quantum state representation and encoding

This work addresses the absence of a systematic framework for classifying and comparing quantum programming languages, a gap that has hindered the evolution of language design in this domain. The authors propose a unified, multidimensional taxonomy and conduct a comprehensive evaluation—combining qualitative and quantitative analyses—of ten mainstream quantum programming languages across critical dimensions such as expressiveness, executability, and suitability for specific application scenarios. By establishing the first structured comparative framework, this study not only clarifies the relative strengths and weaknesses of existing languages but also systematically identifies core challenges related to readability, generality, and toolchain support. These insights provide both theoretical grounding and practical guidance for the future development of quantum programming languages.

This work addresses the efficient encoding of classical matrices into quantum circuits, focusing on two fundamental representations: block encodings and state preparation circuits. We propose a general construction method for block encodings and establish low-overhead bidirectional conversion algorithms between the two representations, providing the first rigorous proof of their functional equivalence. Furthermore, we design a higher-order Pauli-basis transformation algorithm based on constant-depth multiplexers, enabling efficient conversion between standard-basis and Pauli-basis matrix expansions. Our methods significantly reduce the quantum resource overhead—particularly qubit count and circuit depth—associated with data encoding in quantum linear algebra algorithms. They also enhance flexibility and practicality in input representation, thereby facilitating the real-world deployment of quantum algorithms. (149 words)

Quantum computing suffers from high conceptual barriers, unintuitive interfaces, and ambiguous documentation, severely hindering efficient adoption by novices and domain experts alike. To address this, we propose the first usability-centered interactive framework for quantum computing, systematically bridging quantum theory and human-centered design through iterative HCI methodologies. Our approach integrates four core technical components: (1) iterative interaction design grounded in quantum programming practices; (2) high-fidelity prototyping; (3) abstract modeling of quantum circuits; and (4) visual programming with interpretable result visualization. The resulting platform supports conceptual coding, comparative program optimization, collaborative result sharing, and quantum hardware exploration. Empirical evaluation demonstrates significant improvements in non-expert users’ comprehension, debugging efficiency, and collaborative confidence—establishing a foundational, systematic interaction paradigm to advance quantum programming accessibility.

Quantum programming suffers from high cognitive load and steep learning curves due to low-level gate-level modeling. This paper introduces Qwerty, a high-level quantum language oriented toward computational basis states, enabling semantic, direct manipulation of quantum states while eliminating manual gate design. Its core contribution is the first-ever “basis-state type system”, which enables type-driven automatic gate synthesis, seamless quantum-classical hybrid programming, and native interoperability with Python. Leveraging this type system, we design a compiler that automatically translates high-level quantum logic into equivalent, executable gate sequences. Experimental evaluation on canonical quantum algorithms demonstrates that Qwerty achieves functional equivalence while improving development efficiency by over 3× compared to conventional gate-based approaches. The language significantly reduces the abstraction gap in quantum programming and lowers the barrier to entry for practitioners and researchers alike.

How can meta-level generalization be achieved in quantum experimental design to autonomously discover universal physical design principles—rather than merely optimizing for specific instances? Method: We propose a sequence-to-sequence Transformer model fine-tuned on synthetically generated data, specifically designed to generate structured, executable, and physically interpretable Python code that directly outputs experimental blueprints for entire classes of quantum systems. Contribution: This work achieves the first demonstration of meta-level generalization in quantum experimental design, uncovering previously unknown universal rules shared across infinitely many quantum states. The generated protocols exhibit high verifiability, human readability, and physical interpretability; crucially, they generalize to novel quantum systems without retraining. By enabling autonomous discovery of scientific principles—not just solutions to concrete problems—this approach advances AI’s role from computational tool to scientific discovery engine.

Quantum Intermediate Representation (QIR) faces challenges in practical deployment within existing quantum circuit simulators, often introducing non-negligible runtime overhead and hindering broad adoption. Method: This work proposes a low-overhead, scalable QIR integration paradigm. We systematically analyze QIR’s role in cross-platform compilation, hardware adaptation, and circuit optimization; integrate compiler design principles, quantum circuit optimization techniques, and hardware abstraction layer (HAL) concepts to build a simulator adaptation framework enabling native QIR ingestion; and explicitly characterize the performance–compatibility trade-offs across distinct integration pathways. Contribution/Results: We present the first comprehensive taxonomy of QIR support patterns across diverse quantum tools; introduce a phased adoption strategy, empirically demonstrating that QIR translation overhead on critical execution paths remains below 3%; and deliver a practice-oriented, theoretically grounded guideline for standardizing the quantum software stack—balancing formal rigor with engineering feasibility.

This study addresses the lack of standardized conventions in quantum circuit visualization, which leads to inconsistent cross-platform representations and impedes comprehension and collaboration. By systematically analyzing 182 static and 12 interactive visualization examples, the work proposes the first structured design space specifically tailored for quantum circuits. Through qualitative content analysis, it establishes a comprehensive framework encompassing encoding dimensions, interaction modalities, and rendering strategies, elucidating both their connections to and distinctions from established principles in classical information visualization. This contribution lays a theoretical foundation for a unified visual grammar for quantum circuits and identifies key directions for future research, including data structures, cognitive mechanisms, and system integration.

Quantum simulation of fermionic Hamiltonians often suffers from excessive circuit depth due to inefficient qubit encodings. Method: This work proposes a deterministic ternary-tree encoding optimization method jointly tailored to hardware connectivity and Hamiltonian structure. Preserving the ternary-tree topology, it employs analytical modeling, graph-structure-driven encoding construction, and qDRIFT time-evolution analysis to achieve auxiliary-qubit-free, zero-SWAP-overhead encoding customization. Contribution/Results: Unlike existing heuristic or resource-augmented approaches, this is the first deterministic, hardware-aware optimization that co-adapts to both device constraints and Hamiltonian features. In STO-3G-basis water molecule simulations, it reduces uncompiled and compiled qDRIFT circuit depths by 27.7% and 26.0% on average, respectively—significantly enhancing simulation efficiency on noisy intermediate-scale quantum (NISQ) devices.

Although block encoding theoretically underpins numerous advanced quantum algorithms—such as Quantum Signal Processing (QSP) and Quantum Singular Value Transformation (QSVT)—its intricate implementation has hindered practical adoption. This work introduces, for the first time, a generalized programming interface that abstracts block encoding and integrates it into the Eclipse Qrisp framework. The interface encapsulates key techniques including qubitization, the Childs–Kothari–Somma construction, and arithmetic composition, enabling high-level expression and automated resource estimation for algorithms like matrix inversion, polynomial filtering, and Hamiltonian simulation. By providing clear mechanisms for constructing and composing block encodings, this interface substantially lowers the barrier to using state-of-the-art quantum algorithms, enhances developer productivity, and improves accessibility, as demonstrated through illustrative code examples.

This work addresses the longstanding challenges in implementing block-encoding–based quantum linear algebra algorithms, which have been hindered by the complexity of underlying circuit construction and the difficulty of verification. We introduce Unitaria, a NumPy/SciPy-like Python library that provides a composable, array-oriented interface for directly manipulating encoded matrices and vectors without requiring ancilla qubits. By unifying block encoding, quantum singular value transformation, and standard linear algebra operations—augmented with automated circuit synthesis and resource analysis—our approach enables efficient classical validation and scalable simulation. Compared to conventional state-vector simulators, Unitaria significantly extends the attainable problem scale and accurately estimates key resources such as gate count, qubit count, and normalization constants without executing the quantum circuit.

Graduate students in computer science often exhibit a disconnect between theoretical understanding of quantum computing and practical research capabilities. Method: This paper designs and implements a practice-oriented course wherein students develop a quantum circuit simulator from scratch, implementing four mainstream simulation paradigms—state-vector, density-matrix, stabilizer, and matrix-product-state formalisms—to model superposition, entanglement, and noise. The pedagogy adopts an “implementation-as-understanding” approach, moving beyond traditional lecture-based instruction. Contribution/Results: Evaluation demonstrates significant improvements in students’ ability to conduct independent quantum computing research and model complex quantum systems. The course strengthens intuitive comprehension of abstract concepts and cultivates hands-on proficiency with state-of-the-art simulation tools, thereby establishing a robust foundation for subsequent scholarly work in quantum information science.