Abstract: A method for encoding quantum information comprising at least one Kronecker product of Pauli X, Y, Z matrices, an identity matrix e and a phase term comprises providing binary indices for each term and using them in a binary representation of the Kronecker product, including first and second arrays corresponding to respective digits of a two-digit binary code. The encoding method provides computational and storage advantages. A set of ILC entanglers can be generated using the encoding method. Entanglers encoded in a binary representation can be conveniently prioritized and selected for a provided Hamiltonian, including in a multiple loop iterative fashion, to provide a set of quantum logic gates in a quantum circuit of a quantum computer.

Abstract: A method of solving a problem can include providing a fermionic Hamiltonian, transformation of the fermionic Hamiltonian to qubit operators, transformation of the fermionic Hamiltonian in qubit operators to a mean-field Hamiltonian, and embedding the Hamiltonian onto a quantum computer. Such systems and methods may improve upon existing methods for solving electronic structure problems on a computer by adapting the problem to available hardware, reducing computational cost, and reducing the number of required qubits to solve electronic structure problems for larger number of atoms.

Abstract: A method of solving a problem can include providing a fermionic Hamiltonian, transformation of the fermionic Hamiltonian to qubit operators, transformation of the fermionic Hamiltonian in qubit operators to a mean-field Hamiltonian, and embedding the Hamiltonian onto a quantum computer. Such systems and methods may improve upon existing methods for solving electronic structure problems on a computer by adapting the problem to available hardware, reducing computational cost, and reducing the number of required qubits to solve electronic structure problems for larger number of atoms.