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 computer-implemented method and system for implementing a n-fold fermionic excitation generator using linear combination of directly differentiable operators on a quantum computer. Computer-readable data is generated and stored which when executed on the quantum computer, causes a quantum circuit of the quantum computer to execute repeatedly to perform a sequence of operations that implements the unitary (I) generated by a fermionic n-fold excitation operator G. The Gradient with respect to the angle ? of arbitrary expectation values involving the unitary operation can, in the general case, be evaluated by four expectation values obtained from replacing the corresponding unitary with fermionic shift operations (II). Fermionic shift operations can be constructed through the original unitary and unitary operations generated by the nullspace projector P0 of the fermionic excitation generator. Other operators and generators are disclosed.

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.

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.

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.