Related papers: Dissipative ground state preparation and the Dissi…
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…
Dissipative state engineering is a general term for a protocol which prepares the ground state of a complex many-body Hamiltonian using engineered dissipation or engineered environments. Recently, it was shown that a version of this…
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 local Hamiltonian (LH) problem, the quantum analog of the classical constraint satisfaction problem, is a cornerstone of quantum computation and complexity theory. It is known to be QMA-complete, indicating that it is challenging even…
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…
A new Quasiparticle Random Phase Approximation approach is presented. The corresponding ground state is variationally determined and exhibits a minimum energy. New solutions for the ground state, some with spontaneously broken symmetry, of…
Local Hamiltonian Problems (LHPs) are important problems that are computationally QMA-complete and physically relevant for many-body quantum systems. Quantum MaxCut (QMC), which equates to finding ground states of the quantum Heisenberg…
The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm for quantum simulation that can be run on near-term quantum hardware. A challenge in VQE -- as well as any other heuristic algorithm for finding ground states…
The deterministic preparation of quantum many-body ground states is essential for advanced quantum simulation, yet optimal algorithms often require prohibitive hardware resources. Here, we propose a highly efficient, non-variational…
The design of time-independent local Hamiltonians that realise quantum algorithms is derived from the study of perfect state transfer. The novel features of this evolution are the perfect realisation of the computation, and the ability to…
The direct compilation of algorithm-specific graph states in measurement-based quantum computation (MBQC) can lead to resource reductions in terms of circuit depth, entangling gates, and even the number of physical qubits. In this work, we…
This paper explores several aspects of the adiabatic quantum computation model. We first show a way that directly maps any arbitrary circuit in the standard quantum computing model to an adiabatic algorithm of the same depth. Specifically,…
Under suitable assumptions, the quantum phase estimation (QPE) algorithm is able to achieve Heisenberg-limited precision scaling in estimating the ground state energy. However, QPE requires a large number of ancilla qubits and large circuit…
The propagation of errors severely compromises the reliability of quantum computations. The quantum adiabatic algorithm is a physically motivated method to prepare ground states of classical and quantum Hamiltonians. Here, we analyze the…
We present a novel method for improving the quantum simulation of the ground state energy of molecules. We perform a pre-processing step classically, which reduces the dimensionality of the problem by generating a custom mapping which…
We propose a distinct approach to solving linear and nonlinear differential equations (DEs) on quantum computers by encoding the problem into ground states of effective Hamiltonian operators. Our algorithm relies on constructing such…
Accurate state preparation is a critical bottleneck in many quantum algorithms, particularly those for ground state energy estimation. Even in fault-tolerant quantum computing, preparing a quantum state with sufficient overlap to the…
Quantum optimization algorithms offer a promising route to finding the ground states of target Hamiltonians on near-term quantum devices. None the less, it remains necessary to limit the evolution time and circuit depth as much as possible,…
The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are…
Large-scale eigenvalue problems pose a significant challenge to classical computers. While there are efficient quantum algorithms for unitary or Hermitian matrices, eigenvalue problems for non-normal matrices remain open in quantum…