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Improving the efficiency and accuracy of energy calculations has been of significant and continued interest in the area of materials informatics, a field that applies machine learning techniques to computational materials data. Here, we…
In this thesis, we focus on the energetic analysis within autonomous quantum systems. To this aim, we propose a novel and general formalism for a dynamic description of the energy exchanges between interacting subsystems. From the Schmidt…
A major obstacle to non-convex optimization is the problem of getting stuck in local minima. We introduce a novel metaheuristic to handle this issue, creating an alternate Hamiltonian that shares minima with the original Hamiltonian only…
We propose the variational quantum cavity method to construct a minimal energy subspace of wave vectors that are used to obtain some upper bounds for the energy cost of the low-temperature excitations. Given a trial wave function we use the…
The variational approach is a cornerstone of computational physics, considering both conventional and quantum computing computational platforms. The variational quantum eigensolver (VQE) algorithm aims to prepare the ground state of a…
One of the most promising applications for near term quantum computers is the simulation of physical quantum systems, particularly many-electron systems in chemistry and condensed matter physics. In solid state physics, finding the correct…
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…
We describe an algorithm that computes the ground state energy and correlation functions for 2-local Hamiltonians in which interactions between qubits are weak compared to single-qubit terms. The running time of the algorithm is polynomial…
The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer. We show here that this is the case even for translationally invariant systems. We also show that a quantum…
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…
The No Low-energy Trivial States (NLTS) conjecture of Freedman and Hastings, 2014 -- which posits the existence of a local Hamiltonian with a super-constant quantum circuit lower bound on the complexity of all low-energy states --…
Ensuring a satisfactory statistical convergence of anharmonic thermodynamic properties requires sampling of many atomic configurations, however the methods to obtain those necessarily produce correlated samples, thereby reducing the…
Accurate solution of the many-electron problem including correlations remains intractable except for few-electron systems. Describing interacting electrons as a superposition of independent electron configurations results in an apparent…
We design two variational algorithms to optimize specific 2-local Hamiltonians defined on graphs. Our algorithms are inspired by the Quantum Approximate Optimization Algorithm. We develop formulae to analyze the energy achieved by these…
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…
A quantum state for being an eigenstate of some local Hamiltonian should be constraint by zero energy variance and consequently, the constraint is rather strong that a single eigenstate may uniquely determine the Hamiltonian. For…
We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the…
Many physically interesting models show a quantum phase transition when a single parameter is varied through a critical point, where the ground state and the first excited state become degenerate. When this parameter appears as a coupling…
The estimation of low energies of many-body systems is a cornerstone of computational quantum sciences. Variational quantum algorithms can be used to prepare ground states on pre-fault-tolerant quantum processors, but their lack of…
We introduce a variational approach for preparing low energy states of arbitrary target Hamiltonians. The protocol is defined in terms of a repeated cycle consisting of p layers of unitary gates applied to the system and ancilla "bath"…