Related papers: Block encoding of sparse matrices with a periodic …
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…
Block encoding of sparse matrices underpins powerful quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear solvers, yet its efficient gate-level realization for general sparse matrices…
Block encoding severs as an important data input model in quantum algorithms, enabling quantum computers to simulate non-unitary operators effectively. In this paper, we propose an efficient block-encoding protocol for sparse matrices based…
The cost of data input can dominate the run-time of quantum algorithms. Here, we consider data input of arithmetically structured matrices via block encoding circuits, the input model for the quantum singular value transform and related…
While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…
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…
Block-encoding operators are one of the essential components in quantum algorithms based on Quantum Signal Processing. Their gate complexity largely determines the overall gate complexity of the full algorithm. Using variational methods, we…
The data input model is a fundamental component of every quantum algorithm, as its efficiency is crucial for achieving potential speed-ups over classical methods. For quantum linear algebra tasks that utilize quantum eigenvalue or singular…
Quantum block encoding (QBE) is a crucial step in the development of most quantum algorithms, as it provides an embedding of a given matrix into a suitable larger unitary matrix. Historically, the development of efficient techniques for QBE…
Block encoding lies at the core of many existing quantum algorithms. Meanwhile, efficient and explicit block encodings of dense operators are commonly acknowledged as a challenging problem. This paper presents a comprehensive study of the…
Solving differential equations is one of the most computationally expensive problems in classical computing, occupying the vast majority of high-performance computing resources devoted towards practical applications in various fields of…
Over a decade ago, it was demonstrated that quantum computing has the potential to revolutionize numerical linear algebra by enabling algorithms with complexity superior to what is classically achievable, e.g., the seminal HHL algorithm for…
Quantum circuits naturally implement unitary operations on input quantum states. However, non-unitary operations can also be implemented through block encodings, where additional ancilla qubits are introduced and later measured. While block…
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…
Discrete Laplacian operators arise ubiquitously in scientific computing and frequently appear in quantum algorithms for tasks such as linear algebra, Hamiltonian simulation, and partial differential equations. Block encoding provides the…
With the Quantum Singular Value Transformation (QSVT) emerging as a unifying framework for diverse quantum speedups, the efficient construction of block encodings -- their fundamental input model -- has become increasingly crucial. However,…
We present an efficient quantum circuit for block encoding pairing Hamiltonian often studied in nuclear physics. Our block encoding scheme does not require mapping the creation and annihilation operators to the Pauli operators and…
Many quantum algorithms for numerical linear algebra assume black-box access to a block-encoding of the matrix of interest, which is a strong assumption when the matrix is not sparse. Kernel matrices, which arise from discretizing a kernel…
Quantum signal processing combined with quantum eigenvalue transformation has recently emerged as a unifying framework for several quantum algorithms. In its standard form, it consists of two separate routines: block encoding, which encodes…
Block encoding is a key ingredient in the recently developed quantum singular value transformation (QSVT) framework, which provides a unifying description for many quantum algorithms. Initially introduced to simplify and optimize resource…