Quantum circuit for chemistry simulation
Quantum circuits for chemistry simulation are based on second quantization Hamiltonian coefficients for one-body and two-body interactions. Jordan-Wigner series that conserve parity can be defined so that selected CNOT gates are removed from the associated circuits. Basis change gates such as Hadamard or Y-gates can be coupled to some or all qubits of a quantum circuit or cancelled in view of corresponding gates in adjacent circuits. In some examples, CNOT gates can be moved to different circuit locations.
1. A quantum circuit, comprising:
at least one reduced Jordan-Wigner circuit coupled to a plurality of qubits and including a plurality of CNOT gates corresponding to respective spin orbitals p,q,r,s, wherein p,q,r,s are integers such that p<q<r<s; and
a reduced Hamiltonian circuit coupled to p,q,r,s qubits associated with the p,q,r,s spin orbitals.
2. The quantum circuit of claim 1 , further comprising a plurality of reduced Hamiltonian circuits situated in series and having different basis change gates.
3. The quantum circuit of claim 2 , further comprising an output side reduced Jordan-Wigner string corresponding to the input side reduced Jordan-Wigner string, the output side reduced Jordan-Wigner string situated after the plurality of reduced Hamiltonian circuits.
4. The quantum circuit of claim 1 , wherein the basis change gates are Hadamard gates and Y-gates.
5. The quantum circuit of claim 1 , wherein CNOT gates of the reduced Jordan-Wigner circuit couple selected qubits in a set of qubits associated with spin orbitals p, . . . , s to each other.
6. The quantum circuit of claim 1 , wherein CNOT gates of the reduced Jordan-Wigner circuit are coupled to an entanglement qubit.
7. The quantum circuit of claim 1 , further comprising at least one one-body reduced Jordan-Wigner circuit coupled to the plurality of qubits and including a plurality of CNOT gates corresponding to respective spin orbitals p,q, wherein p,q are integers such that p<q; and
a one-body reduced Hamiltonian circuit coupled to p,q qubits associated with the p,q spin orbitals.
8. A method of defining a quantum circuit associated with at least a selected one-body or two-body Hamiltonian coefficient associated with second quantization, comprising:
defining a reduced Jordan-Wigner string associated with spin orbitals coupled by a Hamiltonian coefficient;
defining a reduced Hamiltonian circuit based at least on selected Hamiltonian coefficient; and
coupling the reduced Jordan-Wigner string to the reduced Hamiltonian on an input side.
9. The method of claim 8 , further comprising defining a series of reduced Hamiltonian circuits associated with at least two basis operators and one or more Hamiltonian coefficients, and coupling the reduced Jordan-Wigner string in series with the series of reduced Hamiltonian circuits on the input side.
10. The method of claim 8 , wherein the Hamiltonian coefficient is a one-body Hamiltonian coefficient or a two-body Hamiltonian coefficient.
11. The method of claim 8 , wherein the basis operators are defined by Hadamard gates, Y-gates, or combinations thereof.
12. The method of claim 11 , further comprising defining the reduced Hamiltonian circuit to include input side basis change gates corresponding to a selected set of spin orbitals, and output side basis change gates for at most one of the selected spin orbitals.
13. The method of claim 12 , defining the reduced Jordan-Wigner string as a series of CNOT gates coupled to an entanglement qubit.
14. The method of claim 12 , wherein the Hamiltonian coefficient is associated with a two body Hamiltonian coefficient coupling spin orbitals p,q,r,s, wherein p,q,r,s are integers such that p<q<r<s, and the reduced Jordan-Wigner string is an interior Jordan-Wigner string coupling the p,q,r,s spin orbitals.
15. The method of claim 14 , wherein the reduced Hamiltonian circuit is defined to include input side basis change gates for p,q,r,s qubits associated with the p,q,r,s spin orbitals.
16. The method of claim 15 , further comprising defining a plurality of reduced Hamiltonian circuits coupled in series based on selected Hamiltonian coefficients, and coupling a first reduced Hamiltonian circuit of the plurality to the reduced Jordan-Wigner string and a last reduced Hamiltonian circuit of the plurality to a final Jordan-Wigner string.
17. The method of claim 15 , wherein the reduced Jordan-Wigner string is associated with spin orbitals coupled by a Hamiltonian coefficient of the form H pqrs , and further comprising:
defining a reduced Hamiltonian circuit associated a Hamiltonian coefficient of the form H p′q′r′s′ ; and
defining a coupling of the reduced Hamiltonian circuits together with CNOT gates corresponding to respective Jordan-Wigner strings in which CNOT gates coupled to common qubits are omitted, wherein the Jordan-Wigner strings include CNOT gates coupled to an entanglement qubit.
18. The method of claim 17 , further comprising removing at least one CNOT gate associated with the Jordan-Wigner strings in the defined circuit.
19. The method of claim 8 , wherein at least one qubit in the reduced Hamiltonian circuit is situated so as to be processed without a basis change at one or both of an input or output of the reduced Hamiltonian circuit.
20. A computing device having computer executable instructions stored therein for performing a method, comprising:
defining a plurality of reduced Hamiltonian circuits associated with one-body and two-body interactions in a second quantized Hamiltonian;
determining a plurality of Jordan-Wigner series for coupling the reduced Hamiltonian circuits;
cancelling at least selected CNOT gates in the plurality of series that couple to common qubits; and
identifying common basis change gates in the defined reduced Hamiltonian circuits that are applied to a common qubit and removing the common basis change gates from the reduced Hamiltonian circuit definitions.