arXiv subjects

Junyu Liu

Publications and source records attributed to Junyu Liu.

At least 127 records · Page 7Linked to original sources

arXiv2023

Fundamental causal bounds of quantum random access memories

Quantum devices should operate in adherence to quantum physics principles. Quantum random access memory (QRAM), a fundamental component of many essential quantum algorithms for tasks such as linear algebra, data search, and machine learning, is often proposed to offer $\mathcal{O}(\log N)$ circuit depth for $\mathcal{O}(N)$ data size, given $N$ qubits. However, this claim appears to breach the principle of relativity when dealing with a large number of qubits in quantum materials interacting locally. In our study we critically explore the intrinsic bounds of rapid quantum memories based on causality, employing the relativistic quantum field theory and Lieb-Robinson bounds in quantum many-body systems. In this paper, we consider a hardware-efficient QRAM design in hybrid quantum acoustic systems. Assuming clock cycle times of approximately $10^{-3}$ seconds and a lattice spacing of about 1 micrometer, we show that QRAM can accommodate up to $\mathcal{O}(10^7)$ logical qubits in 1 dimension, $\mathcal{O}(10^{15})$ to $\mathcal{O}(10^{20})$ in various 2D architectures, and $\mathcal{O}(10^{24})$ in 3 dimensions. We contend that this causality bound broadly applies to other quantum hardware systems. Our findings highlight the impact of fundamental quantum physics constraints on the long-term performance of quantum computing applications in data science and suggest potential quantum memory designs for performance enhancement.

quant-ph↗

arXiv2023

Analytic theory for the dynamics of wide quantum neural networks

Parameterized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on practical problems are heuristic in nature. In particular, the convergence rate for the training of quantum neural networks is not fully understood. Here, we analyze the dynamics of gradient descent for the training error of a class of variational quantum machine learning models. We define wide quantum neural networks as parameterized quantum circuits in the limit of a large number of qubits and variational parameters. We then find a simple analytic formula that captures the average behavior of their loss function and discuss the consequences of our findings. For example, for random quantum circuits, we predict and characterize an exponential decay of the residual training error as a function of the parameters of the system. We finally validate our analytic results with numerical experiments.

quant-ph↗

arXiv2023

Estimating the randomness of quantum circuit ensembles up to 50 qubits

Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any random unitaries has consequences on their complexity, expressibility, and trainability. To study this property of random circuits, we develop numerical protocols for estimating the frame potential, the distance between a given ensemble and the exact randomness. Our tensor-network-based algorithm has polynomial complexity for shallow circuits and is high-performing using CPU and GPU parallelism. We study 1. local and parallel random circuits to verify the linear growth in complexity as stated by the Brown-Susskind conjecture, and; 2. hardware-efficient ansätze to shed light on its expressibility and the barren plateau problem in the context of variational algorithms. Our work shows that large-scale tensor network simulations could provide important hints toward open problems in quantum information science.

quant-ph↗

arXiv2023

Symmetric Pruning in Quantum Neural Networks

Many fundamental properties of a quantum system are captured by its Hamiltonian and ground state. Despite the significance of ground states preparation (GSP), this task is classically intractable for large-scale Hamiltonians. Quantum neural networks (QNNs), which exert the power of modern quantum machines, have emerged as a leading protocol to conquer this issue. As such, how to enhance the performance of QNNs becomes a crucial topic in GSP. Empirical evidence showed that QNNs with handcraft symmetric ansatzes generally experience better trainability than those with asymmetric ansatzes, while theoretical explanations have not been explored. To fill this knowledge gap, here we propose the effective quantum neural tangent kernel (EQNTK) and connect this concept with over-parameterization theory to quantify the convergence of QNNs towards the global optima. We uncover that the advance of symmetric ansatzes attributes to their large EQNTK value with low effective dimension, which requests few parameters and quantum circuit depth to reach the over-parameterization regime permitting a benign loss landscape and fast convergence. Guided by EQNTK, we further devise a symmetric pruning (SP) scheme to automatically tailor a symmetric ansatz from an over-parameterized and asymmetric one to greatly improve the performance of QNNs when the explicit symmetry information of Hamiltonian is unavailable. Extensive numerical simulations are conducted to validate the analytical results of EQNTK and the effectiveness of SP.

quant-ph↗

arXiv2022

Towards a variational Jordan-Lee-Preskill quantum algorithm

Rapid developments of quantum information technology show promising opportunities for simulating quantum field theory in near-term quantum devices. In this work, we formulate the theory of (time-dependent) variational quantum simulation of the 1+1 dimensional $λϕ^4$ quantum field theory including encoding, state preparation, and time evolution, with several numerical simulation results. These algorithms could be understood as near-term variational quantum circuit (quantum neural network) analogs of the Jordan-Lee-Preskill algorithm, the basic algorithm for simulating quantum field theory using universal quantum devices. Besides, we highlight the advantages of encoding with harmonic oscillator basis based on the LSZ reduction formula and several computational efficiency such as when implementing a bosonic version of the unitary coupled cluster ansatz to prepare initial states. We also discuss how to circumvent the "spectral crowding" problem in the quantum field theory simulation and appraise our algorithm by both state and subspace fidelities.

quant-ph↗

arXiv2022

Embedding Learning in Hybrid Quantum-Classical Neural Networks

Quantum embedding learning is an important step in the application of quantum machine learning to classical data. In this paper we propose a quantum few-shot embedding learning paradigm, which learns embeddings useful for training downstream quantum machine learning tasks. Crucially, we identify the circuit bypass problem in hybrid neural networks, where learned classical parameters do not utilize the Hilbert space efficiently. We observe that the few-shot learned embeddings generalize to unseen classes and suffer less from the circuit bypass problem compared with other approaches.

quant-ph↗

arXiv2022

Quantum Computing Methods for Supply Chain Management

Quantum computing is expected to have transformative influences on many domains, but its practical deployments on industry problems are underexplored. We focus on applying quantum computing to operations management problems in industry, and in particular, supply chain management. Many problems in supply chain management involve large state and action spaces and pose computational challenges on classic computers. We develop a quantized policy iteration algorithm to solve an inventory control problem and demonstrative its effectiveness. We also discuss in-depth the hardware requirements and potential challenges on implementing this quantum algorithm in the near term. Our simulations and experiments are powered by \texttt{IBM Qiskit} and the \texttt{qBraid} system.

quant-ph↗

arXiv2022

Quantum Kerr Learning

Quantum machine learning is a rapidly evolving field of research that could facilitate important applications for quantum computing and also significantly impact data-driven sciences. In our work, based on various arguments from complexity theory and physics, we demonstrate that a single Kerr mode can provide some "quantum enhancements" when dealing with kernel-based methods. Using kernel properties, neural tangent kernel theory, first-order perturbation theory of the Kerr non-linearity, and non-perturbative numerical simulations, we show that quantum enhancements could happen in terms of convergence time and generalization error. Furthermore, we make explicit indications on how higher-dimensional input data could be considered. Finally, we propose an experimental protocol, that we call \emph{quantum Kerr learning}, based on circuit QED.

quant-ph↗

arXiv2022

Quantum Power Flows: From Theory to Practice

Climate change is becoming one of the greatest challenges to the sustainable development of modern society. Renewable energies with low density greatly complicate the online optimization and control processes, where modern advanced computational technologies, specifically quantum computing, have significant potential to help. In this paper, we discuss applications of quantum computing algorithms toward state-of-the-art smart grid problems. We suggest potential, exponential quantum speedup by the use of the Harrow-Hassidim-Lloyd (HHL) algorithms for sparse matrix inversions in power-flow problems. However, practical implementations of the algorithm are limited by the noise of quantum circuits, the hardness of realizations of quantum random access memories (QRAM), and the depth of the required quantum circuits. We benchmark the hardware and software requirements from the state-of-the-art power-flow algorithms, including QRAM requirements from hybrid phonon-transmon systems, and explicit gate counting used in HHL for explicit realizations. We also develop near-term algorithms of power flow by variational quantum circuits and implement real experiments for 6 qubits with a truncated version of power flows.

quant-ph↗

arXiv2022

Laziness, Barren Plateau, and Noise in Machine Learning

We define \emph{laziness} to describe a large suppression of variational parameter updates for neural networks, classical or quantum. In the quantum case, the suppression is exponential in the number of qubits for randomized variational quantum circuits. We discuss the difference between laziness and \emph{barren plateau} in quantum machine learning created by quantum physicists in \cite{mcclean2018barren} for the flatness of the loss function landscape during gradient descent. We address a novel theoretical understanding of those two phenomena in light of the theory of neural tangent kernels. For noiseless quantum circuits, without the measurement noise, the loss function landscape is complicated in the overparametrized regime with a large number of trainable variational angles. Instead, around a random starting point in optimization, there are large numbers of local minima that are good enough and could minimize the mean square loss function, where we still have quantum laziness, but we do not have barren plateaus. However, the complicated landscape is not visible within a limited number of iterations, and low precision in quantum control and quantum sensing. Moreover, we look at the effect of noises during optimization by assuming intuitive noise models, and show that variational quantum algorithms are noise-resilient in the overparametrization regime. Our work precisely reformulates the quantum barren plateau statement towards a precision statement and justifies the statement in certain noise models, injects new hope toward near-term variational quantum algorithms, and provides theoretical connections toward classical machine learning. Our paper provides conceptual perspectives about quantum barren plateaus, together with discussions about the gradient descent dynamics in \cite{together}.

cs.LG↗

arXiv2022

Geometry-Based Stochastic Probability Models for the LoS and NLoS Paths of A2G Channels under Urban Scenario

Path probability prediction is essential to describe the dynamic birth and death of propagation paths, and build the accurate channel model for air-to-ground (A2G) communications. The occurrence probability of each path is complex and time-variant due to fast changeable altitudes of UAVs and scattering environments. Considering the A2G channels under urban scenarios, this paper presents three novel stochastic probability models for the line-of-sight (LoS) path, ground specular (GS) path, and building-scattering (BS) path, respectively. By analyzing the geometric stochastic information of three-dimensional (3D) scattering environments, the proposed models are derived with respect to the width, height, and distribution of buildings. The effect of Fresnel zone and altitudes of transceivers are also taken into account. Simulation results show that the proposed LoS path probability model has good performance at different frequencies and altitudes, and is also consistent with existing models at the low or high altitude. Moreover, the proposed LoS and NLoS path probability models show good agreement with the ray-tracing (RT) simulation method.

eess.SP↗

arXiv2022

Quantum Simulation for High Energy Physics

It is for the first time that Quantum Simulation for High Energy Physics (HEP) is studied in the U.S. decadal particle-physics community planning, and in fact until recently, this was not considered a mainstream topic in the community. This fact speaks of a remarkable rate of growth of this subfield over the past few years, stimulated by the impressive advancements in Quantum Information Sciences (QIS) and associated technologies over the past decade, and the significant investment in this area by the government and private sectors in the U.S. and other countries. High-energy physicists have quickly identified problems of importance to our understanding of nature at the most fundamental level, from tiniest distances to cosmological extents, that are intractable with classical computers but may benefit from quantum advantage. They have initiated, and continue to carry out, a vigorous program in theory, algorithm, and hardware co-design for simulations of relevance to the HEP mission. This community whitepaper is an attempt to bring this exciting and yet challenging area of research to the spotlight, and to elaborate on what the promises, requirements, challenges, and potential solutions are over the next decade and beyond.

quant-ph↗

arXiv2022

Characterizing Differentially-Private Techniques in the Era of Internet-of-Vehicles

Recent developments of advanced Human-Vehicle Interactions rely on the concept Internet-of-Vehicles (IoV), to achieve large-scale communications and synchronizations of data in practice. The concept of IoV is highly similar to a distributed system, where each vehicle is considered as a node and all nodes are grouped with a centralized server. In this manner, the concerns of data privacy are significant since all vehicles collect, process and share personal statistics (e.g. multi-modal, driving statuses and etc.). Therefore, it's important to understand how modern privacy-preserving techniques suit for IoV. We present the most comprehensive study to characterize modern privacy-preserving techniques for IoV to date. We focus on Differential Privacy (DP), a representative set of mathematically-guaranteed mechanisms for both privacy-preserving processing and sharing on sensitive data. The purpose of our study is to demystify the tradeoffs of deploying DP techniques, in terms of service quality. We first characterize representative privacy-preserving processing mechanisms, enabled by advanced DP approaches. Then we perform a detailed study of an emerging in-vehicle, Deep-Neural-Network-driven application, and study the upsides and downsides of DP for diverse types of data streams. Our study obtains 11 key findings and we highlight FIVE most significant observations from our detailed characterizations. We conclude that there are a large volume of challenges and opportunities for future studies, by enabling privacy-preserving IoV with low overheads for service quality.

cs.CR↗

arXiv2022

HUT: Enabling High-UTility, Batched Queries under Differential Privacy Protection for Internet-of-Vehicles

The emerging trends of Internet-of-Vehicles (IoV) demand centralized servers to collect/process sensitive data with limited computational resources on a single vehicle. Such centralizations of sensitive data demand practical privacy protections. One widely-applied paradigm, Differential Privacy, can provide strong guarantees over sensitive data by adding noises. However, directly applying DP for IoV incurs significant challenges for data utility and effective protection. We observe that the key issue about DP-enabled protection in IoV lies in how to synergistically combine DP with special characteristics of IoV, whose query sequences are usually formed as unbalanced batches due to frequent interactions between centralized servers and edge vehicles. To this end, we propose HUT, a new algorithm to enable High UTility for DP-enabled protection in IoV. Our key insight is to leverage the inherent characteristics in IoV: the unbalanced batches. Our key idea is to aggregate local batches and apply Order Constraints, so that information loss from DP protection can be mitigated. We evaluate the effectiveness of HUT against the state-of-the-art DP protection mechanisms. The results show that HUT can provide much lower information loss by 95.69\% and simultaneously enable strong mathematically-guaranteed protection over sensitive data.

cs.CR↗

arXiv2022

BROOK Dataset: A Playground for Exploiting Data-Driven Techniques in Human-Vehicle Interactive Designs

Emerging Autonomous Vehicles (AV) breed great potentials to exploit data-driven techniques for adaptive and personalized Human-Vehicle Interactions. However, the lack of high-quality and rich data supports limits the opportunities to explore the design space of data-driven techniques, and validate the effectiveness of concrete mechanisms. Our goal is to initialize the efforts to deliver the building block for exploring data-driven Human-Vehicle Interaction designs. To this end, we present BROOK dataset, a multi-modal dataset with facial video records. We first brief our rationales to build BROOK dataset. Then, we elaborate how to build the current version of BROOK dataset via a year-long study, and give an overview of the dataset. Next, we present three example studies using BROOK to justify the applicability of BROOK dataset. We also identify key learning lessons from building BROOK dataset, and discuss about how BROOK dataset can foster an extensive amount of follow-up studies.

cs.HC↗

arXiv2021

Polyphonic Sound Event Detection Using Capsule Neural Network on Multi-Type-Multi-Scale Time-Frequency Representation

The challenges of polyphonic sound event detection (PSED) stem from the detection of multiple overlapping events in a time series. Recent efforts exploit Deep Neural Networks (DNNs) on Time-Frequency Representations (TFRs) of audio clips as model inputs to mitigate such issues. However, existing solutions often rely on a single type of TFR, which causes under-utilization of input features. To this end, we propose a novel PSED framework, which incorporates Multi-Type-Multi-Scale TFRs. Our key insight is that: TFRs, which are of different types or in different scales, can reveal acoustics patterns in a complementary manner, so that the overlapped events can be best extracted by combining different TFRs. Moreover, our framework design applies a novel approach, to adaptively fuse different models and TFRs symbiotically. Hence, the overall performance can be significantly improved. We quantitatively examine the benefits of our framework by using Capsule Neural Networks, a state-of-the-art approach for PSED. The experimental results show that our method achieves a reduction of 7\% in error rate compared with the state-of-the-art solutions on the TUT-SED 2016 dataset.

cs.SD↗

arXiv2021

Bootstrapping Heisenberg Magnets and their Cubic Instability

We study the critical $O(3)$ model using the numerical conformal bootstrap. In particular, we use a recently developed cutting-surface algorithm to efficiently map out the allowed space of CFT data from correlators involving the leading $O(3)$ singlet $s$, vector $ϕ$, and rank-2 symmetric tensor $t$. We determine their scaling dimensions to be $(Δ_{s}, Δ_ϕ, Δ_{t}) = (0.518942(51), 1.59489(59), 1.20954(23))$, and also bound various OPE coefficients. We additionally introduce a new "tip-finding" algorithm to compute an upper bound on the leading rank-4 symmetric tensor $t_4$, which we find to be relevant with $Δ_{t_4} < 2.99056$. The conformal bootstrap thus provides a numerical proof that systems described by the critical $O(3)$ model, such as classical Heisenberg ferromagnets at the Curie transition, are unstable to cubic anisotropy.

hep-th↗

arXiv2021

Representation Learning via Quantum Neural Tangent Kernels

Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks. Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear. Here we discuss these problems, analyzing variational quantum circuits using the theory of neural tangent kernels. We define quantum neural tangent kernels, and derive dynamical equations for their associated loss function in optimization and learning tasks. We analytically solve the dynamics in the frozen limit, or lazy training regime, where variational angles change slowly and a linear perturbation is good enough. We extend the analysis to a dynamical setting, including quadratic corrections in the variational angles. We then consider hybrid quantum-classical architecture and define a large-width limit for hybrid kernels, showing that a hybrid quantum-classical neural network can be approximately Gaussian. The results presented here show limits for which analytical understandings of the training dynamics for variational quantum circuits, used for quantum machine learning and optimization problems, are possible. These analytical results are supported by numerical simulations of quantum machine learning experiments.

quant-ph↗