相关论文: Ladder Operator Block-Encoding

We introduce a new family of multi-mode, rotationally symmetric bosonic codes inspired by the group-theoretic framework of [Phys. Rev. Lett. 133, 240603 (2024)]. Such a construction inverts the traditional paradigm of code design by…

Three sets of ladder operators in spheroconal coordinates and their respective actions on Lam\'e spheroconal harmonic polynomials are presented in this article. The polynomials are common eigenfunctions of the square of the angular momentum…

The attention mechanism is a critical component of Large Language Models (LLMs) that allows tokens in a sequence to interact with each other, but is order-invariant. Incorporating position encoding (PE) makes it possible to address by…

Rotation symmetric bosonic codes are an attractive encoding for qubits into oscillator degrees of freedom, particularly in superconducting qubit experiments. While these codes can tolerate considerable loss and dephasing, they will need to…

In contexts where relevant problems can easily attain configuration spaces of enormous sizes, solving Linear Differential Equations (LDEs) can become a hard achievement for classical computers; on the other hand, the rise of quantum…

Mixture of Vision Encoders (MoVE) has emerged as a powerful approach to enhance the fine-grained visual understanding of multimodal large language models (MLLMs), improving their ability to handle tasks such as complex optical character…

Positional encoding (PE) underpins how permutation-invariant Transformers represent sequence order, yet how positional information is processed and stored remains poorly understood. Modern PE methods such as RoPE still struggle on tasks…

In recent years, quantum computing has started to demonstrate superior efficiency to classical computing. In quantum computing, quantum circuits that implement specific quantum algorithms are usually not directly executable on quantum…

Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…

Bosonic codes encode quantum information into a single infinite-dimensional physical system endowed with error correction capabilities. This reduces the need for complex management of many physical constituents compared with standard…

Block-encoding is a critical subroutine in quantum computing, enabling the transformation of classical data into a matrix representation within a quantum circuit. The resource trade-offs in simulating a block-encoding can be quantified by…

New ladder operators are constructed for a rational extension of the harmonic oscillator associated with type III Hermite exceptional orthogonal polynomials and characterized by an even integer $m$. The eigenstates of the Hamiltonian…

As quantum machines have scaled up in their number of qubits, significant research has turned towards increasing their fidelity with quantum error correction codes. Although promising results have been shown with the surface code, which…

Reinforcement learning (RL) with limited samples is common in real-world applications. However, offline RL performance under this constraint is often suboptimal. We consider an alternative approach to dealing with limited samples by…

We present COMPOSER, a compile-once modular parametric oracle for similarity-encoded effective reduction of electronic-structure operators (e.g., Schrieffer-Wolff-type constructions). Low-rank factorizations compress Hamiltonians and…

Encoding and indexing of lattice codes is generalized from self-similar lattice codes to a broader class of lattices. If coding lattice $\Lambda_{\textrm{c}}$ and shaping lattice $\Lambda_{\textrm{s}}$ satisfy $\Lambda_{\textrm{s}}…

Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computation with constant overhead. Recent advancements have shown that qLDPC codes can outperform the quantum memory capability of…

It is a long standing open problem to find search to decision reductions for structured versions of the decoding problem of linear codes. Such results in the lattice-based setting have been carried out using number fields: Polynomial-LWE,…

Block encodings are a fundamental primitive in quantum algorithms, but can often have large ancilla overhead. In this work, we introduce novel techniques for reducing this overhead in two distinct ways. In Part I, we prove the existence of…

Implementing polynomial functions of Hermitian matrices on quantum hardware is a foundational task in quantum computing, critical for accurate Hamiltonian simulation, quantum linear system solving, high-fidelity state preparation, machine…