arXiv subjects

Min-Hsiu Hsieh

Publications and source records attributed to Min-Hsiu Hsieh.

At least 109 records · Page 6Linked to original sources

arXiv2022

Quantum circuit architecture search for variational quantum algorithms

Variational quantum algorithms (VQAs) are expected to be a path to quantum advantages on noisy intermediate-scale quantum devices. However, both empirical and theoretical results exhibit that the deployed ansatz heavily affects the performance of VQAs such that an ansatz with a larger number of quantum gates enables a stronger expressivity, while the accumulated noise may render a poor trainability. To maximally improve the robustness and trainability of VQAs, here we devise a resource and runtime efficient scheme termed quantum architecture search (QAS). In particular, given a learning task, QAS automatically seeks a near-optimal ansatz (i.e., circuit architecture) to balance benefits and side-effects brought by adding more noisy quantum gates to achieve a good performance. We implement QAS on both the numerical simulator and real quantum hardware, via the IBM cloud, to accomplish data classification and quantum chemistry tasks. In the problems studied, numerical and experimental results show that QAS can not only alleviate the influence of quantum noise and barren plateaus, but also outperforms VQAs with pre-selected ansatze.

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arXiv2022

A Grover-search Based Quantum Learning Scheme for Classification

The hybrid quantum-classical learning scheme provides a prominent way to achieve quantum advantages on near-term quantum devices. A concrete example towards this goal is the quantum neural network (QNN), which has been developed to accomplish various supervised learning tasks such as classification and regression. However, there are two central issues that remain obscure when QNN is exploited to accomplish classification tasks. First, a quantum classifier that can well balance the computational cost such as the number of measurements and the learning performance is unexplored. Second, it is unclear whether quantum classifiers can be applied to solve certain problems that outperform their classical counterparts. Here we devise a Grover-search based quantum learning scheme (GBLS) to address the above two issues. Notably, most existing QNN-based quantum classifiers can be seamlessly embedded into the proposed scheme. The key insight behind our proposal is reformulating the classification tasks as the search problem. Numerical simulations exhibit that GBLS can achieve comparable performance with other quantum classifiers under various noise settings, while the required number of measurements is dramatically reduced. We further demonstrate a potential quantum advantage of GBLS over classical classifiers in the measure of query complexity. Our work provides guidance to develop advanced quantum classifiers on near-term quantum devices and opens up an avenue to explore potential quantum advantages in various classification tasks.

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arXiv2022

Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms

Many quantum algorithms that claim speed-up over their classical counterparts only generate quantum states as solutions instead of their final classical description. The additional step to decode quantum states into classical vectors normally will destroy the quantum advantage in most scenarios because all existing tomographic methods require runtime that is polynomial with respect to the state dimension. In this work, we present an efficient read-out protocol that yields the classical vector form of the generated state, so it will achieve the end-to-end advantage for those quantum algorithms. Our protocol suits the case that the output state lies in the row space of the input matrix, of rank $r$, that is stored in the quantum random access memory. The quantum resources for decoding the state in $\ell^2$ norm with $ε$ error require $\poly(r,1/ε)$ copies of the output state and $\poly(r, κ^r,1/ε)$ queries to the input oracles, where $κ$ is the condition number of the input matrix. With our read-out protocol, we completely characterise the end-to-end resources for quantum linear equation solvers and quantum singular value decomposition. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure, which we believe, will be of independent interest.

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arXiv2022

Matrix Infinitely Divisible Series: Tail Inequalities and Their Applications

In this paper, we study tail inequalities of the largest eigenvalue of a matrix infinitely divisible (i.d.) series, which is a finite sum of fixed matrices weighted by i.d. random variables. We obtain several types of tail inequalities, including Bennett-type and Bernstein-type inequalities. This allows us to further bound the expectation of the spectral norm of a matrix i.d. series. Moreover, by developing a new lower-bound function for $Q(s)=(s+1)\log(s+1)-s$ that appears in the Bennett-type inequality, we derive a tighter tail inequality of the largest eigenvalue of the matrix i.d. series than the Bernstein-type inequality when the matrix dimension is high. The resulting lower-bound function is of independent interest and can improve any Bennett-type concentration inequality that involves the function $Q(s)$. The class of i.d. probability distributions is large and includes Gaussian and Poisson distributions, among many others. Therefore, our results encompass the existing work \cite{tropp2012user} on matrix Gaussian series as a special case. Lastly, we show that the tail inequalities of a matrix i.d. series have applications in several optimization problems including the chance constrained optimization problem and the quadratic optimization problem with orthogonality constraints. In addition, we also use the resulting tail bounds to show that random matrices constructed from i.d. random variables satisfy the restricted isometry property (RIP) when it acts as a measurement matrix in compressed sensing.

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arXiv2022

Quantum Differentially Private Sparse Regression Learning

The eligibility of various advanced quantum algorithms will be questioned if they can not guarantee privacy. To fill this knowledge gap, here we devise an efficient quantum differentially private (QDP) Lasso estimator to solve sparse regression tasks. Concretely, given $N$ $d$-dimensional data points with $N\ll d$, we first prove that the optimal classical and quantum non-private Lasso requires $Ω(N+d)$ and $Ω(\sqrt{N}+\sqrt{d})$ runtime, respectively. We next prove that the runtime cost of QDP Lasso is \textit{dimension independent}, i.e., $O(N^{5/2})$, which implies that the QDP Lasso can be faster than both the optimal classical and quantum non-private Lasso. Last, we exhibit that the QDP Lasso attains a near-optimal utility bound $\tilde{O}(N^{-2/3})$ with privacy guarantees and discuss the chance to realize it on near-term quantum chips with advantages.

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arXiv2022

One-Shot Hybrid State Redistribution

We consider state redistribution of a "hybrid" information source that has both classical and quantum components. The sender transmits classical and quantum information at the same time to the receiver, in the presence of classical and quantum side information both at the sender and at the decoder. The available resources are shared entanglement, and noiseless classical and quantum communication channels. We derive one-shot direct and converse bounds for these three resources, represented in terms of the smooth conditional entropies of the source state. Various coding theorems for two-party source coding problems are systematically obtained by reduction from our results, including the ones that have not been addressed in previous literature.

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arXiv2022

Unentangled quantum reinforcement learning agents in the OpenAI Gym

Classical reinforcement learning (RL) has generated excellent results in different regions; however, its sample inefficiency remains a critical issue. In this paper, we provide concrete numerical evidence that the sample efficiency (the speed of convergence) of quantum RL could be better than that of classical RL, and for achieving comparable learning performance, quantum RL could use much (at least one order of magnitude) fewer trainable parameters than classical RL. Specifically, we employ the popular benchmarking environments of RL in the OpenAI Gym, and show that our quantum RL agent converges faster than classical fully-connected neural networks (FCNs) in the tasks of CartPole and Acrobot under the same optimization process. We also successfully train the first quantum RL agent that can complete the task of LunarLander in the OpenAI Gym. Our quantum RL agent only requires a single-qubit-based variational quantum circuit without entangling gates, followed by a classical neural network (NN) to post-process the measurement output. Finally, we could accomplish the aforementioned tasks on the real IBM quantum machines. To the best of our knowledge, none of the earlier quantum RL agents could do that.

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arXiv2022

Good quantum LDPC codes with linear time decoder from lossless expanders

Quantum low-density parity-check (qLDPC) codes are quantum stabilizer codes where each stabilizer acts on a constant number of qubits and each qubit is acted on by a constant number of stabilizers. We study qLDPC codes constructed from balanced products and lossless expanders. We found that assuming the existence of 2-sided lossless expander graphs with free group action, the resulting qLDPC codes have constant rate, linear distance, and linear time decoders.

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arXiv2022

Quantum sensing on magnetic field inspired by Avian compass

Magnetic measurement can be performed by various sensors, such as SQUID and Giant Magnetoresistance. This device can achieve high accuracy while losing efficiency and convenience. The model of biological magnetic sensing in avian proposes a radical pair response to the external field on the FLY results in regulating animal behaviour. Inspired by the radical pair system found in biological system, the effect of intra-radical coupling and the initial condition is studied in this simplified radical pair model as the quantum advantage results from entanglement and superposition are investigated in metrology. To identify the sensing benefit from the cooperation between the radical pairs, the inter-radical coupling is considered. We find the intra-radical coupling determines the sensing regime while the coupled radical pair system enables a new sensing scheme that provides a more general and flexible way for magnetic sensing in a broader range through a easier manipulation to the system.

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arXiv2022

Entanglement-assisted concatenated quantum codes

Entanglement-assisted concatenated quantum codes (EACQCs), constructed by concatenating two quantum codes, are proposed. These EACQCs show several advantages over the standard concatenated quantum codes (CQCs). Several families of EACQCs that, unlike standard CQCs, can beat the nondegenerate Hamming bound for entanglement-assisted quantum error correction codes (EAQECCs) are derived. Further, a number of EACQCs with better parameters than the best known standard quantum error correction codes (QECCs) and EAQECCs are also derived. In particular, several catalytic EACQCs with better parameters than the best known QECCs of the same length and net transmission are constructed. Furthermore, each catalytic EACQC consumes only one or two ebits. It is also shown that EACQCs make entanglement-assisted quantum communication possible even if the ebits are noisy. Finally, it is shown that EACQCs can outperform CQCs in entanglement fidelity over depolarizing channels if the ebits are less noisy than the qubits. Moreover, the threshold error probability of EACQCs is larger than that of CQCs when the error probability of ebits is sufficiently lower than that of qubits. Therefore EACQCs are not only competitive in quantum communication but also applicable in fault-tolerant quantum computation.

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arXiv2022

$c^3$-Locally Testable Codes from Lossless Expanders

A locally testable code (LTC) is an error correcting code with a property tester. The tester tests if a word is codeword by reading constant random bits and rejects the word with probability proportional to the distance from the word to the closest codeword. An important open question until recently is whether there exist $c^3$-LTCs which are LTCs with constant rate, constant relative distance and constant locality. In this work, we construct a new LTC family using 1-sided lossless expanders and balanced products.

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arXiv2022

Quantum circuit architecture search on a superconducting processor

Variational quantum algorithms (VQAs) have shown strong evidences to gain provable computational advantages for diverse fields such as finance, machine learning, and chemistry. However, the heuristic ansatz exploited in modern VQAs is incapable of balancing the tradeoff between expressivity and trainability, which may lead to the degraded performance when executed on the noisy intermediate-scale quantum (NISQ) machines. To address this issue, here we demonstrate the first proof-of-principle experiment of applying an efficient automatic ansatz design technique, i.e., quantum architecture search (QAS), to enhance VQAs on an 8-qubit superconducting quantum processor. In particular, we apply QAS to tailor the hardware-efficient ansatz towards classification tasks. Compared with the heuristic ansatze, the ansatz designed by QAS improves test accuracy from 31% to 98%. We further explain this superior performance by visualizing the loss landscape and analyzing effective parameters of all ansatze. Our work provides concrete guidance for developing variable ansatze to tackle various large-scale quantum learning problems with advantages.

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arXiv2021

Randomized benchmarking for non-Markovian noise

Estimating the features of noise is the first step in a chain of protocols that will someday lead to fault tolerant quantum computers. The randomized benchmarking (RB) protocol is designed with this exact mindset, estimating the average strength of noise in a quantum processor with relative ease in practice. However, RB, along with most other benchmarking and characterization methods, is limited in scope because it assumes that the noise is temporally uncorrelated (Markovian), which is increasingly evident not to be the case. Here, we combine the RB protocol with a recent framework describing non-Markovian quantum phenomena to derive a general analytical expression of the average sequence fidelity (ASF) for non-Markovian RB with the Clifford group. We show that one can identify non-Markovian features of the noise directly from the ASF through its deviations from the Markovian case, proposing a set of methods to collectively estimate these deviations, non-Markovian memory time-scales, and diagnose (in)coherence of non-Markovian noise in an RB experiment. Finally, we demonstrate the efficacy of our proposal by means of several proof-of-principle examples. Our methods are directly implementable and pave the pathway to better understanding correlated noise in quantum processors.

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arXiv2021

Sublinear quantum algorithms for estimating von Neumann entropy

Entropy is a fundamental property of both classical and quantum systems, spanning myriad theoretical and practical applications in physics and computer science. We study the problem of obtaining estimates to within a multiplicative factor $γ>1$ of the Shannon entropy of probability distributions and the von Neumann entropy of mixed quantum states. Our main results are: $\quad\bullet$ an $\widetilde{\mathcal{O}}\left( n^{\frac{1+η}{2γ^2}}\right)$-query quantum algorithm that outputs a $γ$-multiplicative approximation of the Shannon entropy $H(\mathbf{p})$ of a classical probability distribution $\mathbf{p} = (p_1,\ldots,p_n)$; $\quad\bullet$ an $\widetilde{\mathcal{O}}\left( n^{\frac12+\frac{1+η}{2γ^2}}\right)$-query quantum algorithm that outputs a $γ$-multiplicative approximation of the von Neumann entropy $S(ρ)$ of a density matrix $ρ\in\mathbb{C}^{n\times n}$. In both cases, the input is assumed to have entropy bounded away from zero by a quantity determined by the parameter $η>0$, since, as we prove, no polynomial query algorithm can multiplicatively approximate the entropy of distributions with arbitrarily low entropy. In addition, we provide $Ω\left(n^{\frac{1}{3γ^2}}\right)$ lower bounds on the query complexity of $γ$-multiplicative estimation of Shannon and von Neumann entropies. We work with the quantum purified query access model, which can handle both classical probability distributions and mixed quantum states, and is the most general input model considered in the literature.

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arXiv2021

Experimental Quantum Generative Adversarial Networks for Image Generation

Quantum machine learning is expected to be one of the first practical applications of near-term quantum devices. Pioneer theoretical works suggest that quantum generative adversarial networks (GANs) may exhibit a potential exponential advantage over classical GANs, thus attracting widespread attention. However, it remains elusive whether quantum GANs implemented on near-term quantum devices can actually solve real-world learning tasks. Here, we devise a flexible quantum GAN scheme to narrow this knowledge gap, which could accomplish image generation with arbitrarily high-dimensional features, and could also take advantage of quantum superposition to train multiple examples in parallel. For the first time, we experimentally achieve the learning and generation of real-world hand-written digit images on a superconducting quantum processor. Moreover, we utilize a gray-scale bar dataset to exhibit the competitive performance between quantum GANs and the classical GANs based on multilayer perceptron and convolutional neural network architectures, respectively, benchmarked by the Fréchet Distance score. Our work provides guidance for developing advanced quantum generative models on near-term quantum devices and opens up an avenue for exploring quantum advantages in various GAN-related learning tasks.

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arXiv2021

Hierarchy of quantum operations in manipulating coherence and entanglement

Quantum resource theory under different classes of quantum operations advances multiperspective understandings of inherent quantum-mechanical properties, such as quantum coherence and quantum entanglement. We establish hierarchies of different operations for manipulating coherence and entanglement in distributed settings, where at least one of the two spatially separated parties are restricted from generating coherence. In these settings, we introduce new classes of operations and also characterize those maximal, i.e., the resource-non-generating operations, progressing beyond existing studies on incoherent versions of local operations and classical communication and those of separable operations. The maximal operations admit a semidefinite-programming formulation useful for numerical algorithms, whereas the existing operations not. To establish the hierarchies, we prove a sequence of inclusion relations among the operations by clarifying tasks where separation of the operations appears. We also demonstrate an asymptotically non-surviving separation of the operations in the hierarchy in terms of performance of the task of assisted coherence distillation, where a separation in a one-shot scenario vanishes in the asymptotic limit. Our results serve as fundamental analytical and numerical tools to investigate interplay between coherence and entanglement under different operations in the resource theory.

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arXiv2021

Noisy quantum state redistribution with promise and the Alpha-bit

We consider a variation of the well-studied quantum state redistribution task, in which the starting state is known only to the receiver Bob and not to the sender Alice. We refer to this as quantum state redistribution with a one-sided promise. In addition, we consider communication from Alice to Bob over a noisy channel $\mathcal{N}$, instead of the noiseless channel, as is usually considered in state redistribution. We take a natural approach towards the solution of this problem where we "embed" the promise as part of the state and then invoke known protocols for quantum state redistribution composed with known protocols for transfer of quantum information over noisy channels. Using our approach, we are able to reproduce the Alpha-bit capacities with or without entanglement assistance in Ref. [ArXiv:1706.09434], using known protocols for quantum state redistribution and quantum communication over noisy channels. Furthermore, we generalize the entanglement assisted classical Alpha-bit capacity, showing that any quantum state redistribution protocol can be used as a black box to simulate classical communication.

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arXiv2021

Entanglement-assisted capacity regions and protocol designs for quantum multiple-access channels

We solve the entanglement-assisted (EA) classical capacity region of quantum multiple-access channels with an arbitrary number of senders. As an example, we consider the bosonic thermal-loss multiple-access channel and solve the one-shot capacity region enabled by an entanglement source composed of sender-receiver pairwise two-mode squeezed vacuum states. The EA capacity region is strictly larger than the capacity region without entanglement-assistance. With two-mode squeezed vacuum states as the source and phase modulation as the encoding, we also design practical receiver protocols to realize the entanglement advantages. Four practical receiver designs, based on optical parametric amplifiers, are given and analyzed. In the parameter region of a large noise background, the receivers can enable a simultaneous rate advantage of 82.0% for each sender. Due to teleportation and superdense coding, our results for EA classical communication can be directly extended to EA quantum communication at half of the rates. Our work provides a unique and practical network communication scenario where entanglement can be beneficial.

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