Related papers: Unitaria: Quantum Linear Algebra via Block Encodin…
Quaternion-valued representations provide a convenient way to model coupled multi-channel signals (e.g., RGB imagery, polarization data, vector fields, and multi-detector time series). Yet practical and numerically reliable software support…
Currently available quantum hardware allows for small scale implementations of quantum machine learning algorithms. Such experiments aid the search for applications of quantum computers by benchmarking the near-term feasibility of candidate…
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 address the question of efficient implementation of quantum protocols, with small communication and entanglement, and short depth circuit for encoding or decoding. We introduce two new methods to achieve this, the first method involving…
Quantum algorithms for computing classical nonlinear maps are widely known for toy problems but might not suit potential applications to realistic physics simulations. Here, we propose how to compute a general differentiable invertible…
To implement a quantum error correction protocol, we first need a scheme to prepare our state in the correct subspace of the code, and this can be done using a unitary encoding circuit. Majorana codes are special since any gates that…
Vectorized quantum block encoding provides a way to embed classical data into Hilbert space, offering a pathway for quantum models, such as Quantum Transformers (QT), that replace classical self-attention with quantum circuit simulations to…
We present a theoretical analysis of the paradigm of encoded universality, using a Lie algebraic analysis to derive specific conditions under which physical interactions can provide universality. We discuss the significance of the tensor…
As the most central and computationally intensive component of deep neural networks, the execution efficiency of matrix multiplication directly determines the training and inference performance of models. Harnessing the parallel processing…
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations…
Within the general context of the architecture in quantum computer design, this paper aims is to provide a general strategy to obtain a block-matrix representation of quantum gates applied to qubits placed in arbitrary positions over an…
Unitary Fourier transform lies at the core of the multitudinous computational and metrological algorithms. Here we show experimentally how the unitary Fourier transform-based phase estimation protocol, used namely in quantum metrology, can…
The field of quantum algorithms is vibrant. Still, there is currently a lack of programming languages for describing quantum computation on a practical scale, i.e., not just at the level of toy problems. We address this issue by introducing…
We propose a protocol for solving systems of linear algebraic equations via quantum mechanical methods using the minimal number of qubits. We show that $(M+1)$-qubit system is enough to solve a system of $M$ equations for one of the…
With the applications of quantum computing becoming more and more widespread, finding ways that allow end users without experience in the field to apply quantum computers to solve their individual problems is becoming a crucial task.…
In the study of quantum computation, data is represented in terms of linear operators which form a generalized model of probability, and computations are most commonly described as products of unitary transformations, which are the…
Matrix-product unitaries (MPUs) are many-body unitary operators that, as a consequence of their tensor-network structure, preserve the entanglement area law in 1D systems. However, it is unknown how to implement an MPU as a quantum circuit…
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…
When writing high-performance code for numerical computation in a scripting language like MATLAB, it is crucial to have the operations in a large for-loop vectorized. If not, the code becomes too slow to use, even for a moderately large…
The use of advanced quantum neuron models for pattern recognition applications requires fault tolerance. Therefore, it is not yet possible to test such models on a large scale in currently available quantum processors. As an alternative, we…