Variational quantum algorithms (VQA) based on Hamiltonian simulation represent a specialized class of quantum programs well-suited for near-term quantum computing applications due to its modest resource requirements in terms of qubits and circuit depth. Unlike the conventional single-qubit (1 Q) and two-qubit (2 Q) gate sequence representation, Hamiltonian simulation programs are essentially composed of disciplined subroutines known as Pauli exponentiations (Pauli strings with coefficients) that are variably arranged. To capitalize on these distinct program features, this study introduces PHOENIX, a highly effective compilation framework that primarily operates at the high-level Pauli-based intermediate representation (IR) for generic Hamiltonian simulation programs. PHOENIX exploits global program optimization opportunities to the greatest extent, compared to existing SOTA methods despite some of them also utilizing similar IRs. PHOENIX employs the binary symplectic form (BSF) to formally describe Pauli strings and reformulates IR synthesis as reducing the column weights of BSF by appropriate Clifford transformations. It comes with a heuristic BSF simplification algorithm that searches for the most appropriate 2Q Clifford operators in sequence to maximally simplify the BSF at each step, until the BSF can be directly synthesized by basic 1 Q and 2Q gates. PHOENIX further performs a global ordering strategy in a TETRIS-like fashion for these simplified IR groups, carefully balancing optimization opportunities for gate cancellation, minimizing circuit depth, and managing qubit routing overhead. Experimental results demonstrate that PHOENIX outperforms SOTA VQA compilers across diverse program categories, backend ISAs, and hardware topologies.

Ion traps stand at the forefront of quantum hardware technology, presenting unparalleled benefits for quantum computing, such as high-fidelity gates, extensive connectivity, and prolonged coherence times. In this context, we explore the critical role of shuttling operations within these systems, especially their influence on the fidelity loss and elongated execution times. To address these challenges, we have developed BOSS, an efficient blocking algorithm tailored to enhance shuttling efficiency. This optimization not only bolsters the shuttling process but also elevates the overall efficacy of ion trap devices. We experimented on multiple applications using two qubit gates up to 4000+ and qubits ranging from 64 to 78. Our method significantly reduces the number of shuttles on most applications, with a maximum reduction of $96.1 \%$. Additionally, our investigation includes simulations of realistic experimental parameters that incorporate sympathetic cooling, offering a higher fidelity and a refined estimate of execution times that align more closely with practical scenarios.

The Quantum Charge-Coupled Device (QCCD) architecture is a modular design to expand trapped-ion quantum computer that relies on the coherent shuttling of qubits across an array of segmented electrodes.Leveraging trapped ions for their long coherence times and high-fidelity quantum operations, QCCD technology represents a significant advancement toward practical, large-scale quantum processors.However, shuttling increases thermal motion and consistently necessitates qubit swaps, significantly extend execution time and negatively affect application success rates.In this paper, we introduce S-SYNC -a compiler designed to co-optimize the number of shuttling and swapping operations.S-SYNC exploits the unique properties of QCCD and incorporates generic SWAP operations to efficiently manage shuttle and SWAP counts simultaneously.Building on the static topology formulation of QCCD, we develop scheduling heuristics to enhance overall performance.Our evaluations demonstrate that our approach reduces the shuttling number by 3.69x on average and improves the success rate of quantum applications by 1.73x on average.Moreover, we apply S-SYNC to gain insights into executing applications across various QCCD topologies and to compare the trade-offs between different initial mapping methods.

The unique features of entanglement and non-locality in quantum systems, where there are pairs of bipartite states perfectly distinguishable by general entangled measurements yet indistinguishable by local operations and classical communication, hold significant importance in quantum entanglement theory, distributed quantum information processing, and quantum data hiding. This paper delves into the entanglement cost for discriminating two bipartite quantum states, employing positive operator-valued measures (POVMs) with positive partial transpose (PPT) to achieve optimal success probability through general entangled measurements. We first introduce two quantities called the spectral PPT-distance and relative spectral PPT-distance of a POVM to quantify the localness of a general measurement. We show these quantities are related to the entanglement cost of optimal discrimination by PPT POVMs. Following this, we establish bounds and develop SDP hierarchies to estimate the entanglement cost of optimal discrimination by PPT POVMs for any pair of states. Leveraging these results, we show that a pure state can be optimally discriminated against any other state with the assistance of a single Bell state. This study advances our understanding of the pivotal role played by entanglement in quantum state discrimination, serving as a crucial element in unlocking quantum data hiding against locally constrained measurements.

The unique features of entanglement and non-locality in quantum systems, where there are pairs of bipartite states perfectly distinguishable by general entangled measure-ments yet indistinguishable by local operations and classical communication, hold significant importance in quantum entanglement theory, distributed quantum information processing, and quantum data hiding. This paper delves into the entanglement cost for discriminating two quantum states, employing positive operator-valued measures (POVMs) with positive partial trans-pose (PPT) to achieve optimal success probability through general entangled measurements. First, we introduce an efficiently com-putable quantity called the spectral PPT-distance of a POVM to quantify the localness of a general measurement. We show that it can be a lower bound for the entanglement cost of optimal discrimination by PPT POVMs. Second, we establish an upper bound on the entanglement cost of optimal discrimination by PPT POVMs for any pair of states. Leveraging this result, we show that a pure state can be optimally discriminated against any other state with the assistance of a single Bell state. This study advances our understanding of the pivotal role played by entanglement in quantum state discrimination, serving as a crucial element in unlocking quantum data hiding against locally constrained measurements.

Quantum Internet relies on quantum entanglement as a fundamental resource for secure and efficient quantum communication, reshaping data transmission. In this context, entanglement distillation emerges as a crucial process that plays a pivotal role in realizing the full potential of the quantum internet. Nevertheless, it remains challenging to accurately estimate the distillable entanglement and its closely related essential quantity, the quantum capacity. In this work, we consider a general resource measure known as the reverse divergence of resources which quantifies the minimum divergence between a target state and the set of free states. Leveraging this measure, we propose efficiently computable upper bounds for both quantities based on the idea that the useless entanglement within a state or a quantum channel does not contribute to the distillable entanglement or the quantum capacity, respectively. Our bounds can be computed via semidefinite programming and have practical applications for purifying maximally entangled states under practical noises, such as depolarizing and amplitude damping noises, leading to improvements in estimating the one-way distillable entanglement. Furthermore, we provide valuable benchmarks for evaluating the quantum capacities of qubit quantum channels, including the Pauli channels and the random mixed unitary channels, which are of great interest for the development of a quantum internet.

Quantum neural networks (QNNs) have been a promising framework in pursuing near-term quantum advantage in various fields, where many applications can be viewed as learning a quantum state that encodes useful data. As a quantum analog of probability distribution learning, quantum state learning is theoretically and practically essential in quantum machine learning. In this paper, we develop a no-go theorem for learning an unknown quantum state with QNNs even starting from a high-fidelity initial state. We prove that when the loss value is lower than a critical threshold, the probability of avoiding local minima vanishes exponentially with the qubit count, while only grows polynomially with the circuit depth. The curvature of local minima is concentrated to the quantum Fisher information times a loss-dependent constant, which characterizes the sensibility of the output state with respect to parameters in QNNs. These results hold for any circuit structures, initialization strategies, and work for both fixed ansatzes and adaptive methods. Extensive numerical simulations are performed to validate our theoretical results. Our findings place generic limits on good initial guesses and adaptive methods for improving the learnability and scalability of QNNs, and deepen the understanding of prior information's role in QNNs.