Related papers: Real-Time Krylov Theory for Quantum Computing Algo…
Krylov subspace methods in quantum dynamics identify the minimal subspace in which a process unfolds. To date, their use is restricted to time evolutions governed by time-independent generators. We introduce a generalization valid for…
Quantum algorithms based on classical processing of individual samples have recently emerged as the most effective and robust methods to approximate ground-state wave functions of many-body quantum systems on pre-fault-tolerant and…
Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory, but offer higher accuracy. Accordingly, quantum computers have been…
Theoretical descriptions of excited states of molecular systems in high-energy regimes are crucial for supporting and driving many experimental efforts at light source facilities. However, capturing their complicated correlation effects…
Computational methods are the most effective tools we have besides scientific experiments to explore the properties of complex biological systems. Progress is slowing because digital silicon computers have reached their limits in terms of…
Quantum Computing allows, in principle, the encoding of the exponentially scaling many-electron wave function onto a linearly scaling qubit register, offering a promising solution to overcome the limitations of traditional quantum chemistry…
First-quantized, real-space formulations of quantum chemistry on quantum computers are appealing: qubit count scales logarithmically with spatial resolution, and Coulomb operators achieve quadratic instead of quartic computational scaling…
Many researchers have been heavily investigated on quantum phase estimation (QPE) algorithms to find the unknown phase, since QPE is the core building block of the most quantum algorithms such as the Shor's factoring algorithm, quantum…
Near-term quantum computers will be limited in the number of qubits on which they can process information as well as the depth of the circuits that they can coherently carry out. To-date, experimental demonstrations of algorithms such as…
Harnessing the full power of nascent quantum processors requires the efficient management of a limited number of quantum bits with finite lifetime. Hybrid algorithms leveraging classical resources have demonstrated promising initial results…
Quantum computers have been widely speculated to offer significant advantages in obtaining the ground state of difficult Hamiltonian in chemistry and physics. In this work, we first propose a Lyapunov control-inspired strategy to accelerate…
Variational quantum eigensolvers (VQEs) are among the most promising quantum algorithms for solving electronic structure problems in quantum chemistry, particularly during the Noisy Intermediate-Scale Quantum (NISQ) era. In this study, we…
This thesis explores the application of the Symmetry-Breaking/Symmetry-Restoration methodology on quantum computers to better approximate a Hamiltonian's ground state energy within a variational framework in many-body physics. This involves…
The variational quantum eigensolver (VQE) is one of the most appealing quantum algorithms to simulate electronic structure properties of molecules on near-term noisy intermediate-scale quantum devices. In this work, we generalize the VQE…
Krylov quantum diagonalization methods have emerged as a promising use case for quantum computers. However, many existing implementations rely on controlled operations, which pose challenges to near-term quantum hardware. We introduce a…
Quantum chemistry is envisioned as an early and disruptive application for quantum computers. Yet, closer scrutiny of the proposed algorithms shows that there are considerable difficulties along the way. Here, we propose two criteria for…
Quantum Krylov subspace diagonalization is a prominent candidate for early fault tolerant quantum simulation of many-body and molecular systems, but so far the focus has been mainly on computing ground-state energies. We go beyond this by…
The Variational Quantum Eigensolver (VQE) algorithm has been developed to target near term Noisy Intermediate Scale Quantum (NISQ) computers as a method to find the eigenvalues of Hamiltonians. Unlike fully quantum algorithms such as…
The task of estimating the ground state of Hamiltonians is an important problem in physics with numerous applications ranging from solid-state physics to combinatorial optimization. We provide a hybrid quantum-classical algorithm for…
Determining the ground state of a many-body Hamiltonian is a central problem across physics, chemistry, and combinatorial optimization, yet it is often classically intractable due to the exponential growth of Hilbert space with system size.…