arXiv subjects

Yu-Chun Wu

Publications and source records attributed to Yu-Chun Wu.

At least 73 records · Page 4Linked to original sources

arXiv2021

Variational Quantum Algorithms for Steady States of Open Quantum Systems

Solving problems related to open quantum systems has attracted many interests. Here, we propose a variational quantum algorithm to find the steady state of open quantum systems. In this algorithm, we employ parameterized quantum circuits to prepare the purification of the steady state and define the cost function based on the Lindblad master equation, which can be efficiently evaluated with quantum circuits. Then we optimize the parameters of the quantum circuit to find the steady state. Numerical simulations are performed on the one-dimensional transverses field Ising model with dissipative channels. The result showed that the fidelity between the optimal mixed state and the true steady state is over 99\%. This algorithm is derived from the natural idea of expressing mixed states with purification and provides a reference for the study of open quantum systems.

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arXiv2021

Quantum Finite Volume Method for Computational Fluid Dynamics with Classical Input and Output

Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical methods to solve fluid flows. The finite volume method (FVM) is an important one. In FVM, space is discretized to many grid cells. When the number of grid cells grows, massive computing resources are needed correspondingly. Recently, quantum computing has been proven to outperform a classical computer on specific computational tasks. However, the quantum CFD (QCFD) solver remains a challenge because the conversion between the classical and quantum data would become the bottleneck for the time complexity. Here we propose a QCFD solver with exponential speedup over classical counterparts and focus on how a quantum computer handles classical input and output. By utilizing quantum random access memory, the algorithm realizes sublinear time at every iteration step. The QCFD solver could allow new frontiers in the CFD area by allowing a finer mesh and faster calculation.

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arXiv2021

Special-Purpose Quantum Processor Design

Full connectivity of qubits is necessary for most quantum algorithms, which is difficult to directly implement on Noisy Intermediate-Scale Quantum processors. However, inserting swap gate to enable the two-qubit gates between uncoupled qubits significantly decreases the computation result fidelity. To this end, we propose a Special-Purpose Quantum Processor Design method that can design suitable structures for different quantum algorithms. Our method extends the processor structure from two-dimensional lattice graph to general planar graph and arranges the physical couplers according to the two-qubit gate distribution between the logical qubits of the quantum algorithm and the physical constraints. Experimental results show that our design methodology, compared with other methods, could reduce the number of extra swap gates per two-qubit gate by at least 104.2% on average. Also, our method's advantage over other methods becomes more obvious as the depth and qubit number increase. The result reveals that our method is competitive in improving computation result fidelity and it has the potential to demonstrate quantum advantage under the technical conditions.

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arXiv2020

Measurement-device-independent quantification of irreducible high-dimensional entanglement

The certification of entanglement dimensionality is of great importance in characterizing quantum systems. Recently, it is pointed out that quantum correlation of high-dimensional states can be simulated with a sequence of lower-dimensional states. Such problem may render existing characterization protocols unreliable---the observed entanglement may not be a truly high-dimensional one. Here, we introduce the notion of irreducible entanglement to capture its dimensionality that is indecomposable in terms of a sequence of lower-dimensional entangled systems. We prove this new feature can be detected in a measurement-device-independent manner with an entanglement witness protocol. To demonstrate the practicability of this technique, we experimentally apply it on a 3-dimensional bipartite state and the result certifies the existence of irreducible (at least) 3-dimensional entanglement.

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arXiv2020

Entanglement Area Law for Shallow and Deep Quantum Neural Network States

A study of the artificial neural network representation of quantum many-body states is presented. The locality and entanglement properties of states for shallow and deep quantum neural networks are investigated in detail. By introducing the notion of local quasi-product states, for which the locally connected shallow feed-forward neural network states and restricted Boltzmann machine states are special cases, we show that Rényi entanglement entropies of all these states obey the entanglement area law. Besides, we also investigate the entanglement features of deep Boltzmann machine states and show that locality constraints imposed on the neural networks make the states obey the entanglement area law. Finally, as an application, we apply the notion of Rényi entanglement entropy to understanding the power of neural networks and show that image classification problems which can be efficiently solved must obey the area law.

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arXiv2019

State preparation based on quantum phase estimation

State preparation is a process encoding the classical data into the quantum systems. Based on quantum phase estimation, we propose the specific quantum circuits for a deterministic state preparation algorithm and a probabilistic state preparation algorithm. To discuss the gate complexity in these algorithms, we decompose the diagonal unitary operators included in the phase estimation algorithms into the basic gates. Thus, we associate the state preparation problem with the decomposition problem of the diagonal unitary operators. We analyse the fidelities in the two algorithms and discuss the success probability in the probabilistic algorithm. In this case, we explain that the efficient decomposition of the corresponding diagonal unitary operators is the sufficient condition for state preparation problems.

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arXiv2019

Effects of Quantum Noise on Quantum Approximate Optimization Algorithm

The quantum-classical hybrid algorithm is an algorithm that holds promise in demonstrating the quantum advantage in NISQ devices. When running such algorithms, effects from quantum noise are inevitable. In our work, we consider a well-known hybrid algorithm, the quantum approximate optimization algorithm (QAOA). We study the effects on QAOA from typical quantum noise channels and produce several numerical results. Our research indicates that the output state fidelity, the cost function, and its gradient obtained from QAOA decrease exponentially with respect to the number of gates and noise strength. Moreover, we find that noise merely flattens the parameter space without changing its structure, so optimized parameters will not deviate from their ideal values. Our result provides evidence for the effectiveness of hybrid algorithms running on NISQ devices.

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arXiv2019

Building quantum neural networks based on swap test

Artificial neural network, consisting of many neurons in different layers, is an important method to simulate humain brain. Usually, one neuron has two operations: one is linear, the other is nonlinear. The linear operation is inner product and the nonlinear operation is represented by an activation function. In this work, we introduce a kind of quantum neuron whose inputs and outputs are quantum states. The inner product and activation operator of the quantum neurons can be realized by quantum circuits. Based on the quantum neuron, we propose a model of quantum neural network in which the weights between neurons are all quantum states. We also construct a quantum circuit to realize this quantum neural network model. A learning algorithm is proposed meanwhile. We show the validity of learning algorithm theoretically and demonstrate the potential of the quantum neural network numerically.

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arXiv2019

Quantum Neural Network States: A Brief Review of Methods and Applications

One of the main challenges of quantum many-body physics is that the dimensionality of the Hilbert space grows exponentially with the system size, which makes it extremely difficult to solve the Schrödinger equations of the system. But typically, many physical systems have a simplified internal structure which makes the parameters needed to characterize their ground states exponentially smaller. This makes many numerical methods possible in capture the physics of the system. Among these modern numerical techniques, neural networks, which show great power in approximating functions and extracting features of the big data, are now attracting many interests. Neural network representation of quantum many-body states shows great potential in solving some traditionally difficult quantum problems involving large number of freedoms. In this work, we briefly review the progress of using the artificial neural network to build quantum many-body ansatz states. We take Boltzmann machine representation as a prototypical example to illustrate various aspects of neural network representation of quantum many-body states. We first briefly review the classical neural networks, then we illustrate how to use neural networks to represent quantum states and density operators. Some physical properties of the neural network states, including entanglement features, representational power, and the relation with tensor network states, are discussed. For applications, we briefly review the progress of many-body calculating based on neural network states, neural network state approach to tomography, and also the classical simulation of quantum computing based on Boltzmann machine states. At the end of the work, some outlooks and open problems are given.

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arXiv2018

Efficient Machine Learning Representations of Surface Code with Boundaries, Defects, Domain Walls and Twists

Machine learning representations of many-body quantum states have recently been introduced as an ansatz to describe the ground states and unitary evolutions of many-body quantum systems. We explore one of the most important representations, restricted Boltzmann machine (RBM) representation, in stabilizer formalism. We give the general method of constructing RBM representation for stabilizer code states and find the exact RBM representation for several types of stabilizer groups with the number of hidden neurons equal or less than the number of visible neurons, which indicates that the representation is extremely efficient. Then we analyze the surface code with boundaries, defects, domain walls and twists in full detail and find that all the models can be efficiently represented via RBM ansatz states. Besides, the case for Kitaev's $D(\Zb_d)$ model, which is a generalized model of surface code, is also investigated.

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arXiv2018

Geometric Steering Criterion for Two-qubit States

According to the geometric characterization of measurement assemblages and local hidden state (LHS) models, we propose a steering criterion which is both necessary and sufficient for two-qubit states under arbitrary measurement sets. A quantity is introduced to describe the required local resources to reconstruct a measurement assemblage for two-qubit states. We show that the quantity can be regarded as a quantification of steerability and be used to find out optimal LHS models. Finally we propose a method to generate unsteerable states, and construct some two-qubit states which are entangled but unsteerable under all projective measurements.

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arXiv2018

Experimentally Robust Self-testing for Bipartite and Tripartite Entangled States

Self-testing refers to a method with which a classical user can certify the state and measurements of quantum systems in a device-independent way. Especially, the self-testing of entangled states is of great importance in quantum information process. A comprehensible example is that violating the CHSH inequality maximally necessarily implies the bipartite shares a singlet. One essential question in self-testing is that, when one observes a non-maximum violation, how close is the tested state to the target state (which maximally violates certain Bell inequality)? The answer to this question describes the robustness of the used self-testing criterion, which is highly important in a practical sense. Recently, J. Kaniewski predicts two analytic self-testing bounds for bipartite and tripartite systems. In this work, we experimentally investigate these two bounds with high quality two-qubit and three-qubit entanglement sources. The results show that these bounds are valid for various of entangled states we prepared, and thus, we implement robust self-testing processes which improve the previous results significantly.

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arXiv2018

Entropic No-Disturbance as a Physical Principle

The celebrated Bell-Kochen-Specker no-go theorem asserts that quantum mechanics does not present the property of realism, the essence of the theorem is the lack of a joint probability distributions for some experiment settings. In this work, we exploit the information theoretic form of the theorem using information measure instead of probabilistic measure and indicate that quantum mechanics does not present such entropic realism neither. The entropic form of Gleason's no-disturbance principle is developed and it turns out to be characterized by the intersection of several entropic cones. Entropic contextuality and entropic nonlocality are investigated in depth in this framework. We show how one can construct monogamy relations using entropic cone and basic Shannon-type inequalities. The general criterion for several entropic tests to be monogamous is also developed, using the criterion, we demonstrate that entropic nonlocal correlations are monogamous, entropic contextuality tests are monogamous and entropic nonlocality and entropic contextuality are also monogamous. Finally, we analyze the entropic monogamy relations for multiparty and many-test case, which plays a crucial role in quantum network communication.

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arXiv2018

Demonstration of Einstein-Podolsky-Rosen Steering with Enhanced Subchannel Discrimination

Einstein-Podolsky-Rosen (EPR) steering describes a quantum nonlocal phenomenon in which one party can nonlocally affect the other's state through local measurements. It reveals an additional concept of quantum nonlocality, which stands between quantum entanglement and Bell nonlocality. Recently, a quantum information task named as subchannel discrimination (SD) provides a necessary and sufficient characterization of EPR steering. The success probability of SD using steerable states is higher than using any unsteerable states, even when they are entangled. However, the detailed construction of such subchannels and the experimental realization of the corresponding task are still technologically challenging. In this work, we designed a feasible collection of subchannels for a quantum channel and experimentally demonstrated the corresponding SD task where the probabilities of correct discrimination are clearly enhanced by exploiting steerable states. Our results provide a concrete example to operationally demonstrate EPR steering and shine a new light on the potential application of EPR steering.

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arXiv2018

Experimentally detecting a quantum change point via Bayesian inference

Detecting a change point is a crucial task in statistics that has been recently extended to the quantum realm. A source state generator that emits a series of single photons in a default state suffers an alteration at some point and starts to emit photons in a mutated state. The problem consists in identifying the point where the change took place. In this work, we consider a learning agent that applies Bayesian inference on experimental data to solve this problem. This learning machine adjusts the measurement over each photon according to the past experimental results finds the change position in an online fashion. Our results show that the local-detection success probability can be largely improved by using such a machine learning technique. This protocol provides a tool for improvement in many applications where a sequence of identical quantum states is required.

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arXiv2017

Hierarchy of Genuine Multipartite Quantum Correlations

Classifying states which exhibiting different statistical correlations is among the most important problems in quantum information science and quantum many-body physics. In bipartite case, there is a clear hierarchy of states with different correlations: total correlation (T) $\supsetneq$ discord (D) $\supsetneq$ entanglement (E) $\supsetneq$ steering (S) $\supsetneq$ Bell~nonlocality (NL). However, very little is known about genuine multipartite correlations (GM$\mathcal{C}$) for both conceptual and technical difficulties. In this work, we show that, for any $N$-partite qudit states, there also exist such a hierarchy: genuine multipartite total correlations (GMT) $\supseteq$ genuine multipartite discord (GMD) $\supseteq$ genuine multipartite entanglement (GME) $\supseteq$ genuine multipartite steering (GMS) $\supseteq$ genuine multipartite nonlocality (GMNL). Furthermore, by constructing precise states, we show that GMT, GME and GMS are inequivalent with each other, thus GMT $\supsetneq$ GME $\supsetneq$ GMS.

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arXiv2017

Characterizing Nonlocal Correlations via Universal Uncertainty Relations

Characterization and certification of nonlocal correlations is one of the the central topics in quantum information theory. In this work, we develop the detection methods of entanglement and steering based on the universal uncertainty relations and fine-grained uncertainty relations. In the course of our study, the uncertainty relations are formulated in majorization form, and the uncertainty quantifier can be chosen as any convex Schur concave functions, this leads to a large set of inequalities, including all existing criteria based on entropies. We address the question that if all steerable states (or entangled states) can be witnessed by some uncertainty-based inequality, we find that for pure states and many important families of states, this is the case.

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arXiv2016

Monogamy Relation in No-disturbance Theories

The monogamy is a fundamental property of Bell nonlocality and contextuality. In this article, we studied the $n$-cycle noncontextual inequalities and generalized CHSH inequalities in detail and found the sufficient conditions for those inequalities to be hold. According to those conditions, we provide several kind of tradeoff relations: monogamy of generalized Bell inequalities in non-signaling framework, monogamy of cycle type noncontextual inequalities and monogamy between Bell inequality and noncontextual inequality in general no-disturbance framework. At last, some generic tradeoff relations of generalized CHSH inequalities for $n$-party physical systems, which are beyond one-to-many scenario, are discussed.

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