Efficient reduction of resources for the simulation of Fermionic Hamiltonians on quantum hardware

A computer-implemented method of reducing a number of hardware qubits required on a quantum computer, the method comprising:

• characterizing a Fermionic system in terms of a Hamiltonian, the Fermionic system including Fermions and Fermionic modes;
• transforming the Hamiltonian utilizing a Fermion to qubit mapping;
• finding Pauli symmetry operators of the Hamiltonian;
• transforming the Pauli symmetry operators into single qubit Pauli operators;
• and
• removing every qubit that the single qubit Pauli operators are acting upon, the removing causing a reduced number of hardware qubits to be utilized in the quantum computer.

A computer-implemented method of reducing a number of hardware qubits required on a quantum computer, the method comprising:

• characterizing a Fermionic system in terms of a Hamiltonian, the Fermionic system including Fermions and Fermionic modes with a total number of M Fermionic modes, wherein the Hamiltonian has particle number symmetry and N particles;
• transforming the Hamiltonian utilizing a Fermion to qubit mapping that transforms from M Fermionic modes to M qubits, wherein the M qubits are represented by M-bit strings in a computational basis;
• and
• applying a compression map to the Hamiltonian such that the Hamiltonian having the M qubits is mapped to a transformed Hamiltonian with Q qubits where Q<M, wherein the compression map maps the M-bit strings labeling the M qubits in the computational basis with Hamming weight N to Q-bit strings, the transformed Hamiltonian causing a reduced number of the hardware qubits to be utilized in the quantum computer.

A system comprising:

• memory including computer-executable instructions for reducing a number of hardware qubits required on a quantum computer;
• and
• a processor executing the computer-executable instructions, the computer-executable instructions causing the processor to perform operations comprising:
• characterizing a Fermionic system in terms of a Hamiltonian, the Fermionic system including Fermions and Fermionic modes with a total number of 2M Fermionic modes, wherein the Hamiltonian has a parity symmetry encoded by spin up and spin down parity operators;
• sorting the Fermionic modes on the Hamiltonian, such that the first half of the 2M modes corresponds to spin up and the second half of the 2M modes corresponds to spin down;
• transforming the Hamiltonian and the parity operators utilizing a Fermion to qubit mapping, wherein the Fermion to qubit mapping transforms the parity operators to a first single qubit Pauli operator on a qubit M and a second single qubit Pauli operator on a qubit 2M;
• and
• removing the qubit M having been operated on by the first single qubit Pauli operator and the qubit 2M having been operated on by the second single qubit Pauli operator, the removing causing a reduced number of hardware qubits to be utilized in the quantum computer.

A system comprising:

• memory including computer-executable instructions for reducing a number of hardware qubits required on a quantum computer;
• and
• a processor executing the computer-executable instructions, the computer-executable instructions causing the processor to perform operations comprising:
• characterizing a Fermionic system in terms of a Hamiltonian, the Fermionic system including Fermions and Fermionic modes;
• transforming the Hamiltonian utilizing a Fermion to qubit mapping;
• finding Pauli symmetry operators of the Hamiltonian;
• transforming the Pauli symmetry operators into single qubit Pauli operators;
• and
• removing every qubit that the single qubit Pauli operators are acting upon, the removing causing a reduced number of hardware qubits to be utilized in the quantum computer.