Determining properties of molecules and materials is one of the premier applications of quantum computing. A major question in the thesis is: how might we use long- and near-term quantum computers to solve problems of chemical interest? First, we give an overview of the standard model in electronic structure theory. Electronic structure methods have been improved significantly in the last decades; however, it is still a non-trivial task to fit experimental results for complex molecular systems. Second, we introduce quantum computation and quantum algorithms as an alternative device to solve the electronic structure problem. In the remaining part of the thesis, we describe the research projects. The thesis covers two (rather different) research directions: software and hardware projects. For the software part, we contribute with two new algorithms: Phase-Estimation Interval Target Energy Readout (PHILTER) and Recursive Variational Series Estimation (RVSE), where both are designed to be run on a quantum digital computer and extract materials and molecular properties. The PHILTER algorithm is a modification of the Quantum Phase Estimation and is designed to compute excited state energies within a target energy-interval for cases where good approximations for the states in the target energy-interval are either unknown or hard to prepare. For the RVSE algorithm, we pose the question: how might we use imperfect near-term quantum computers to solve problems of practical value? In this work, we introduce a method to compute expectation values of general functions of a Hamiltonian with respect to an input state using low depth quantum circuits suitable for noisy intermediate-scale quantum computers. For the hardware part, we propose a new chemical quantum computer by using molecular electronics as a basis for quantum computing. In this work, we pose the question: can scattering of electrons in molecules produce quantum gates? We construct one-qubit gates using one-electron scattering in molecules, and two-qubit controlled-phase gates using electron-electron scattering along metallic leads. We show initial applications of the framework by illustrating one-qubit gates using the molecular electronic structure of molecular hydrogen as a baseline model.
It is exponentially hard to simulate quantum systems by classical algorithms, while quantum computer could in principle solve this problem polynomially. We demonstrate such an quantum-simulation algorithm on our NMR system to simulate an hydrogen molecule and calculate its ground-state energy. We utilize the NMR interferometry method to measure the phase shift and iterate the process to get a high precision. Finally we get 17 precise bits of the energy value, and we also analyze the source of the error in the simulation.
We present an efficient quantum algorithm for preparing a pure state on a quantum computer, where the quantum state corresponds to that of a molecular system with a given number
m of electrons occupying a given number
n of spin orbitals. Each spin orbital is mapped to a qubit: the states
∣1⟩ and
∣0⟩ of the qubit represent, respectively, whether the spin orbital is occupied by an electron or not. To prepare a general state in the full Hilbert space of
n qubits, which is of dimension
2n,
O(2n) controlled-NOT gates are needed, i.e., the number of gates scales exponentially with the number of qubits. We make use of the fact that the state to be prepared lies in a smaller Hilbert space, and we find an algorithm that requires at most
O(2m+1nm/m!) gates, i.e., scales polynomially with the number of qubits
n, provided
n⪢m. The algorithm is simulated numerically for the cases of the hydrogen molecule and the water molecule. The numerical simulations show that when additional symmetries of the system are considered, the number of gates to prepare the state can be drastically reduced, in the examples considered in this paper, by several orders of magnitude, from the above estimate.
We present an efficient quantum algorithm for preparing a pure state on a quantum computer, where the quantum state corresponds to that of a molecular system with a given number
m of electrons occupying a given number
n of spin orbitals. Each spin orbital is mapped to a qubit: the states
∣1> and
∣0> of the qubit represent, respectively, whether the spin orbital is occupied by an electron or not. To prepare a general state in the full Hilbert space of
n qubits, which is of dimension
2n%,
O(2n) CNOT gates are needed, i.e. the number of gates scales \emph{% exponentially} with the number of qubits. We make use of the fact that the state to be prepared lies in a smaller Hilbert space, and we find an algorithm that requires at most
O((2n)m/m!) CNOT gates, i.e. scales \emph{polynomially} with the number of qubits
n, provided
n≫m. The algorithm is simulated numerically to prepare the electronic states of the hydrogen molecule and the water molecule. We show that when additional symmetries of the system are considered, the number of gates to prepare the state can be reduced dramatically.
Simulating a quantum system is more efficient on a quantum computer than on a classical computer. The time required for solving the Schrödinger equation to obtain molecular energies has been demonstrated to scale polynomially with system size on a quantum computer, in contrast to the well-known result of exponential scaling on a classical computer. In this paper, we present a quantum algorithm to obtain the energy spectrum of molecular systems based on the multiconfigurational self-consistent field (MCSCF) wave function. By using a MCSCF wave function as the initial guess, the excited states are accessible. Entire potential energy surfaces of molecules can be studied more efficiently than if the simpler Hartree-Fock guess was employed. We show that a small increase of the MCSCF space can dramatically increase the success probability of the quantum algorithm, even in regions of the potential energy surface that are far from the equilibrium geometry. For the treatment of larger systems, a multi-reference configuration interaction approach is suggested. We demonstrate that such an algorithm can be used to obtain the energy spectrum of the water molecule.
Quantum computers are capable to efficiently perform full configuration interaction (FCI) calculations of atoms and molecules by using the quantum phase estimation (QPE) algorithm. Because the success probability of the QPE depends on the overlap between approximate and exact wave functions, efficient methods to prepare accurate initial guess wave functions enough to have sufficiently large overlap with the exact ones are highly desired. Here, we propose a quantum algorithm to construct the wave function consisting of one configuration state function, which is suitable for the initial guess wave function in QPE-based FCI calculations of open-shell molecules, based on the addition theorem of angular momentum. The proposed quantum algorithm enables us to prepare the wave function consisting of an exponential number of Slater determinants only by a polynomial number of quantum operations.