Related papers: TARE: Block Encoding Linear Combinations of Pauli …
We present a novel framework for Linear Combination of Unitaries (LCU)-style decomposition tailored to structured sparse matrices, which frequently arise in the numerical solution of partial differential equations (PDEs). While LCU is a…
We present a quantum process-tomography protocol based on a low-degree ansatz for the quantum channel, i.e. when it can be expressed as a fixed-degree polynomial in terms of Pauli operators. We demonstrate how to perform tomography of such…
Binary embeddings provide efficient and powerful ways to perform operations on large scale data. However binary embedding typically requires long codes in order to preserve the discriminative power of the input space. Thus binary coding…
Traditional fixed-depth architectures scale quality by increasing training FLOPs, typically through increased parameterization, at the expense of a higher memory footprint, or data. A potential alternative is looped architectures, which…
In this paper, we introduce an algorithm for extracting topological data from translation invariant generalized Pauli stabilizer codes in two-dimensional systems, focusing on the analysis of anyon excitations and string operators. The…
Implicit neural representation (INR) is a popular approach for arbitrary-scale image super-resolution (SR), as a key component of INR, position encoding improves its representation ability. Motivated by position encoding, we propose…
We present quantum algorithms for the estimation of n-time correlation functions, the local and non-local density of states, and dynamical linear response functions. These algorithms are all based on block-encodings - a versatile technique…
Algorithm and hardware-aware compilation co-design is essential for the efficient deployment of near-term quantum programs. We present a compilation case-study implementing QCrank -- an efficient encoding protocol for storing sequenced…
The Byte Pair Encoding algorithm can be safely batched to merge hundreds of pairs of tokens at a time when building up a tokenizer's vocabulary. This technique combined with reducing the memory footprint of text used in vocabulary training…
Recent studies have demonstrated the effectiveness of position encoding in transformer architectures. By incorporating positional information, this approach provides essential guidance for modeling dependencies between elements across…
Simulating real-time quantum dynamics in interacting spin systems is a fundamental challenge, where exact diagonalization suffers from exponential Hilbert-space growth and tensor-network methods face entanglement barriers. Recently,…
The quantum simulation kernel is an important subroutine appearing as a very long gate sequence in many quantum programs. In this paper, we propose Paulihedral, a block-wise compiler framework that can deeply optimize this subroutine by…
Partial differential equations (PDEs) are fundamental across numerous scientific fields. As these problems scale to high dimensions, classical numerical schemes introduce severe computational bottlenecks, known as the curse of…
Quantum signal processing and quantum singular value transformation are powerful tools to implement polynomial transformations of block-encoded matrices on quantum computers, and has achieved asymptotically optimal complexity in many…
The assumed hardness of the Linear Code Equivalence problem (LCE) lies at the core of the security of the LESS signature scheme and other signature schemes with advanced functionalities. The LCE problem asks to determine whether two linear…
Inspired by compressive sensing principles, we propose novel error control coding techniques for communication systems. The information bits are encoded in the support and the non-zero entries of a sparse signal. By selecting a dictionary…
In a gauge theory, a collection of kinematical degrees of freedom is used to redundantly describe a smaller amount of gauge-invariant information. In a quantum error correcting code (QECC), a collection of computational degrees of freedom…
Quantum annealing (QA) has emerged as a promising candidate for fast solvers for combinatorial optimization problems (COPs) and has attracted the interest of many researchers. Since COP is logically encoded in the Ising interaction among…
Recent work has demonstrated that using a carefully designed sensing matrix rather than a random one, can improve the performance of compressed sensing. In particular, a well-designed sensing matrix can reduce the coherence between the…
We consider the problem of computing a binary linear transformation using unreliable components when all circuit components are unreliable. Two noise models of unreliable components are considered: probabilistic errors and permanent errors.…