Systems and methods for performing quantum evolution in quantum computation
A computational method via a hybrid processor comprising an analog processor and a digital processor includes determining a first classical spin configuration via the digital processor, determining preparatory biases toward the first classical spin configuration, programming an Ising problem and the preparatory biases in the analog processor via the digital processor, evolving the analog processor in a first direction, latching the state of the analog processor for a first dwell time, programming the analog processor to remove the preparatory biases via the digital processor, determining a tunneling energy via the digital processor, determining a second dwell time via the digital processor, evolving the analog processor in a second direction until the analog processor reaches the tunneling energy, and evolving the analog processor in the first direction until the analog processor reaches a second classical spin configuration.
1 . 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 solution to a computational problem represented by a problem Hamiltonian embedded onto the quantum processor by an embedded Hamiltonian, wherein the sample solution to the computational problem comprises one or more broken chains;
defining, by the at least one digital processor, a post-processing Hamiltonian representing the computational problem, the 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 based on the post-processing Hamiltonian to a state representative of the sample solution to the computational problem represented by the problem Hamiltonian in which the one or more broken chains are repaired.
2 . The method of claim 1 , wherein the sample solution to the computational problem includes one or more intact chains, and the defining, by the at least one digital processor, a post-processing Hamiltonian further comprises: determining the qubit bias of each of the chain component variables through collection of qubit biases of the embedded Hamiltonian along a respective set of connected qubits in one of the one or more broken chains and determination of a spin bias contributed by one of the one or more intact chains.
3 . The method of claim 1 , wherein the sample solution to the computational problem includes one or more intact chains that each comprise a set of chained qubits, and the defining, by the at least one digital processor, a post-processing Hamiltonian further comprises: determining the qubit bias of each of the chain component variables based at least partially on interaction strengths between each qubit of the respective set of connected qubits and each qubit of at least one of the sets of chained qubits.
4 . The method of claim 3 , wherein the defining the post-processing Hamiltonian such that the qubit bias of each of the chain component variables is at least partially based on interactions between each qubit of the respective set of connected qubits and each qubit of one or more of the sets of chained qubits further comprises: defining the post-processing Hamiltonian such that a spin bias of the qubit bias of each of the chain component variables is based on a spin value shared by all qubits of the set of chained qubits.
5 . The method of claim 1 , wherein the defining, by the at least one digital processor, a post-processing Hamiltonian further comprises: determining interaction strengths between chain component variables belonging to different ones of the one or more broken chains.
6 . The method of claim 5 , wherein the determining interaction strengths between chain component variables belonging to different ones of the one or more broken chains further comprises: determining a sum of interaction strengths of the embedded Hamiltonian between each qubit of a set of connected qubits of a first broken chain and each qubit of a set of connected qubits of a second broken chain of the one or more broken chains.
7 . The method of claim 1 , wherein the causing, by the at least one digital processor, the quantum processor to evolve based on the post-processing Hamiltonian to a state representative of the sample solution to the computational problem represented by the problem Hamiltonian in which the one or more broken chains are repaired comprises: causing the quantum processor to perform quantum annealing based on the post-processing Hamiltonian.
8 . The method of claim 1 , further comprising: reading out, by the at least one digital processor, the state of the quantum processor representative of the sample solution to the computational problem represented by the problem Hamiltonian in which the one or more broken chains are repaired.
9 . The method of claim 1 , wherein prior to the receiving, by the at least one digital processor, a sample solution to a computational problem represented by a problem Hamiltonian embedded onto the quantum processor, the method comprises:
embedding, by the at least one digital processor, a representation of the computational problem onto the quantum processor according to the embedded Hamiltonian; and,
causing, by the at least one digital processor, the quantum processor to evolve to reach the sample solution to the computational problem represented by the problem Hamiltonian,
and wherein the receiving, by the at least one digital processor, a sample solution to a computational problem represented by a problem Hamiltonian embedded onto the quantum processor comprises:
reading out, by the at least one digital processor, the sample solution to the computational problem represented by the problem Hamiltonian, and
determining, by the at least one digital processor, that the sample solution to the computational problem represented by the problem Hamiltonian comprises the one or more broken chains.
10 . 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 solution to a computational problem represented by a problem Hamiltonian embedded onto the quantum processor by an embedded Hamiltonian, wherein the sample solution to the computational problem comprises one or more broken chains,
define, by the at least one digital processor, a post-processing Hamiltonian representing the computational problem, the 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 based on the post-processing Hamiltonian to a state representative of the sample solution to the computational problem represented by the problem Hamiltonian in which the one or more broken chains are repaired.
11 . The hybrid computing system of claim 10 , wherein the quantum processor is a quantum annealer.
12 . The hybrid computing system of claim 10 , wherein the plurality of qubits comprise a plurality of superconducting qubits.
13 . The hybrid computing system of claim 10 , wherein the sample solution to the computational problem includes one or more intact chains, and the qubit bias of each of the chain component variables is based on:
a sum of qubit biases of the embedded Hamiltonian along a respective set of connected qubits in one of the one or more broken chains; and,
a spin bias contributed by one of the one or more intact chains.
14 . The hybrid computing system of claim 10 , the sample solution to the computational problem includes one or more intact chains that each comprise a set of chained qubits of the plurality of qubits, and the qubit bias of each of the chain component variables is based at least partially on interaction strengths between each qubit of the respective set of connected qubits and each qubit of at least one of the sets of chained qubits.
15 . The hybrid computing system of claim 14 , wherein a spin bias of the qubit bias of each of the chain component variables is based on a spin value shared by all qubits of the set of chained qubits.
16 . The hybrid computing system of claim 10 , wherein the post-processing Hamiltonian comprises interaction strengths between chain component variables belonging to different ones of the one or more broken chains.
17 . The hybrid computing system of claim 15 , wherein each interaction strength between chain component variables belonging to different ones of the one or more broken chains is based on a sum of interaction strengths of the embedded Hamiltonian between each qubit of a set of connected qubits of a first broken chain and each qubit of a set of connected qubits of a second broken chain of the one or more broken chains.
18 . The hybrid computing system of claim 10 , wherein the at least one digital processor reads out the state of the quantum processor representative of the sample solution to the computational problem represented by the problem Hamiltonian in which the one or more broken chains are repaired.
19 . The hybrid computing system of claim 10 , wherein before the at least one digital processor receives the sample solution to the computational problem represented by the problem Hamiltonian embedded onto the quantum processor, the at least one digital processor:
embeds a representation of the computational problem onto the quantum processor according to the embedded Hamiltonian; and,
causes the quantum processor to evolve based on the embedded Hamiltonian to reach the sample solution to the computational problem represented by the problem Hamiltonian,
and wherein causing the at least one digital processor to receive, by the at least one digital processor, a sample solution to a computational problem represented by a problem Hamiltonian embedded onto the quantum processor includes causing the at least one digital processor to:
read out the sample solution to the computational problem represented by the problem Hamiltonian, and
determine that the sample solution to the computational problem represented by the problem Hamiltonian comprises the one or more broken chains.