相关论文: Ladder Operator Block-Encoding

Existing error correction mechanisms in lattice-based public key encryption (PKE) rely on either naive modulation or its concatenation with error correction codes (ECC). This paper shows that lattice coding, as a joint ECC and modulation…

Partial differential equation (PDE)-constrained optimization, where an optimization problem is subject to PDE constraints, arises in various applications such as design, control, and inference. Solving such problems is computationally…

Bosonic codes offer a hardware-efficient approach to encoding and protecting quantum information with a single continuous-variable bosonic system. In this paper, we introduce a new universal quantum gate set composed of only one type of…

Topological quantum error correction is a milestone in the scaling roadmap of quantum computers, which targets circuits with trillions of gates that would allow running quantum algorithms for real-world problems. The square-lattice surface…

Quantum error correction allows inherently noisy quantum devices to emulate an ideal quantum computer with reasonable resource overhead. As a crucial component, decoding architectures have received significant attention recently. In this…

A shape invariant nonseparable and nondiagonalizable two-dimensional model with quadratic complex interaction, first studied by Cannata, Ioffe, and Nishnianidze, is re-examined with the purpose of exhibiting its hidden algebraic structure.…

Fault-tolerant quantum computation (FTQC) is expected to address a wide range of computational problems. To realize large-scale FTQC, it is essential to encode logical qubits using quantum error-correcting codes. High-rate concatenated…

Relative positional encodings determine which functions of query-key lag can enter the primitive attention logit. RoPE supplies a rotary phase, while ALiBi supplies an additive distance bias. Motivated by group-theoretic views of linear…

We introduce a novel positional encoding strategy for Transformer-style models, addressing the shortcomings of existing, often ad hoc, approaches. Our framework provides a flexible mapping from the algebraic specification of a domain to an…

We apply the recent graphical framework of "Quantum Lego" to XP stabilizer codes where the stabilizer group is generally non-Abelian. We show that the idea of operator matching continues to hold for such codes and is sufficient for…

Ensuring safety in robotic systems remains a fundamental challenge, especially when deploying offline policy-learning methods such as imitation learning in dynamic environments. Traditional behavior cloning (BC) often fails to generalize…

One of the challenges in quantum computing is the synthesis of unitary operators into quantum circuits with polylogarithmic gate complexity. Exact synthesis of generic unitaries requires an exponential number of gates in general. We propose…

We present a lattice-based scheme for homomorphic evaluation of quantum programs and proofs that remains secure against quantum adversaries. Classical homomorphic encryption is lifted to the quantum setting by replacing composite-order…

Block-encodings are ubiquitous in quantum computing as a way to represent data within a unitary operator. While several unstructured methods are applicable to arbitrary data, these techniques are burdened by hidden costs and poor accuracy.…

Current quantization methods for LLMs predominantly rely on block-wise structures to maintain efficiency, often at the cost of representational flexibility. In this work, we demonstrate that element-wise quantization can be made as…

We propose Parabolic Position Encoding (PaPE), a parabola-based position encoding for vision modalities in attention-based architectures. Given a set of vision tokens-such as from videos, event camera streams, images, or point clouds-our…

Random permutation circuits were recently introduced as minimal models for local many-body dynamics that can be interpreted both as classical and quantum. Standard dynamical complexity indicators such as damage spreading and…

Large language models (LLMs) experience significant performance degradation when the input exceeds the pretraining context window, primarily due to the out-of-distribution (OOD) behavior of Rotary Position Embedding (RoPE). Recent studies…

We study a quantum-algorithmic framework for parameterizing partial differential equations (PDEs). For a broad class of problems in which the discretized parameter field admits a diagonal representation, block-encodings of diagonal…

We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions…