Related papers: Quantum Discrete Variable Representations
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
Inspired by random walk on graphs, diffusion map (DM) is a class of unsupervised machine learning that offers automatic identification of low-dimensional data structure hidden in a high-dimensional dataset. In recent years, among its many…
This work proposes double-bracket iterations as a framework for obtaining diagonalizing quantum circuits. Their implementation on a quantum computer consists of interlacing evolutions generated by the input Hamiltonian with diagonal…
Variational Quantum Circuits are being used as versatile Quantum Machine Learning models. Some empirical results exhibit an advantage in supervised and generative learning tasks. However, when applied to Reinforcement Learning, less is…
We introduce a quantum extension of dynamic programming, a fundamental computational method that efficiently solves recursive problems using memory. Our innovation lies in showing how to coherently generate recursion step unitaries by using…
Due to the significant progress made in the implementation of quantum hardware, efficient methods and tools to design corresponding algorithms become increasingly important. Many of these tools rely on functional representations of certain…
Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed to determine the singular values and their associated singular vectors of a given matrix. Although…
Variational quantum algorithms (VQAs) provide a promising approach to achieving quantum advantage for practical problems on near-term noisy intermediate-scale quantum (NISQ) devices. Thus far, most studies on VQAs have focused on…
Quantum variational algorithms (QVAs) are increasingly potent tools for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. This work examines the application of the Variational Quantum Eigensolver (VQE)…
A quantum algorithm for solving the advection equation by embedding the discrete time-marching operator into Hamiltonian simulations is presented. One-dimensional advection can be simulated directly since the central finite difference…
In the near future, material and drug design may be aided by quantum computer assisted simulations. These have the potential to target chemical systems intractable by the most powerful classical computers. However, the resources offered by…
One of the most promising applications of quantum computing is simulating quantum many-body systems. However, there is still a need for methods to efficiently investigate these systems in a native way, capturing their full complexity. Here,…
We propose a divide-and-conquer method for the quantum-classical hybrid algorithm to solve larger problems with small-scale quantum computers. Specifically, we concatenate a variational quantum eigensolver (VQE) with a reduction in the…
Quantum dynamics simulations (QDSs) are one of the most highly anticipated applications of quantum computing. Quantum circuit depth for implementing Hamiltonian simulation algorithms is commonly time dependent so that long time dynamics…
Variational quantum algorithms (VQAs) have emerged as a promising approach for achieving quantum advantage on current noisy intermediate-scale quantum devices. However, their large-scale applications are significantly hindered by…
Variational quantum algorithms offer a promising framework for solving eigenvalue problems on near-term quantum hardware, yet their applicability beyond electronic structure calculations remains relatively unexplored. In this work, we…
Quantum Random Access Memory (QRAM) holds the promise of enabling several large scale applications of quantum computers. However, designing fault tolerant QRAMs for large scale applications is still an open problem due to the poor error and…
The use of digitally reconstructed radiographs (DRRs) to solve inverse problems such as slice-to-volume registration and 3D reconstruction is well-studied in preoperative settings. In intraoperative imaging, the utility of DRRs is limited…
Adaptive Variational Quantum Dynamics (AVQD) algorithms offer a promising approach to providing quantum-enabled solutions for systems treated within the purview of open quantum dynamical evolution. In this study, we employ the unrestricted…
With the aim of establishing a framework to efficiently perform the practical application of quantum chemistry simulation on near-term quantum devices, we envision a hybrid quantum--classical framework for leveraging problem decomposition…