![]() In some embodiments, the system may comprise a quantum computer which is a quantum annealer. ![]() In some embodiments, the system may comprise a transformation of the fermionic Hamiltonian comprising using the Bravyi-Kitaev method. In some embodiments, the system may comprise a transformation of the fermionic Hamiltonian comprising using the Jordan-Wigner transformation. In some embodiments, the system may comprise a qubit Hamiltonian comprising a transformation of the fermionic Hamiltonian. In some embodiments, the system may comprise a qubit Hamiltonian which is a mean-field Hamiltonian. In some embodiments, the molecule may be a molecular crystal. In some embodiments, the molecule may be a polymer. In some embodiments, the molecule may comprise one or more main group elements. In some embodiments, the molecule may be an organic optoelectronic material. In some embodiments, the solution may comprise a quantum state which is a ground state. In some embodiments, the system may comprise a solution to the problem being a quantum state of a molecule. In some embodiments, the system may comprise a value of the bias terms and a value of the coupling terms which is determined using a classical computer. In some embodiments, the system may comprise a qubit Hamiltonian in Pauli Z rotation comprising bias terms and coupling terms for each of the plurality of qubits. In some embodiments, the system may comprise a qubit Hamiltonian comprising a quadratic unconstrained boundary optimization problem. In some embodiments, the system may comprise a qubit Hamiltonian comprising an Ising type Hamiltonian. ![]() In some embodiments, the system may comprise the operation of one or more quantum logic gates comprising a qubit mean-field ansatz. In some embodiments, the system may comprise a spin coherent state comprising an expression in spherical polar coordinates on the Bloch sphere. In some embodiments, the system comprises a quantum computer comprising a plurality of qubits a qubit Hamiltonian, wherein one or more coordinates in the qubit Hamiltonian comprises a parametrization in spin coherent states, wherein the parametrization comprises either an operation of one or more quantum logic gates or an expression of the qubit Hamiltonian in Pauli Z rotations, wherein the Hamiltonian is embedded on the quantum computer, wherein one or more eigenvalues of the qubit Hamiltonian is a variational upper bound to an exact energy, and wherein a lower eigenvalue of the qubit Hamiltonian comprises a solution to the problem. In an aspect, a system operable to solve a problem is provided. Systems and methods disclosed herein may modify the Hamiltonian to improve embedding on a quantum annealer For example, since each quantum gate operation may introduce noise into the calculation, reducing the number of gate operations may reduce the final error. ![]() the circuit depth) to perform a calculation and, in some cases, may even reduce the number of quantum circuit gate operations to achieve the full configuration interaction equivalent energy. Systems and methods disclosed herein may reduce the number of quantum circuit gate operations (e.g. Recognized herein is a need to improve computational accuracy and to reduce the number of qubits required to simulate a molecule of a given size, thereby reducing the computational cost and improving the function of the quantum computer. While it may be possible to simulate larger molecules as quantum computing technology improves, even as greater numbers of qubits become available there will remain a need to simulate larger and larger molecules. However, currently available quantum computers may have significant hardware limitations in terms of number of qubits available, gate depth, and gate fidelity/accuracy, which may limit the use of such hardware. Quantum computers may be particularly suited to solving these problems. In molecular simulations, electrons, protons, and neutrons-all quantum mechanical in nature-interact in many body interactions whose solution may be intractable using conventional computers and conventional numerical methods due to long computational times. 62/678,936, filed May 31, 2018, which applications are incorporated herein by reference in their entireties. This application claims the benefit of U.S.
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