provide as excellent agreement with experiments. We hypothesize that this disagreement is due to phase transients in the pulse due to abrupt phase and amplitude changes resulting in a large bandwidth. We apply the gradient optimization using parametrization algorithm that gives high fidelity pulses with a low bandwidth compared to the typical gradient ascent pulse engineering pulses. Our results obtain a better agreement between experiments and simulations supporting our hypothesis and solution to the problem.

Global optimization of quantum dynamics with AlphaZero deep exploration

Published in npj Quantum Information on 14 January 2020.

Authors: Mogens Dalgaard, Felix Motzoi, Jens Jakob Sørensen, Jacob F. Sherson

While a large number of algorithms for optimizing quantum dynamics for different objectives have been developed, a common limitation is the reliance on good initial guesses, being either random or based on heuristics and intuitions. Here we implement a tabula rasa deep quantum exploration version of the Deepmind AlphaZero algorithm for systematically averting this limitation. AlphaZero employs a deep neural network in conjunction with deep look ahead in a guided tree search, which allows for predictive hidden-variable approximation of the quantum parameter landscape. To emphasize transferrability, we apply and benchmark the algorithm on three classes of control problems using only a single common set of algorithmic hyperparameters. AlphaZero achieves substantial improvements in both the quality and quantity of good solution clusters compared to earlier methods. It is able to spontaneously learn unexpected hidden structure and global symmetry in the solutions, going beyond even human heuristics.

Time-optimal control of collisional √SWAP gates in ultracold atomic systems

Paper published in Physical Review A 12 November 2019

arXiv link here

Authors: J.H.M. Jensen, J.J. Sørensen, K. Mølmer, J.F. Sherson

We use quantum optimal control to identify fast collision-based two-qubit √SWAP gates in ultracold atoms. We show that a significant speed up can be achieved by optimizing the full gate instead of separately optimizing the merge-wait-separate sequence of the trapping potentials. Our optimal strategy does not rely on the atoms populating the lowest eigenstates of the merged potential, and it crucially includes accumulation of quantum phases before the potentials are fully merged. Our analyses transcend the particular trapping geometry, but to compare with previous works, we present systematic results for an optical lattice and find greatly improved gate durations and fidelities.

QEngine: A C++ library for quantum optimal control of ultracold atoms

Paper published in Computer Physics Communications 10 January 2019.

Authors: J.J. Sørensen, J.H.M. Jensen, T. Heinzel, J.F. Sherson

We present the first version of the QEngine, an open-source C++ library for performing optimal control of ultracold quantum systems. The most notable systems presented here are Bose–Einstein condensates, many-body systems described by Bose–Hubbard type models, and two interacting particles. These systems can all be realized experimentally using ultracold atoms in various trapping geometries including optical lattices and tweezers. We provide several optimal control algorithms including the group method. The QEngine library has a strong focus on accessibility and performance. We provide several examples of how to prepare simulations of the physical systems and apply optimal control.

Do physicists stop searches too early? A remote-science, optimization landscape investigation.

The manuscript for the results of our Alice Challenge is now submitted for review and available on the arxiv.

Despite recent advances driven by machine learning algorithms, experts agree that such algorithms are still often unable to match the experience-based and intuitive problem solving skills of humans in highly complex settings. Recent studies have demonstrated how the intuition of lay people in citizen science games [1] and the experience of fusion-scientists [2] have assisted automated search algorithms by restricting the size of the active search space leading to optimized results. Humans, thus, have an uncanny ability to detect patterns and solution strategies based on observations, calculations, or physical insight. Here we explore the fundamental question: Are these strategies truly distinct or merely labels we attach to dierent points in a high dimensional continuum of solutions? In the latter case, our human desire to identify patterns may lead us to terminate search too early. We demonstrate that this is the case in a theoretical study of single atom transport in an optical tweezer, where more than 200,000 citizen scientists helped probe the Quantum Speed Limit [1]. With this insight, we develop a novel global entirely deterministic search methodology yielding dramatically improved results. We demonstrate that this \bridging" of solution strategies can also be applied to closed-loop optimization of the production of Bose-Einstein condensates. Here we nd improved solutions using two implementations of a novel remote interface. First, a team of theoretical optimal control researchers employ a Remote version of their dCRAB optimization algorithm (RedCRAB), and secondly a gamied interface allowed 600 citizen scientists from around the world to participate in the optimization. Finally, the \real world" nature of such problems allow for an entirely novel approach to the study of human problem solving, enabling us to run a hypothesis-driven social science experiment \in the wild". (09/2017)

Knowledge Formation and Inter-Game Transfer With Classical and Quantum Physics

Published as Work in Progress Paper at ECGBL ’16

In order to facilitate an intuitive understanding of classical physics concepts we have developed Potential Penguin - a game where players manipulate the landscape around a sliding penguin in order to control its movement. The learning goal of Potential Penguin is to familiarize players with kinetic energy and potential energy - the energies associated with movement and position in the landscape respectively. The game levels introduce the concepts one by one, as players are tasked with sliding the penguin through a landscape towards a specific location, while keeping the velocity under control. When the player manipulates the landscape, the potential energy of the penguin is changed, which determines the penguin's movement. To build a strong connection between theory and game the analytical expressions for kinetic and potential energy are displayed during play with font sizes continually growing and shrinking according to changes in each energy type. With Potential Penguin we hope to study whether visualizing the amount of kinetic and potential energy through visible mathematical expressions generates a connection between the intuitive actions taken in the game and the underlying physics concepts. The knowledge about kinetic and potential energy gained with Potential Penguin can also be used to understand most of the physics behind the citizen science game Quantum Moves, which has the goal of building a working quantum computer. The two games share the principle of the core interaction - manipulating the potential-energy landscape. We aim to investigate whether a proficiency and understanding of Potential Penguin predicts a better performance in Quantum Moves and a deeper understanding of the quantum physics behind that game.  (08/2016)

Measurement-enhanced determination of BEC phase diagrams

Is now submitted for review and available on the arxiv.

We demonstrate how dispersive atom number measurements during evaporative cooling can be used for enhanced determination of the non-linear parameter dependence of the transition to a Bose-Einstein condensate (BEC). Our analysis demonstrates that conventional averaging of shot-to-shot fluctuations introduces systematic errors and reduces precision in comparison with our method. We furthermore compare in-situ images from dispersive probing of a BEC with corresponding absorption images in time-of-flight. This allows for the determination of the transition point in a single experimental realization by applying multiple dispersive measurements. Finally, we explore the continuous probing of several consecutive phase transition crossings using the periodic addition of a focused "dimple" potential.  (07/2016)

Manipulating matter waves in an optical superlattice

Published in Phys. Rev. A with the group of Gabriele De Chiara, Belfast

We investigate the potential for controlling a noninteracting Bose-Einstein condensate loaded into a one-dimensional optical superlattice. Our control strategy combines Bloch oscillations, originating from accelerating the lattice, with time-dependent control of the superlattice parameters. We investigate two experimentally viable scenarios, very low and very high potential depths, in order to gain a better understanding of matter wave control available within the system. Multiple lattice parameters and a versatile energy band structure allow us to obtain a wide range of control over energy band populations. Finally, we consider several examples of quantum state preparation in the superlattice structure that may be difficult to achieve in a regular lattice. (12/2016)

Preparation of ultracold atom clouds at the shot noise level

Published in Phys. Rev. Lett. with the group of Jan Arlt

We prepare number stabilized ultracold atom clouds through the real-time analysis of nondestructive images and the application of feedback. In our experiments, the atom number N∼106 is determined by high precision Faraday imaging with uncertainty ΔN below the shot noise level, i.e., ΔN<√N. Based on this measurement, feedback is applied to reduce the atom number to a user-defined target, whereupon a second imaging series probes the number stabilized cloud. By this method, we show that the atom number in ultracold clouds can be prepared below the shot noise level. (08/2016)

Universal three-body physics in ultracold KRb mixtures

Published in Phys. Rev. Lett. with the group of Jan Arlt (Editor’s suggestion) See also Physics Focus story

Ultracold atomic gases have recently become a driving force in few-body physics due to the observation of the Efimov effect. While initially observed in equal mass systems, one expects even richer few-body physics in the heteronuclear case. In previous experiments with ultracold mixtures of potassium and rubidium, an unexpected nonuniversal behavior of Efimov resonances was observed. In contrast, we measure the scattering length dependent three-body recombination coefficient in ultracold heteronuclear mixtures of 39K−87Rb and 41K−87Rb and do not observe any signatures of Efimov resonances for accessible scattering lengths in either mixture. Our results show good agreement with our theoretical model for the scattering dependent three-body recombination coefficient and reestablish universality across isotopic mixtures. (10/2016)

Inferring causality from noisy time series data

Published in COMPLEXIS 2016

Convergent Cross-Mapping (CCM) has shown high potential to perform causal inference in the absence of models. We assess the strengths and weaknesses of the method by varying coupling strength and noise levels in coupled logistic maps. We find that CCM fails to infer accurate coupling strength and even causality direction in synchronized time-series and in the presence of intermediate coupling. We find that the presence of noise deterministically reduces the level of cross-mapping fidelity, while the convergence rate exhibits higher levels of robustness. Finally, we propose that controlled noise injections in intermediate-to-strongly coupled systems could enable more accurate causal inferences. Given the inherent noisy nature of real-world systems, our findings enable a more accurate evaluation of CCM applicability and advance suggestions on how to overcome its weaknesses.  (03/2016)

Manipulation of collective quantum states in Bose-Einstein condensates by continuous imaging

Published in Phys. Rev. A with the group of Klaus Mølmer

We develop a Gaussian state treatment that allows a transparent quantum description of the continuous, nondestructive imaging of and feedback on a Bose-Einstein condensate. We have previously demonstrated [A. C. J. Wade et al., Phys. Rev. Lett. 115, 060401 (2015)] that the measurement backaction of stroboscopic imaging leads to selective squeezing and entanglement of quantized density oscillations. Here, we investigate how the squeezing and entanglement are affected by the finite spatial resolution and geometry of the probe laser beam and of the detector and how they can be optimized. (02/2016)

Virtual learning environment for interactive engagement with advanced quantum mechanics

Published in Phys. Rev. Phys. Education

A virtual learning environment can engage university students in the learning process in ways that the traditional lectures and lab formats cannot. We present our virtual learning environment StudentResearcher, which incorporates simulations, multiple-choice quizzes, video lectures, and gamification into a learning path for quantum mechanics at the advanced university level. StudentResearcher is built upon the experiences gathered from workshops with the citizen science game Quantum Moves at the high-school and university level, where the games were used extensively to illustrate the basic concepts of quantum mechanics. The first test of this new virtual learning environment was a 2014 course in advanced quantum mechanics at Aarhus University with 47 enrolled students. We found increased learning for the students who were more active on the platform independent of their previous performances. (04/2016)

Play or science?: a study of learning and framing in crowdscience games

Published in Well Played 4(2), 30 (2015)

Crowdscience games may hold unique potentials as learning opportunities compared to games made for fun or education. They are part of an actual science problem solving process: By playing, players help scientists, and thereby interact with real continuous research processes. This mixes the two worlds of play and science in new ways. During usability testing we discovered that users of the crowdscience game Quantum Dreams tended to answer questions in game terms, even when directed explicitly to give science explanations.We then examined these competing frames of understanding through a mixed correlational and grounded theory analysis. This essay presents the core ideas of crowdscience games as learning opportunities, and reports how a group of players used "game", "science" and "conceptual" frames to interpret their experience. Our results suggest that oscillating between the frames instead of sticking to just one led to the largest number of correct science interpretations, as players could participate legitimately and autonomously at multiple levels of understanding. (10/2015)

Non-Gaussian distribution of collective operators in quantum spin chains

Published in New Journ. Phys.

We numerically analyse the behavior of the full distribution of collective observables in quantum spin chains. While most of previous studies of quantum critical phenomena are limited to the first moments, here we demonstrate how quantum fluctuations at criticality lead to highly non-Gaussian distributions. Interestingly, we show that the distributions for different system sizes collapse on the same curve after scaling for a wide range of transitions: first and second order quantum transitions and transitions of the Berezinskii–Kosterlitz–Thouless type. We propose and analyse the feasibility of an experimental reconstruction of the distribution using light–matter interfaces for atoms in optical lattices or in optical resonators. (10/2016)

Time-limited optimal dynamics beyond the quantum speed limit
Gajdacz, M., Das, K. K., Arlt, J., Sherson, J. F., & Opatrný, T. 
Physical review

Squeezing and entanglement of density oscillations in a Bose-Einstein condensate
A. Wade, J. F. Sherson, and K. Mølmer
Physical Review Letters

Getting humans to do quantum optimization: User acquisition, engagement and early results from the citizen cyberscience game quantum moves
Lieberoth, A., Pedersen, M. K., Marin, A. C., Planke, T., & Sherson, J. F.