Related papers: Quantum Computational Method of Finding the Ground…
We present a method to estimate the probabilities of outcomes of a quantum observable, its mean value, and higher moments by measuring any other observable. This method is general and can be applied to any quantum system. In the case of…
Iterative phase estimation has long been used in quantum computing to estimate Hamiltonian eigenvalues. This is done by applying many repetitions of the same fundamental simulation circuit to an initial state, and using statistical…
Preparing the ground state of a Hamiltonian is a problem of great significance in physics with deep implications in the field of combinatorial optimization. The adiabatic algorithm is known to return the ground state for sufficiently long…
The calculation of excited state energies of electronic structure Hamiltonians has many important applications, such as the calculation of optical spectra and reaction rates. While low-depth quantum algorithms, such as the variational…
We present exact results for the periodic Anderson model for finite Hubbard interaction 0 <= U < +infinity on certain restricted domains of the model's phase diagram, in d=1 dimension. Decomposing the Hamiltonian into positive semidefinite…
We propose to use a quantum adiabatic and simulated-annealing framework to compute theground state of small molecules. The initial Hamiltonian of our algorithms is taken to be themaximum commuting Hamiltonian that consists of a maximal set…
A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground state energy analytically using our method provided certain consistency relations are satisfied. Analytic…
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…
We describe a semidefinite relaxation method which finds lower bounds to the ground state energy of a quantum Hamiltonian subject to Hermitian linear constraints along with approximations of ground state expectation values. We show that…
We present and analyze large-scale simulation results of a hybrid quantum-classical variational method to calculate the ground state energy of the anti-ferromagnetic Heisenberg model. Using a massively parallel universal quantum computer…
Calculating the molecular ground-state energy is a central challenge in computational chemistry. Conventional methods such as the Complete Active Space Configuration Interaction scale exponentially with molecular size, limiting their…
Quantum phase transitions materialize as level crossings in the ground-state energy when the parameters of the Hamiltonian are varied. The resulting ground-state phase diagrams are straightforward to determine by exact diagonalization on…
One of the main applications of future quantum computers will be the simulation of quantum models. While the evolution of a quantum state under a Hamiltonian is straightforward (if sometimes expensive), using quantum computers to determine…
We formulate a novel ground state quantum computation approach that requires no unitary evolution of qubits in time: the qubits are fixed in stationary states of the Hamiltonian. This formulation supplies a completely time-independent…
The study of ground-state properties of the Fermi-Hubbard model is a long-lasting task in the research of strongly correlated systems. Owing to the exponentially growing complexity of the system, a quantitative analysis usually demands high…
We present a statistical mechanics description to study the ground state of quantum systems. In this approach, averages for the complete system are calculated over the non-interacting energy levels. Taking different interaction parameter,…
We introduce two methods for speeding up adiabatic quantum computations by increasing the energy between the ground and first excited states. Our methods are even more general. They can be used to shift a Hamiltonian's density of states…
The energy spectrum of Dicke Hamiltonians with and without the rotating wave approximation for arbitrary atom-number is obtained analytically with the variational method, in which the effective pseudo-spin Hamiltonian resulted from the…
It is shown that the quantum ground state energy of particle of mass m and electric charge e moving on a compact Riemann surface under the influence of a constant magnetic field of strength B is E_0=eB/2m. Remarkably, this formula is…
Drawing inspiration from the Lyapunov control technique for quantum systems, feedback-based quantum algorithms have been proposed for calculating the ground states of Hamiltonians. In this work, we consider extending these algorithms to…