Error reduction and, or, correction in analog computing including quantum processor-based computing
The systems, devices, articles, and methods described herein generally relate to analog computers, for example quantum processors comprising qubits, couplers, and, or cavities. Analog computers, for example quantum processor based computers, are the subject of various sources of error which can hinder operation, potentially reducing computational accuracy and speed. Sources of error can be broadly characterized, for example as i) a background susceptibility do to inherently characteristics of the circuitry design, ii) as an h/J ratio imbalance, iii) bit flip errors, iv) fidelity, and v) Anderson localization, and various combinations of the aforesaid.
1. A method of operation in a computational system that comprises both a specific instance of a quantum processor and at least one digital processor communicatively coupled to one another, the quantum processor comprising a plurality of qubits, wherein qubits of the plurality of qubits are communicatively couplable to one another, the method comprising:
receiving, by the at least one digital processor, a first submitted problem;
modifying, by the at least one digital processor, the first submitted problem to compensate for communicative couplings between the qubits of the plurality of qubits induced by non-idealities of the specific instance of the quantum processor upon programming the first submitted problem thereon;
producing, by the at least one digital processor, a problem graph representation of the modified first submitted problem;
embedding, by the at least one digital processor, the problem graph representation of the modified first submitted problem in a hardware graph of the quantum processor; and
generating solutions to the first submitted problem via the quantum processor with the problem graph representation of the modified first submitted problem embedded therein.
2. The method of claim 1 wherein modifying the first submitted problem to compensate for the communicative couplings between the qubits of the plurality of qubits induced by the non-idealities of the specific instance of the quantum processor upon programming the first submitted problem thereon includes: modifying the first submitted problem to compensate for a background susceptibility error χ of the specific instance of the quantum processor on which the first submitted problem is to be run or evolved such that a target solution to a problem formulation is a solution with a lowest background susceptibility error χ possible.
3. The method of claim 1 wherein modifying the first submitted problem to compensate for the communicative couplings between the qubits of the plurality of qubits induced by the non-idealities of the specific instance of the quantum processor upon programming the first submitted problem thereon includes: modifying the first submitted problem to compensate for a background susceptibility error χ of the specific instance of the quantum processor on which the first submitted problem is to be run or evolved such that an optimal solution to a problem formulation is a solution with a lowest background susceptibility error χ possible.
4. The method of claim 1 wherein modifying the first submitted problem to compensate for the communicative couplings between the qubits of the plurality of qubits induced by the non-idealities of the specific instance of the quantum processor upon programming the first submitted problem thereon includes: applying a first function to a chosen nominal Hamiltonian or to a vector θ that represents a set of controllable terms of the chosen nominal Hamiltonian to obtain a putative Hamiltonian.
5. The method of claim 4 wherein modifying the first submitted problem to compensate for the communicative couplings between the qubits of the plurality of qubits induced by the non-idealities of the specific instance of the quantum processor upon programming the first submitted problem thereon includes: applying a second function to the putative Hamiltonian to obtain a logical putative Hamiltonian.
6. The method of claim 5 wherein applying the second function to the putative Hamiltonian to obtain a logical putative Hamiltonian includes: applying a second function that represents a native-to-logical conversion to the putative Hamiltonian to obtain a logical putative Hamiltonian.
7. The method of claim 4 wherein applying at least the first function to the chosen nominal Hamiltonian or to the vector θ that represents the set of controllable terms of the chosen nominal Hamiltonian to obtain the putative Hamiltonian includes: applying at least the first function to the chosen nominal Hamiltonian to minimizes a difference between a logical target Hamiltonian and a logical putative Hamiltonian.
8. The method of claim 7 wherein modifying the first submitted problem to compensate for the couplings between the qubits of the plurality of qubits induced by the non-idealities of the specific instance of the quantum processor upon programming the first submitted problem thereon comprises:
applying an unconstrained nonlinear optimization algorithm to minimize the difference between the logical target Hamiltonian and the logical putative Hamiltonian to obtain an optimized set of controllable terms of a logical Hamiltonian; and
modifying the first problem based on the optimized set of controllable terms of the logical Hamiltonian.
9. The method of claim 7 wherein applying at least the first function to the chosen nominal Hamiltonian that minimizes the difference between the logical target Hamiltonian and the logical putative Hamiltonian includes: calculating the logical target Hamiltonian based on native Hamiltonian terms and chains of the chosen nominal Hamiltonian.
10. The method of claim 1 wherein modifying the first submitted problem to compensate for the communicative couplings between the qubits of the plurality of qubits induced by the non-idealities of the specific instance of the quantum processor upon programming the first submitted problem thereon includes:
determining optimized logical Hamiltonian parameters through optimization of a cost function of a logical Hamiltonian, the optimization of the cost function of the logical Hamiltonian including optimization of native Hamiltonian parameters of a nominal Hamiltonian; and
modifying the first submitted problem based on the optimized logical Hamiltonian parameters.
11. A computational system, comprising:
a specific instance of a quantum processor, the quantum processor comprising a plurality of qubits, wherein qubits of the plurality of qubits communicably couplable to one another;
at least one digital processor communicatively coupled to the quantum processor; and
at least one non-transitory processor-readable medium that stores at least one of processor-executable instructions or data which, when executed, cause at least one digital processor to:
receive a first submitted problem;
modify the first submitted problem to compensate for couplings between the qubits of the plurality of qubits-induced by non-idealities of the specific instance of the quantum processor upon programming the first submitted problem thereon;
produce a problem graph representation of the modified first submitted problem;
embed the problem graph representation of the modified first submitted problem in a hardware graph of the quantum processor; and
generate solutions to the first submitted problem via the quantum processor with the problem graph representation of the modified first submitted problem embedded therein.
12. The computational system of claim 11 wherein qubits of the plurality of qubits are operable to be communicatively coupled to one another by one or more couplers, wherein each coupler is operable to provide controllable communicative coupling between at least two qubits of the plurality of qubits.
13. The computational system of claim 12 wherein modification of the first submitted problem comprises: modification of a background susceptibility error χ of the specific instance of the quantum processor on which the first submitted problem is to be run or evolved such that a target solution to a problem formulation is a solution with a lowest background susceptibility error χ possible.
14. The computational system of claim 12 wherein the first submitted problem is modified to compensate for a background susceptibility error χ of the specific instance of the quantum processor on which the first submitted problem is to be run or evolved such that an optimal solution to a problem formulation is a solution with a lowest background susceptibility error χ possible.
15. The computational system of claim 12 wherein the first submitted problem is modified based on optimized logical Hamiltonian parameters, wherein the optimized logical Hamiltonian parameters are determined through optimization of a cost function of a logical Hamiltonian, wherein the optimization of the cost function of the logical Hamiltonian includes optimization of native Hamiltonian parameters of a nominal Hamiltonian.
16. The computational system of claim 12 wherein the first submitted problem is modified based on a putative Hamiltonian that is obtained through application of a first function of a chosen nominal Hamiltonian or a vector θ that represents a set of controllable terms of the chosen nominal Hamiltonian, wherein the first function is to perform native compensation of one or more unintentional or non-direct couplings between the qubits of the plurality of qubits.
17. The computational system of claim 16 wherein the first submitted problem is modified based on a logical putative Hamiltonian that is obtained through application of a second function to the putative Hamiltonian, wherein the second function represents a native-to-logical conversion.
18. The computational system of claim 17 wherein compensation of the communicative couplings between the qubits of the plurality of qubits induced by the non-idealities of the specific instance of the quantum processor upon programming the first submitted problem thereon is based on an optimized set of controllable terms of a logical Hamiltonian, wherein the optimized set of controllable terms of the logical Hamiltonian are obtained through application of an unconstrained nonlinear optimization algorithm that minimizes a difference between a logical target Hamiltonian and the logical putative Hamiltonian.
19. The computational system of claim 11 wherein qubits of the plurality of qubits are superconducting qubits and comprise at least one material that superconducts at and below a critical temperature.
20. The computational system of claim 11 wherein the quantum processor is a quantum processor operable to perform quantum annealing and/or adiabatic quantum computation.