Related papers: Efficient block-encodings require structure

Locating the boundaries of consecutive blocks of quantum information is a fundamental building block for advanced quantum computation and quantum communication systems. We develop a coding theoretic method for properly locating boundaries…

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…

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…

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…

Large-scale distributed storage systems typically use erasure codes to provide durability of data in the face of failures. A set of $k$ blocks to be stored is encoded using an $[n, k]$ code to generate $n$ blocks that are then stored on…

Research on quantum computing has recently gained significant momentum since first physical devices became available. Many quantum algorithms make use of so-called oracles that implement Boolean functions and are queried with highly…

We present a hybrid scheme for quantum computation that combines the modular structure of elementary building blocks used in the circuit model with the advantages of a measurement-based approach to quantum computation. We show how to…

We present a formalism for encoding the logical basis of a qubit into subspaces of multiple physical levels. The need for this multilevel encoding arises naturally in situations where the speed of quantum operations exceeds the limits…

Robust quantum computation requires encoding delicate quantum information into degrees of freedom that are hard for the environment to change. Quantum encodings have been demonstrated in many physical systems by observing and correcting…

Near-term quantum communication protocols suffer inevitably from channel noises, whose alleviation has been mostly attempted with resources such as multiparty entanglement or sophisticated experimental techniques. Generation of multiparty…

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…

Matrices with the displacement structures of circulant, Toeplitz, and Hankel types as well as matrices with structures generalizing these types are omnipresent in computations of sciences and engineering. In this paper, we present efficient…

For quantum algorithms for problems in which the task is to compute an entire field of values, like e.g. computational fluid dynamics (CFD), it is often proposed amplitude encoding w.r.t. multiple qubits; however, the efforts implied by it…

Dense prediction tasks have enjoyed a growing complexity of encoder architectures, decoders, however, have remained largely the same. They rely on individual blocks decoding intermediate feature maps sequentially. We introduce banks, shared…

Block-encoding is a standard framework for embedding matrices into unitary operators in quantum algorithms. Efficient implementation of products between block-encoded matrices is crucial for applications such as Hamiltonian simulation and…

Efficiency techniques are an integral part of Entity Resolution, since its infancy. In this survey, we organized the bulk of works in the field into Blocking, Filtering and hybrid techniques, facilitating their understanding and use. We…

Standard approaches to quantum error correction for fault-tolerant quantum computing are based on encoding a single logical qubit into many physical ones, resulting in asymptotically zero encoding rates and therefore huge resource…

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…

We propose a new cryptographic protocol. It is suggested to encode information in ordinary binary form into many-qubit entangled states with the help of a quantum computer. A state of qubits (realized, e.g., with photons) is transmitted…

We provide modular circuit-level implementations and resource estimates for several methods of block-encoding a dense $N\times N$ matrix of classical data to precision $\epsilon$; the minimal-depth method achieves a $T$-depth of…