Optimizing qubit operating frequencies

1. A method for determining frequencies at which to operate interacting qubits arranged as a two dimensional grid in a quantum device, the method comprising:

defining a first cost function that maps qubit operation frequency values to a cost corresponding to an operating state of the quantum device;

applying one or more constraints to the defined first cost function to define an adjusted cost function; and

adjusting qubit operation frequency values to vary the cost according to the adjusted cost function such that computations performed by the quantum device using the adjusted qubit operation frequency values are less error-prone,

wherein adjusting qubit operation frequency values to vary the cost according to the adjusted cost function comprises performing one or more multi-qubit optimization routines to obtain initial qubit operation frequency values, the one or more multi-qubit optimization routines comprising:

performing a grid-scale optimization routine to obtain coarse-grained initial qubit operation frequency values, and

performing a pair-scale optimization routine to adjust the coarse-grained initial qubit operation frequency values to fine-grained initial qubit operation frequency values.

2. The method of claim 1 , wherein adjusting qubit operation frequency values to vary the cost according to the adjusted cost function further comprises

performing one or more single qubit optimization routines to adjust the initial qubit operation frequency values to obtain final qubit operation frequency values.

3. The method of claim 1 , wherein the one or more multi-qubit optimization routines may be performed in parallel.

4. The method of claim 2 , wherein the one or more single qubit optimization routines may be performed in parallel.

5. A method for determining frequencies at which to operate interacting qubits arranged as a two dimensional grid in a quantum device, the method comprising:

defining a first cost function that maps qubit operation frequency values to a cost corresponding to an operating state of the quantum device, wherein the qubit operation frequency values comprise qubit idling frequencies and qubit interaction frequencies;

applying one or more constraints to the defined first cost function to define an adjusted cost function; and

adjusting qubit operation frequency values to vary the cost according to the adjusted cost function such that computations performed by the quantum device using the adjusted qubit operation frequency values are less error-prone,

wherein adjusting qubit operation frequency values to vary the cost according to the adjusted cost function comprises:

performing one or more multi-qubit optimization routines to obtain initial qubit operation frequency values; and

performing one or more single qubit optimization routines to adjust the initial qubit operation frequency values to obtain final qubit operation frequency values.

6. The method of claim 2 , further comprising identifying multiple idling frequency arrangements for the grid, the identifying comprising:

defining an idling frequency splitting pattern for the grid; and

bounding a range over which the idling frequency splitting pattern can be slid in frequency without exceeding any qubit's accessible frequency range to determine a corresponding vector of qubit operation frequency values for the qubits in the grid.

7. The method of claim 6 , wherein identifying multiple idling frequency arrangements for the grid comprises assuming qubit relaxation time is constant.

8. The method of claim 1 , wherein performing a grid-scale optimization routine to obtain coarse-grained initial qubit operation frequency values comprises evaluating the adjusted cost function for each identified idling frequency arrangement for the grid, comprising:

setting the interaction frequency for each pair of qubits to approximately a mean value of idling frequencies of each pair of qubits constituent qubits;

optimizing the adjusted cost function to determine coarse-grained initial qubit idling frequency values; and

setting the mean value of the idling frequency for each qubit pair as the coarse-grained initial two-qubit interaction frequency for that pair.

9. The method of claim 8 , wherein performing a pair-scale optimization routine to adjust the coarse-grained initial qubit operation frequency values to fine-grained initial qubit operation frequency values comprises:

fixing the coarse-grained initial qubit idling frequency values to the values obtained by the grid-scale optimization routine;

determining fine-grained interaction qubit frequencies by varying the interaction frequency independently for each qubit pair to optimize the cost.

10. The method of claim 9 , further comprising bounding the range of interaction frequency values.

11. The method of claim 9 , wherein performing a single qubit optimization routine to adjust the initial qubit operation frequency values to obtain final qubit operation frequency values comprises:

determining final qubit idling frequency values by varying idling frequencies for each qubit independently to optimize the cost.

12. The method of claim 11 , further comprising bounding the range of idling frequency values.

13. The method of claim 6 , further comprising iteratively identifying multiple idling frequency arrangements for the grid until third termination criteria are met.

14. A method for determining frequencies at which to operate interacting qubits arranged as a two dimensional grid in a quantum device, the method comprising:

defining a first cost function that maps qubit operation frequency values to a cost corresponding to an operating state of the quantum device;

applying one or more constraints to the defined first cost function to define an adjusted cost function; and

repeatedly adjusting qubit operation frequency values to vary the cost according to the adjusted cost function such that the operating state of the quantum device is improved to account for qubit operation frequency time dependence and computations performed by the quantum device using the adjusted qubit operation frequency values are less error-prone.

15. A method for determining frequencies at which to operate interacting qubits arranged as a two dimensional grid in a quantum device, the method comprising:

defining a first cost function that maps qubit operation frequency values to a cost corresponding to an operating state of the quantum device;

 applying one or more constraints to the defined first cost function to define an adjusted cost function, wherein one or more of i) the first or ii) adjusted cost function comprises a weighted sum of cost terms, the cost terms comprising one or more of:

an idling cost term that penalizes i) low qubit relaxation time idling frequencies, ii) low adjacent qubit detuning, or iii) both the low qubit relaxation time idling frequencies and the low adjacent qubit detuning; and

an interaction cost term that penalizes i) low qubit relaxation time interaction frequencies ii) low qubit relaxation time frequency regions between qubit idling frequencies for a pair of qubits and a common interaction frequency for said pair of qubits, or iii) both the low qubit relaxation time interaction frequencies and the low qubit relaxation time frequency regions between qubit idling frequencies for a pair of qubits and a common interaction frequency for said pair of qubits; and

adjusting qubit operation frequency values to vary the cost according to the adjusted cost function such that computations performed by the quantum device using the adjusted qubit operation frequency values are less error-prone.

16. A method for determining frequencies at which to operate interacting qubits arranged as a two dimensional grid in a quantum device, the method comprising:

defining a first cost function that maps qubit operation frequency values to a cost corresponding to an operating state of the quantum device;

applying one or more constraints to the defined first cost function to define an adjusted cost function, wherein the one or more constraints incorporate knowledge of one or more of i) the physics or ii) engineering constraints of the quantum computing device; and

adjusting qubit operation frequency values to vary the cost according to the adjusted cost function such that computations performed by the quantum device using the adjusted qubit operation frequency values are less error-prone.

17. A method for determining frequencies at which to operate interacting qubits arranged as a two dimensional grid in a quantum device, the method comprising:

defining a first cost function that maps qubit operation frequency values to a cost corresponding to an operating state of the quantum device;

applying one or more constraints to the defined first cost function to define an adjusted cost function, wherein the one or more constrains comprise one or more of predetermined differences in frequency between adjacent qubits, predetermined relationships between different types of operating frequencies, and/or predetermined acceptable frequency error tolerances; and

adjusting qubit operation frequency values to vary the cost according to the adjusted cost function such that computations performed by the quantum device using the adjusted qubit operation frequency values are less error-prone.

18. A system comprising one or more classical or quantum computers and one or more storage devices storing instructions that are operable, when executed by the one or more computers, to cause the one or more computers to perform operations for determining frequencies at which to operate interacting qubits arranged as a two dimensional grid in a quantum device, the operations comprising:

defining a first cost function that maps qubit operation frequency values to a cost corresponding to an operating state of the quantum device;

applying one or more constraints to the defined first cost function to define an adjusted cost function; and

adjusting qubit operation frequency values to vary the cost according to the adjusted cost function such that the computations performed by the quantum device using the adjusted qubit operation frequency values are less error-prone,

wherein adjusting qubit operation frequency values to vary the cost according to the adjusted cost function comprises performing one or more multi-qubit optimization routines to obtain initial qubit operation frequency values, the one or more multi-qubit optimization routines comprising:

performing a grid-scale optimization routine to obtain coarse-grained initial qubit operation frequency values; and

performing a pair-scale optimization routine to adjust the coarse-grained initial qubit operation frequency values to fine-grained initial qubit operation frequency values.

19. A computer-readable storage medium comprising instructions stored thereon that are executable by a classical or quantum processing device and upon such execution cause the processing device to perform operations for determining frequencies at which to operate interacting qubits arranged as a two dimensional grid in a quantum device, the operations comprising:

defining a first cost function that maps qubit operation frequency values to a cost corresponding to an operating state of the quantum device;

applying one or more constraints to the defined first cost function to define an adjusted cost function; and

adjusting qubit operation frequency values to vary the cost according to the adjusted cost function such that the computations performed by the quantum device using the adjusted qubit operation frequency values are less error-prone,

wherein adjusting qubit operation frequency values to vary the cost according to the adjusted cost function comprises performing one or more multi-qubit optimization routines to obtain initial qubit operation frequency values, the one or more multi-qubit optimization routines comprising:

performing a grid-scale optimization routine to obtain coarse-grained initial qubit operation frequency values; and

performing a pair-scale optimization routine to adjust the coarse-grained initial qubit operation frequency values to fine-grained initial qubit operation frequency values.