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Joonho Lee

Publications and source records attributed to Joonho Lee.

At least 55 records · Page 3Linked to original sources
arXiv2024

Learning to walk in confined spaces using 3D representation

Legged robots have the potential to traverse complex terrain and access confined spaces beyond the reach of traditional platforms thanks to their ability to carefully select footholds and flexibly adapt their body posture while walking. However, robust deployment in real-world applications is still an open challenge. In this paper, we present a method for legged locomotion control using reinforcement learning and 3D volumetric representations to enable robust and versatile locomotion in confined and unstructured environments. By employing a two-layer hierarchical policy structure, we exploit the capabilities of a highly robust low-level policy to follow 6D commands and a high-level policy to enable three-dimensional spatial awareness for navigating under overhanging obstacles. Our study includes the development of a procedural terrain generator to create diverse training environments. We present a series of experimental evaluations in both simulation and real-world settings, demonstrating the effectiveness of our approach in controlling a quadruped robot in confined, rough terrain. By achieving this, our work extends the applicability of legged robots to a broader range of scenarios.

cs.RO↗
arXiv2024

Solving Multi-Entity Robotic Problems Using Permutation Invariant Neural Networks

Challenges in real-world robotic applications often stem from managing multiple, dynamically varying entities such as neighboring robots, manipulable objects, and navigation goals. Existing multi-agent control strategies face scalability limitations, struggling to handle arbitrary numbers of entities. Additionally, they often rely on engineered heuristics for assigning entities among agents. We propose a data driven approach to address these limitations by introducing a decentralized control system using neural network policies trained in simulation. Leveraging permutation invariant neural network architectures and model-free reinforcement learning, our approach allows control agents to autonomously determine the relative importance of different entities without being biased by ordering or limited by a fixed capacity. We validate our approach through both simulations and real-world experiments involving multiple wheeled-legged quadrupedal robots, demonstrating their collaborative control capabilities. We prove the effectiveness of our architectural choice through experiments with three exemplary multi-entity problems. Our analysis underscores the pivotal role of the end-to-end trained permutation invariant encoders in achieving scalability and improving the task performance in multi-object manipulation or multi-goal navigation problems. The adaptability of our policy is further evidenced by its ability to manage varying numbers of entities in a zero-shot manner, showcasing near-optimal autonomous task distribution and collision avoidance behaviors.

cs.RO↗
arXiv2023

Competing Generalized Wigner Crystal States in Moiré Heterostructures

We present a comprehensive study of generalized Wigner crystals across various filling factors for system sizes up to 162 holes employing Hartree-Fock theory and explicitly correlated wave function approaches. While we find broad agreement with the behavior observed in experiments and classical Monte Carlo simulations, we highlight the fact that the Hartree-Fock energy landscape appears to be remarkably complex, exhibiting many competing states, both ordered and disordered, separated by energies of a fraction of $\sim$ 1 meV/hole. We demonstrate which of the located states are metastable by performing a stability analysis at the Hartree-Fock level. Correlated wave function methods furthermore reveal small correlation energies that are nevertheless large enough to tip the balance of state ordering found within Hartree-Fock theory.

cond-mat.str-el↗
arXiv2023

Matchgate Shadows for Fermionic Quantum Simulation

"Classical shadows" are estimators of an unknown quantum state, constructed from suitably distributed random measurements on copies of that state [Nature Physics 16, 1050-1057]. Here, we analyze classical shadows obtained using random matchgate circuits, which correspond to fermionic Gaussian unitaries. We prove that the first three moments of the Haar distribution over the continuous group of matchgate circuits are equal to those of the discrete uniform distribution over only the matchgate circuits that are also Clifford unitaries; thus, the latter forms a "matchgate 3-design." This implies that the classical shadows resulting from the two ensembles are functionally equivalent. We show how one can use these matchgate shadows to efficiently estimate inner products between an arbitrary quantum state and fermionic Gaussian states, as well as the expectation values of local fermionic operators and various other quantities, thus surpassing the capabilities of prior work. As a concrete application, this enables us to apply wavefunction constraints that control the fermion sign problem in the quantum-classical auxiliary-field quantum Monte Carlo algorithm (QC-AFQMC) [Nature 603, 416-420], without the exponential post-processing cost incurred by the original approach.

quant-ph↗
arXiv2023

Stochastic resolution of identity to CC2 for large systems: excited state properties

We apply a stochastic resolution of identity approximation (sRI) to the CC2 method for excitation energy calculations. A set of stochastic orbitals are employed to decouple the crucial 4-index electron repulsion integrals and optimize the contraction steps in CC2 response theory. The CC2 response for excitations builds upon sRI-CC2 ground-state calculations, which scales as O(N^3), where N is a measure for the system size. Overall, the current algorithm for excited states also allows a sharp scaling reduction from original O(N^5) to O(N^3). We test the sRI-CC2 for different molecular systems and basis sets, and we show our sRI-CC2 method can accurately reproduce the results of deterministic CC2 approach. Our sRI-CC2 exhibits an experimental scaling of O(N^2.88) for a hydrogen dimer chain, allowing us to calculate systems with nearly thousands of electrons.

physics.chem-ph↗
arXiv2023

Measurement-induced entanglement and teleportation on a noisy quantum processor

Measurement has a special role in quantum theory: by collapsing the wavefunction it can enable phenomena such as teleportation and thereby alter the "arrow of time" that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space-time that go beyond established paradigms for characterizing phases, either in or out of equilibrium. On present-day NISQ processors, the experimental realization of this physics is challenging due to noise, hardware limitations, and the stochastic nature of quantum measurement. Here we address each of these experimental challenges and investigate measurement-induced quantum information phases on up to 70 superconducting qubits. By leveraging the interchangeability of space and time, we use a duality mapping, to avoid mid-circuit measurement and access different manifestations of the underlying phases -- from entanglement scaling to measurement-induced teleportation -- in a unified way. We obtain finite-size signatures of a phase transition with a decoding protocol that correlates the experimental measurement record with classical simulation data. The phases display sharply different sensitivity to noise, which we exploit to turn an inherent hardware limitation into a useful diagnostic. Our work demonstrates an approach to realize measurement-induced physics at scales that are at the limits of current NISQ processors.

quant-ph↗
arXiv2023

Evaluation of Constrained Reinforcement Learning Algorithms for Legged Locomotion

Shifting from traditional control strategies to Deep Reinforcement Learning (RL) for legged robots poses inherent challenges, especially when addressing real-world physical constraints during training. While high-fidelity simulations provide significant benefits, they often bypass these essential physical limitations. In this paper, we experiment with the Constrained Markov Decision Process (CMDP) framework instead of the conventional unconstrained RL for robotic applications. We perform a comparative study of different constrained policy optimization algorithms to identify suitable methods for practical implementation. Our robot experiments demonstrate the critical role of incorporating physical constraints, yielding successful sim-to-real transfers, and reducing operational errors on physical systems. The CMDP formulation streamlines the training process by separately handling constraints from rewards. Our findings underscore the potential of constrained RL for the effective development and deployment of learned controllers in robotics.

cs.RO↗
arXiv2023

Quantum computation of stopping power for inertial fusion target design

Stopping power is the rate at which a material absorbs the kinetic energy of a charged particle passing through it -- one of many properties needed over a wide range of thermodynamic conditions in modeling inertial fusion implosions. First-principles stopping calculations are classically challenging because they involve the dynamics of large electronic systems far from equilibrium, with accuracies that are particularly difficult to constrain and assess in the warm-dense conditions preceding ignition. Here, we describe a protocol for using a fault-tolerant quantum computer to calculate stopping power from a first-quantized representation of the electrons and projectile. Our approach builds upon the electronic structure block encodings of Su et al. [PRX Quantum 2, 040332 2021], adapting and optimizing those algorithms to estimate observables of interest from the non-Born-Oppenheimer dynamics of multiple particle species at finite temperature. Ultimately, we report logical qubit requirements and leading-order Toffoli costs for computing the stopping power of various projectile/target combinations relevant to interpreting and designing inertial fusion experiments. We estimate that scientifically interesting and classically intractable stopping power calculations can be quantum simulated with roughly the same number of logical qubits and about one hundred times more Toffoli gates than is required for state-of-the-art quantum simulations of industrially relevant molecules such as FeMoCo or P450.

quant-ph↗
arXiv2023

Response properties in phaseless auxiliary field quantum Monte Carlo

We present a method for calculating first-order response properties in phaseless auxiliary field quantum Monte Carlo (AFQMC) through the application of automatic differentiation (AD). Biases and statistical efficiency of the resulting estimators are discussed. Our approach demonstrates that AD enables the calculation of reduced density matrices (RDMs) with the same computational cost scaling as energy calculations, accompanied by a cost prefactor of less than four in our numerical calculations. We investigate the role of self-consistency and trial orbital choice in property calculations.

physics.chem-ph↗
arXiv2023

Non-Abelian braiding of graph vertices in a superconducting processor

Indistinguishability of particles is a fundamental principle of quantum mechanics. For all elementary and quasiparticles observed to date - including fermions, bosons, and Abelian anyons - this principle guarantees that the braiding of identical particles leaves the system unchanged. However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions. Hence, it can change the observables of the system without violating the principle of indistinguishability. Despite the well developed mathematical description of non-Abelian anyons and numerous theoretical proposals, the experimental observation of their exchange statistics has remained elusive for decades. Controllable many-body quantum states generated on quantum processors offer another path for exploring these fundamental phenomena. While efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasi-particles, superconducting quantum processors allow for directly manipulating the many-body wavefunction via unitary gates. Building on predictions that stabilizer codes can host projective non-Abelian Ising anyons, we implement a generalized stabilizer code and unitary protocol to create and braid them. This allows us to experimentally verify the fusion rules of the anyons and braid them to realize their statistics. We then study the prospect of employing the anyons for quantum computation and utilize braiding to create an entangled state of anyons encoding three logical qubits. Our work provides new insights about non-Abelian braiding and - through the future inclusion of error correction to achieve topological protection - could open a path toward fault-tolerant quantum computing.

quant-ph↗
arXiv2023

Seeing Through the Grass: Semantic Pointcloud Filter for Support Surface Learning

Mobile ground robots require perceiving and understanding their surrounding support surface to move around autonomously and safely. The support surface is commonly estimated based on exteroceptive depth measurements, e.g., from LiDARs. However, the measured depth fails to align with the true support surface in the presence of high grass or other penetrable vegetation. In this work, we present the Semantic Pointcloud Filter (SPF), a Convolutional Neural Network (CNN) that learns to adjust LiDAR measurements to align with the underlying support surface. The SPF is trained in a semi-self-supervised manner and takes as an input a LiDAR pointcloud and RGB image. The network predicts a binary segmentation mask that identifies the specific points requiring adjustment, along with estimating their corresponding depth values. To train the segmentation task, 300 distinct images are manually labeled into rigid and non-rigid terrain. The depth estimation task is trained in a self-supervised manner by utilizing the future footholds of the robot to estimate the support surface based on a Gaussian process. Our method can correctly adjust the support surface prior to interacting with the terrain and is extensively tested on the quadruped robot ANYmal. We show the qualitative benefits of SPF in natural environments for elevation mapping and traversability estimation compared to using raw sensor measurements and existing smoothing methods. Quantitative analysis is performed in various natural environments, and an improvement by 48% RMSE is achieved within a meadow terrain.

cs.RO↗
arXiv2023

Even Faster Exact Exchange for Solids via Tensor Hypercontraction

Hybrid density functional theory (DFT) remains intractable for large periodic systems due to the demanding computational cost of exact exchange. We apply the tensor hypercontraction (THC) (or interpolative separable density fitting) approximation to periodic hybrid DFT calculations with Gaussian-type orbitals. This is done to lower the computational scaling with respect to the number of basis functions ($N$), and $\mathbf k$-points ($N_k$). Additionally, we propose an algorithm to fit only occupied orbital products via THC (i.e. a set of points, $N_\text{ISDF}$) to further reduce computation time and memory usage. This algorithm has linear scaling cost with $\mathbf k$-points, no explicit dependence of $N_\text{ISDF}$ on basis set size, and overall cubic scaling with unit cell size. Significant speedups and reduced memory usage may be obtained for moderately sized systems, with additional gains for large systems. Adequate accuracy can be obtained using THC-oo-K for self-consistent calculations. We perform illustrative hybrid density function theory calculations on the benzene crystal in the basis set and thermodynamic limits to highlight the utility of this algorithm.

physics.comp-ph↗
arXiv2023

Microscopic Theory of Multimode Polariton Dispersion in Multilayered Materials

We develop a microscopic theory for the multimode polariton dispersion in materials coupled to cavity radiation modes. Starting from a microscopic light-matter Hamiltonian, we devise a general strategy for obtaining simple matrix models of polariton dispersion curves based on the structure and spatial location of multi-layered 2D materials inside the optical cavity. Our theory exposes the connections between seemingly distinct models that have been employed in the literature and resolves an ambiguity that has arisen concerning the experimental description of the polaritonic band structure. We demonstrate the applicability of our theoretical formalism by fabricating various geometries of multi-layered perovskite materials coupled to cavities and demonstrating that our theoretical predictions agree with the experimental results presented here.

cond-mat.mtrl-sci↗
arXiv2023

Fault-tolerant quantum simulation of materials using Bloch orbitals

The simulation of chemistry is among the most promising applications of quantum computing. However, most prior work exploring algorithms for block-encoding, time-evolving, and sampling in the eigenbasis of electronic structure Hamiltonians has either focused on modeling finite-sized systems, or has required a large number of plane wave basis functions. In this work, we extend methods for quantum simulation with Bloch orbitals constructed from symmetry-adapted atom-centered orbitals so that one can model periodic \textit{ab initio} Hamiltonians using only a modest number of basis functions. We focus on adapting existing algorithms based on combining qubitization with tensor factorizations of the Coulomb operator. Significant modifications of those algorithms are required to obtain an asymptotic speedup leveraging translational (or, more broadly, Abelian) symmetries. We implement block encodings using known tensor factorizations and a new Bloch orbital form of tensor hypercontraction. Finally, we estimate the resources required to deploy our algorithms to classically challenging model materials relevant to the chemistry of Lithium Nickel Oxide battery cathodes within the surface code.

quant-ph↗
arXiv2023

Learning-based Design and Control for Quadrupedal Robots with Parallel-Elastic Actuators

Parallel-elastic joints can improve the efficiency and strength of robots by assisting the actuators with additional torques. For these benefits to be realized, a spring needs to be carefully designed. However, designing robots is an iterative and tedious process, often relying on intuition and heuristics. We introduce a design optimization framework that allows us to co-optimize a parallel elastic knee joint and locomotion controller for quadrupedal robots with minimal human intuition. We design a parallel elastic joint and optimize its parameters with respect to the efficiency in a model-free fashion. In the first step, we train a design-conditioned policy using model-free Reinforcement Learning, capable of controlling the quadruped in the predefined range of design parameters. Afterwards, we use Bayesian Optimization to find the best design using the policy. We use this framework to optimize the parallel-elastic spring parameters for the knee of our quadrupedal robot ANYmal together with the optimal controller. We evaluate the optimized design and controller in real-world experiments over various terrains. Our results show that the new system improves the torque-square efficiency of the robot by 33% compared to the baseline and reduces maximum joint torque by 30% without compromising tracking performance. The improved design resulted in 11% longer operation time on flat terrain.

cs.RO↗
arXiv2023

Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods

Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory, but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree-Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the $k$-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage.

quant-ph↗
arXiv2022

Formation of robust bound states of interacting microwave photons

Systems of correlated particles appear in many fields of science and represent some of the most intractable puzzles in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles. The lack of general solutions for the 3-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multi-particle bound states. In a ring of 24 superconducting qubits, we develop a high fidelity parameterizable fSim gate that we use to implement the periodic quantum circuit of the spin-1/2 XXZ model, an archetypal model of interaction. By placing microwave photons in adjacent qubit sites, we study the propagation of these excitations and observe their bound nature for up to 5 photons. We devise a phase sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the common wisdom that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit.

quant-ph↗
arXiv2022

Noise-resilient Edge Modes on a Chain of Superconducting Qubits

Inherent symmetry of a quantum system may protect its otherwise fragile states. Leveraging such protection requires testing its robustness against uncontrolled environmental interactions. Using 47 superconducting qubits, we implement the one-dimensional kicked Ising model which exhibits non-local Majorana edge modes (MEMs) with $\mathbb{Z}_2$ parity symmetry. Remarkably, we find that any multi-qubit Pauli operator overlapping with the MEMs exhibits a uniform late-time decay rate comparable to single-qubit relaxation rates, irrespective of its size or composition. This characteristic allows us to accurately reconstruct the exponentially localized spatial profiles of the MEMs. Furthermore, the MEMs are found to be resilient against certain symmetry-breaking noise owing to a prethermalization mechanism. Our work elucidates the complex interplay between noise and symmetry-protected edge modes in a solid-state environment.

quant-ph↗