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Patent US10417370
Issued 2019-09-17
Classical Simulation Constants And Ordering For Quantum Chemistry Simulation
Quantum computations based on second quantization are performed by applying one body and two body terms in a selected order. Typically, terms associated with operators that commute are applied prior to application of other terms. In a particular example, one body terms of the form hpp are applied first, followed by two body terms of the form hprrp.
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- 1. A computer executable method for designing a quantum circuit for computation using a plurality of qubits, the method comprising:
defining a first set of quantum circuits based on one-body Hamiltonian coefficients, the set including one or more gates that apply control-Z rotations based on corresponding one-body Hamiltonian coefficients of the form hpp, wherein p is an integer denoting a spin orbital; defining a second set of quantum circuits based on two-body Hamiltonian coefficients, the set including one or more gates that apply control-Z rotations based on corresponding two-body Hamiltonian coefficients of the form hprrp, wherein r is an integer denoting a spin orbital; and arranging first and second sets of quantum circuits based on the definitions of the first and second sets of quantum circuits so that a plurality of qubits is coupled to the first set of quantum circuits prior to coupling to the second set of quantum circuits.
- 12. An apparatus for specifying a quantum computing circuit, comprising:
a memory device storing one-body and two-body Hamiltonian coefficients associated with a material of interest; and a processor that:
receives the stored one-body and two-body Hamiltonian coefficients;
selects an order in which quantum gates associated with the stored one-body and two-body Hamiltonian coefficients hpq, hpqrs, respectively are to be applied to a plurality of qubits, wherein p, q, r, s are integers identifying orbitals, such that coefficients are applied in the order hpp, for all p, hprrp, for all p and r; and
defines a sequence of quantum gates based on the order.
- 20. A quantum circuit, comprising:
a first series of quantum gates defined based on one-body Hamiltonian coefficients associated with a material of interest, the Hamiltonian coefficients corresponding to commuting operators, wherein the first series of quantum gates is defined based on one-body Hamiltonian coefficients of the form hpp, wherein p is an integer denoting an orbital; and an intermediate series of quantum gates defined based on one-body and two-body Hamiltonian coefficients of the forms hpq, hprrq, respectively, wherein p, q, r, s are integers denoting orbitals and p≠q, and the series includes alternating pairs of gates hpq, hprrq for at least some values of p, q, r; and a second series of quantum gates defined based on one-body or two-body Hamiltonian coefficients associated with the material of interest, wherein the Hamiltonian coefficients are non-commutative, wherein the second series of quantum gates is defined based on two-body Hamiltonian coefficients of the form hpqrs, wherein p, q, r, s are integers denoting orbitals and p≠s and q≠r; and wherein the first series of quantum gates, the intermediate series of quantum gates, and the second series of quantum gates are situated so that the first series precedes the intermediate series and the intermediate series precedes the second series.
