Systems and methods for performing quantum evolution in quantum computation

A method to operate a hybrid computer comprising at least one digital processor communicatively coupled to a quantum processor, the method performed by the at least one digital processor and comprising:

• receiving, by the at least one digital processor, a sample for a problem Hamiltonian embedded onto the quantum processor by an embedded Hamiltonian, wherein the sample comprises one or more broken chains;
• defining, by the at least one digital processor, a post-processing Hamiltonian having chain component variables, each one of the chain component variables corresponding to a respective set of connected qubits in one of the one or more broken chains that have a same spin direction, wherein a qubit bias of each of the chain component variables in the post-processing Hamiltonian is at least partially based on qubit biases of the embedded Hamiltonian of a respective set of connected qubits;
• embedding, by the at least one digital processor, the post-processing Hamiltonian onto the quantum processor;
• and,
• causing, by the at least one digital processor, the quantum processor to evolve to a state representative of the sample for the problem Hamiltonian in which the one or more broken chains are repaired.

A hybrid computing system comprising:

• at least one digital processor;
• a quantum processor comprising a plurality of qubits, the quantum processor communicatively coupled to the at least one digital processor;
• and,
• at least one non-transitory processor-readable medium communicatively coupleable to the at least one digital processor, the non-transitory processor-readable medium which stores at least one of processor-executable instructions or data which, when executed by the at least one digital processor, cause the at least one digital processor to:
• receive, by the at least one digital processor, a sample for a problem Hamiltonian embedded onto the quantum processor by an embedded Hamiltonian, wherein the sample comprises one or more broken chains,
• define, by the at least one digital processor, a post-processing Hamiltonian having chain component variables, each one of the chain component variables corresponding to a respective set of connected qubits of the plurality of qubits that belong to one of the one or more broken chains, and each qubit in a same set of connected qubits having a same spin direction, wherein a qubit bias of each of the chain component variables in the post-processing Hamiltonian is at least partially based on qubit biases of the embedded Hamiltonian of a respective set of connected qubits,
• embed, by the at least one digital processor, the post-processing Hamiltonian onto the quantum processor, and
• cause, by the at least one digital processor, the quantum processor to evolve to a state representative of the sample for the problem Hamiltonian in which the one or more broken chains are repaired.