Related papers: Ground State Preparation via Qubitization
Quantum algorithms for probing ground-state properties of quantum systems require good initial states. Projection-based methods such as eigenvalue filtering rely on inputs that have a significant overlap with the low-energy subspace, which…
Under suitable assumptions, the algorithms in [Lin, Tong, Quantum 2020] can estimate the ground state energy and prepare the ground state of a quantum Hamiltonian with near-optimal query complexities. However, this is based on a block…
Finding the ground state of a Hamiltonian system is of great significance in many-body quantum physics and quantum chemistry. We propose an improved iterative quantum algorithm to prepare the ground state of a Hamiltonian. The crucial point…
Efficient low-energy state preparation is a key objective in quantum computation and quantum simulation. Quantum imaginary-time evolution replaces real-time dynamics with imaginary-time dynamics, exponentially suppressing higher-energy…
We use matrix product techniques to investigate the performance of two algorithms for obtaining the ground state of a quantum many-body Hamiltonian $H = H_A + H_B$ in infinite systems. The first algorithm is a generalization of the quantum…
The preparation of the ground state of a Hamiltonian $H$ with a large spectral radius has applications in many areas such as electronic structure theory and quantum field theory. Given an initial state with a constant overlap with the…
We propose quantum algorithms for projective ground-state preparation and calculations of the many-body Green's functions directly in frequency domain. The algorithms are based on the linear combination of unitary (LCU) operations and…
State preparation is of fundamental importance in quantum physics, which can be realized by constructing the quantum circuit as a unitary that transforms the initial state to the target, or implementing a quantum control protocol to evolve…
Quantum computing holds immense promise for simulating quantum systems, a critical task for advancing our understanding of complex quantum phenomena. One of the primary goals in this domain is to accurately approximate the ground state of…
We study the problems of state preparation, ground state preparation and quantum state preparation. We propose an analytic approach to a stochastic quantum algorithm which prepares the ground state for $n$-qubit Hamiltonian that is…
We present the problem of approximating the time-evolution operator $e^{-i\hat{H}t}$ to error $\epsilon$, where the Hamiltonian $\hat{H}=(\langle G|\otimes\hat{\mathcal{I}})\hat{U}(|G\rangle\otimes\hat{\mathcal{I}})$ is the projection of a…
We present several improvements to the recently developed ground state preparation algorithm based on the Quantum Eigenvalue Transformation for Unitary Matrices (QETU), apply this algorithm to a lattice formulation of U(1) gauge theory in…
Hamiltonian simulation is a domain where quantum computers have the potential to outperform their classical counterparts. One of the main challenges of such quantum algorithms is increasing the system size, which is necessary to achieve…
Many computationally hard problems can be encoded in quantum Hamiltonians. The solution to these problems is given by the ground states of these Hamiltonians. A state-of-the-art algorithm for finding the ground state of a Hamiltonian is the…
Quantum Imaginary-Time Evolution (QITE) is a powerful method for preparing ground states on quantum hardware. However, executing QITE has costly measurement budgets for general Hamiltonians. Both fidelity and computational cost are strongly…
Most quantum algorithms designed to generate or probe properties of the ground state of a quantum many-body system require as input an initial state with a large overlap with the desired ground state. One approach for preparing such a…
We propose a heuristic method to obtain the approximate groundstate for a Hamiltonian in the qubit form, based on the stabilizer formalism. These states may serve as proper initial states for further refined computation. It would be…
Modeling low energy eigenstates of fermionic systems can provide insight into chemical reactions and material properties and is one of the most anticipated applications of quantum computing. We present three techniques for reducing the cost…
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…
We propose a quantum inverse iteration algorithm which can be used to estimate the ground state properties of a programmable quantum device. The method relies on the inverse power iteration technique, where the sequential application of the…