Related papers: Block-Encoding Tensor Networks and QUBO Embeddings
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…
This work presents a novel tensor network algorithm for solving Quadratic Unconstrained Binary Optimization (QUBO) problems, Quadratic Unconstrained Discrete Optimization (QUDO) problems, and Tensor Quadratic Unconstrained Discrete…
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…
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…
Quantum algorithms reformulate computational problems as quantum evolutions in a large Hilbert space. Most quantum algorithms assume that the time-evolution is perfectly unitary and that the full Hilbert space is available. However, in…
The quantum singular value transformation is a powerful quantum algorithm that allows one to apply a polynomial transformation to the singular values of a matrix that is embedded as a block of a unitary transformation. This paper shows how…
We develop new algorithms for Quantum Singular Value Transformation (QSVT), a unifying framework that encapsulates most known quantum algorithms and serves as the foundation for new ones. Existing implementations of QSVT rely on block…
We adopt a two-dimensional tensor-network (TN) ansatz to simulate variational quantum algorithms on two-dimensional qubit architectures, demonstrating its capability to accurately simulate deep circuits through the Quantum Approximate…
Tensor-Network (TN) states are efficient parametric representations of ground states of local quantum Hamiltonians extensively used in numerical simulations. Here we encode a TN ansatz state directly into a quantum simulator, which can…
Tensor networks provide succinct representations of quantum many-body states and are an important computational tool for strongly correlated quantum systems. Their expressive and computational power is characterized by an underlying…
Quadratic Unconstrained Binary Optimization (QUBO) is a standard NP-hard optimization problem. Recently, it has gained renewed interest through quantum computing, as QUBOs directly reduce to the Ising model, on which quantum annealing…
Data encoding remains a fundamental bottleneck in quantum machine learning, where amplitude encoding of high-dimensional classical vectors into quantum states incurs exponential cost. In this work, we propose a pre-trained tensor-train (TT)…
Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we…
We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we…
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…
Quantum Signal Processing (QSP) and Quantum Singular Value Transformation (QSVT) provide an efficient framework for implementing polynomials of block-encoded matrices, and thus offer a systematic approach to quantum algorithm design.…
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.…
This research extends quantum singular value transformation (QSVT) for general bounded operators embedded in unitary operators on possibly infinite-dimensional Hilbert spaces. Through in-depth mathematical exploration, we have achieved a…
Network embedding is a general-purpose machine learning technique that encodes network structure in vector spaces with tunable dimension. Choosing an appropriate embedding dimension -- small enough to be efficient and large enough to be…
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…