arXiv subjects

En-Jui Kuo

Publications and source records attributed to En-Jui Kuo.

52 records · Page 3Linked to original sources

arXiv2023

Energy diffusion in weakly interacting chains with fermionic dissipation-assisted operator evolution

Interacting lattice Hamiltonians at high temperature generically give rise to energy transport governed by the classical diffusion equation; however, predicting the rate of diffusion requires numerical simulation of the microscopic quantum dynamics. For the purpose of predicting such transport properties, computational time evolution methods must be paired with schemes to control the growth of entanglement to tractably simulate for sufficiently long times. One such truncation scheme -- dissipation-assisted operator evolution (DAOE) -- controls entanglement by damping out components of operators with large Pauli weight. In this paper, we generalize DAOE to treat fermionic systems. Our method instead damps out components of operators with large fermionic weight. We investigate the performance of DAOE, the new fermionic DAOE (FDAOE), and another simulation method, density matrix truncation (DMT), in simulating energy transport in an interacting one-dimensional Majorana chain. The chain is found to have a diffusion coefficient scaling like interaction strength to the fourth power, contrary to naive expectations based on Fermi's Golden rule -- but consistent with recent predictions based on the theory of \emph{weak integrability breaking}. In the weak interaction regime where the fermionic nature of the system is most relevant, FDAOE is found to simulate the system more efficiently than DAOE.

cond-mat.str-el↗

arXiv2023

Qubit-oscillator concatenated codes: decoding formalism & code comparison

Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given there are several bosonic codes and concatenation schemes to choose from, including the recently discovered GKP-stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020)}] that allow protection of a logical bosonic mode from fluctuations of the mode's conjugate variables. We develop efficient maximum-likelihood decoders for and analyze the performance of three different concatenations of codes taken from the following set: qubit stabilizer codes, analog/Gaussian stabilizer codes, GKP codes, and GKP-stabilizer codes. We benchmark decoder performance against additive Gaussian white noise, corroborating our numerics with analytical calculations. We observe that the concatenation involving GKP-stabilizer codes outperforms the more conventional concatenation of a qubit stabilizer code with a GKP code in some cases. We also propose a GKP-stabilizer code that suppresses fluctuations in both conjugate variables without extra quadrature squeezing, and formulate qudit versions of GKP-stabilizer codes.

quant-ph↗

arXiv2023

The Computational Complexity of Quantum Determinants

In this work, we study the computational complexity of quantum determinants, a $q$-deformation of matrix permanents: Given a complex number $q$ on the unit circle in the complex plane and an $n\times n$ matrix $X$, the $q$-permanent of $X$ is defined as $$\mathrm{Per}_q(X) = \sum_{σ\in S_n} q^{\ell(σ)}X_{1,σ(1)}\ldots X_{n,σ(n)},$$ where $\ell(σ)$ is the inversion number of permutation $σ$ in the symmetric group $S_n$ on $n$ elements. The function family generalizes determinant and permanent, which correspond to the cases $q=-1$ and $q=1$ respectively. For worst-case hardness, by Liouville's approximation theorem and facts from algebraic number theory, we show that for primitive $m$-th root of unity $q$ for odd prime power $m=p^k$, exactly computing $q$-permanent is $\mathsf{Mod}_p\mathsf{P}$-hard. This implies that an efficient algorithm for computing $q$-permanent results in a collapse of the polynomial hierarchy. Next, we show that computing $q$-permanent can be achieved using an oracle that approximates to within a polynomial multiplicative error and a membership oracle for a finite set of algebraic integers. From this, an efficient approximation algorithm would also imply a collapse of the polynomial hierarchy. By random self-reducibility, computing $q$-permanent remains to be hard for a wide range of distributions satisfying a property called the strong autocorrelation property. Specifically, this is proved via a reduction from $1$-permanent to $q$-permanent for $O(1/n^2)$ points $z$ on the unit circle. Since the family of permanent functions shares common algebraic structure, various techniques developed for the hardness of permanent can be generalized to $q$-permanents.

cs.CC↗

arXiv2022

Quantum state tomography via non-convex Riemannian gradient descent

The recovery of an unknown density matrix of large size requires huge computational resources. The recent Factored Gradient Descent (FGD) algorithm and its variants achieved state-of-the-art performance since they could mitigate the dimensionality barrier by utilizing some of the underlying structures of the density matrix. Despite their theoretical guarantee of a linear convergence rate, the convergence in practical scenarios is still slow because the contracting factor of the FGD algorithms depends on the condition number $κ$ of the ground truth state. Consequently, the total number of iterations can be as large as $O(\sqrtκ\ln(\frac{1}{\varepsilon}))$ to achieve the estimation error $\varepsilon$. In this work, we derive a quantum state tomography scheme that improves the dependence on $κ$ to the logarithmic scale; namely, our algorithm could achieve the approximation error $\varepsilon$ in $O(\ln(\frac{1}{κ\varepsilon}))$ steps. The improvement comes from the application of the non-convex Riemannian gradient descent (RGD). The contracting factor in our approach is thus a universal constant that is independent of the given state. Our theoretical results of extremely fast convergence and nearly optimal error bounds are corroborated by numerical results.

quant-ph↗

arXiv2022

Accurate and Efficient Quantum Computations of Molecular Properties Using Daubechies Wavelet Molecular Orbitals: A Benchmark Study against Experimental Data

Although quantum computation (QC) is regarded as a promising numerical method for computational quantum chemistry, current applications of quantum-chemistry calculations on quantum computers are limited to small molecules. This limitation can be ascribed to technical problems in building and manipulating more qubits and the associated complicated operations of quantum gates in a quantum circuit when the size of the molecular system becomes large. As a result, reducing the number of required qubits is necessary to make QC practical. Currently, the minimal STO-3G basis set is commonly used in benchmark studies because it requires the minimum number of spin orbitals. Nonetheless, the accuracy of using STO-3G is generally low and thus cannot provide useful predictions. We propose to adopt Daubechies wavelet functions as an accurate and efficient method for QCs of molecular electronic properties. We demonstrate that a minimal basis set constructed from Daubechies wavelet basis can yield accurate results through a better description of the molecular Hamiltonian, while keeping the number of spin orbitals minimal. With the improved Hamiltonian through Daubechies wavelets, we calculate vibrational frequencies for H$_2$ and LiH using quantum-computing algorithm to show that the results are in excellent agreement with experimental data. As a result, we achieve quantum calculations in which accuracy is comparable with that of the full configuration interaction calculation using the cc-pVDZ basis set, whereas the computational cost is the same as that of a STO-3G calculation. Thus, our work provides a more efficient and accurate representation of the molecular Hamiltonian for efficient QCs of molecular systems, and for the first time demonstrates that predictions in agreement with experimental measurements are possible to be achieved with quantum resources available in near-term quantum computers.

quant-ph↗

arXiv2022

Boson Sampling for Generalized Bosons

We introduce the notion of "generalized bosons" whose exchange statistics resemble those of bosons, but the local bosonic commutator $[a_i,a_i^\dagger]=1$ is replaced by an arbitrary single-mode operator that is diagonal in the generalized Fock basis. Examples of generalized bosons include boson pairs and spins. We consider the analogue of the boson sampling task for these particles and observe that its output probabilities are still given by permanents, so that the results regarding hardness of sampling directly carry over. Finally, we propose implementations of generalized boson sampling in circuit-QED and ion-trap platforms.

quant-ph↗

arXiv2022

Path sampling of recurrent neural networks by incorporating known physics

Recurrent neural networks have seen widespread use in modeling dynamical systems in varied domains such as weather prediction, text prediction and several others. Often one wishes to supplement the experimentally observed dynamics with prior knowledge or intuition about the system. While the recurrent nature of these networks allows them to model arbitrarily long memories in the time series used in training, it makes it harder to impose prior knowledge or intuition through generic constraints. In this work, we present a path sampling approach based on principle of Maximum Caliber that allows us to include generic thermodynamic or kinetic constraints into recurrent neural networks. We show the method here for a widely used type of recurrent neural network known as long short-term memory network in the context of supplementing time series collected from different application domains. These include classical Molecular Dynamics of a protein and Monte Carlo simulations of an open quantum system continuously losing photons to the environment and displaying Rabi oscillations. Our method can be easily generalized to other generative artificial intelligence models and to generic time series in different areas of physical and social sciences, where one wishes to supplement limited data with intuition or theory based corrections.

cond-mat.dis-nn↗

arXiv2022

Entanglement cost in topological stabilizer models at finite temperature

The notion of entanglement has been useful for characterizing universal properties of quantum phases of matter. From the perspective of quantum information theory, it is tempting to ask whether their entanglement structures possess any operational meanings, e.g., quantifying the cost of preparing an entangled system via free operations such as the local operations and classical communication (LOCC). While the answer is affirmative for pure states in that entanglement entropy coincides with entanglement cost, the case for mixed states is less understood. To this end, we study the entanglement cost required to prepare the thermal Gibbs states of certain many-body systems under positive-partial-transpose (PPT) preserving operations, a set of free operations that include LOCC. Specifically, we show that for the Gibbs states of $d$-dimensional toric code models for $d = 2, 3, 4$, the PPT entanglement cost exactly equals entanglement negativity, a measure of mixed-state entanglement that has been known to diagnose topological order at finite temperature.

quant-ph↗

arXiv2021

Unsupervised Learning of Symmetry Protected Topological Phase Transitions

Symmetry-protected topological (SPT) phases are short-range entangled phases of matter with a non-local order parameter which are preserved under a local symmetry group. Here, by using unsupervised learning algorithm, namely the diffusion maps, we demonstrate that can differentiate between symmetry broken phases and topologically ordered phases, and between non-trivial topological phases in different classes. In particular, we show that the phase transitions associated with these phases can be detected in different bosonic and fermionic models in one dimension. This includes the interacting SSH model, the AKLT model and its variants, and weakly interacting fermionic models. Our approach serves as an inexpensive computational method for detecting topological phases transitions associated with SPT systems which can be also applied to experimental data obtained from quantum simulators.

cond-mat.str-el↗

arXiv2021

Decoding conformal field theories: from supervised to unsupervised learning

We use machine learning to classify rational two-dimensional conformal field theories. We first use the energy spectra of these minimal models to train a supervised learning algorithm. We find that the machine is able to correctly predict the nature and the value of critical points of several strongly correlated spin models using only their energy spectra. This is in contrast to previous works that use machine learning to classify different phases of matter, but do not reveal the nature of the critical point between phases. Given that the ground-state entanglement Hamiltonian of certain topological phases of matter is also described by conformal field theories, we use supervised learning on Réyni entropies and find that the machine is able to identify which conformal field theory describes the entanglement Hamiltonian with only the lowest few Réyni entropies to a high degree of accuracy. Finally, using autoencoders, an unsupervised learning algorithm, we find a hidden variable that has a direct correlation with the central charge and discuss prospects for using machine learning to investigate other conformal field theories, including higher-dimensional ones. Our results highlight that machine learning can be used to find and characterize critical points and also hint at the intriguing possibility to use machine learning to learn about more complex conformal field theories.

cond-mat.str-el↗

arXiv2021

Quantum Architecture Search via Deep Reinforcement Learning

Recent advances in quantum computing have drawn considerable attention to building realistic application for and using quantum computers. However, designing a suitable quantum circuit architecture requires expert knowledge. For example, it is non-trivial to design a quantum gate sequence for generating a particular quantum state with as fewer gates as possible. We propose a quantum architecture search framework with the power of deep reinforcement learning (DRL) to address this challenge. In the proposed framework, the DRL agent can only access the Pauli-$X$, $Y$, $Z$ expectation values and a predefined set of quantum operations for learning the target quantum state, and is optimized by the advantage actor-critic (A2C) and proximal policy optimization (PPO) algorithms. We demonstrate a successful generation of quantum gate sequences for multi-qubit GHZ states without encoding any knowledge of quantum physics in the agent. The design of our framework is rather general and can be employed with other DRL architectures or optimization methods to study gate synthesis and compilation for many quantum states.

quant-ph↗

arXiv2020

Learning Molecular Dynamics with Simple Language Model built upon Long Short-Term Memory Neural Network

Recurrent neural networks (RNNs) have led to breakthroughs in natural language processing and speech recognition, wherein hundreds of millions of people use such tools on a daily basis through smartphones, email servers and other avenues. In this work, we show such RNNs, specifically Long Short-Term Memory (LSTM) neural networks can also be applied to capturing the temporal evolution of typical trajectories arising in chemical and biological physics. Specifically, we use a character-level language model based on LSTM. This learns a probabilistic model from 1-dimensional stochastic trajectories generated from molecular dynamics simulations of a higher dimensional system. We show that the model can not only capture the Boltzmann statistics of the system but it also reproduce kinetics at a large spectrum of timescales. We demonstrate how the embedding layer, introduced originally for representing the contextual meaning of words or characters, exhibits here a nontrivial connectivity between different metastable states in the underlying physical system. We demonstrate the reliability of our model and interpretations through different benchmark systems and a single molecule force spectroscopy trajectory for multi-state riboswitch. We anticipate that our work represents a stepping stone in the understanding and use of RNNs for modeling and predicting dynamics of complex stochastic molecular systems.

cond-mat.dis-nn↗

arXiv2020

Halperin states can produce any filling fractions

We study bilayer Fractional Quantum Hall State also known as Halperin state. We prove that for any filling fractions (positive rational numbers), there are infinite solutions that imply that infinite topological states are corresponding to any given filling fraction. Our results can apply to any charge vectors.

math-ph↗

arXiv2018

Towards Spinning Mellin Amplitudes

We construct the Mellin representation of four point conformal correlation function with external primary operators with arbitrary integer spacetime spins, and obtain a natural proposal for spinning Mellin amplitudes. By restricting to the exchange of symmetric traceless primaries, we generalize the Mellin transform for scalar case to introduce discrete Mellin variables for incorporating spin degrees of freedom. Based on the structures about spinning three and four point Witten diagrams, we also obtain a generalization of the Mack polynomial which can be regarded as a natural kinematical polynomial basis for computing spinning Mellin amplitudes using different choices of interaction vertices.

hep-th↗

arXiv2017

Anatomy of Geodesic Witten Diagrams

We revisit the so-called "Geodesic Witten Diagrams" (GWDs) \cite{ScalarGWD}, proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we explicitly consider three point GWDs which are natural building blocks of all possible four point GWDs, discuss their gluing procedure through integration over spectral parameter, and this leads us to a direct identification with the integral representation of CFT conformal partial waves. As a main application of this general construction, we consider the holographic dual of the conformal partial waves for external primary operators with spins. Moreover, we consider the closely related "split representation" for the bulk to bulk spinning propagator, to demonstrate how ordinary scalar Witten diagram with arbitrary spin exchange, can be systematically decomposed into scalar GWDs. We also discuss how to generalize to spinning cases.

hep-th↗

arXiv2015

Extremal RN/CFT in Both Hands Revisited

We study RN/CFT correspondence for four dimensional extremal Reissner-Nordstrom black hole. We uplift the 4d RN black hole to a 5d rotating black hole and make a geometric regularization of the 5d space-time. Both hands central charges are obtained correctly at the same time by Brown-Henneaux technique.

hep-th↗