# US 2021/0334689 A1 · Optimizing qubit operating frequencies

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- Number: US 2021/0334689 A1
- Document ID: US20210334689A1
- Status: Published application
- Kind: A1
- Application number: 16/971,512
- Filed: 2018-03-02
- Published: 2021-10-28
- Earliest claimed: 2018-03-02
- Assignees: Google Inc.
- Applicants: Google LLC
- Inventors: Paul Klimov; Julian Shaw Kelly
- Web page: https://patentgrep.com/patent/US20210334689A1

## CPC

- G06N 10/40: Physical realisations or architectures of quantum processors or components for manipulating qubits, e.g. qubit coupling or qubit control
- G06N 5/01: Dynamic search techniques; Heuristics; Dynamic trees; Branch-and-bound
- G06N 10/20: Models of quantum computing, e.g. quantum circuits or universal quantum computers
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS

## Abstract

Methods, systems, and apparatus for determining frequencies at which to operate interacting qubits arranged as a two dimensional grid in a quantum device. In one aspect, a method includes the actions of defining a first cost function that characterizes technical operating characteristics of the system. The cost function 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 operating state of the quantum device is improved.

## Claims

### Claim 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 the computations performed by the quantum device using the adjusted qubit operation frequency values are less error-prone.

### Claim 2 (depends on 1)

The method of claim 1, 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.

### Claim 3 (depends on 2)

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

### Claim 4 (depends on 2)

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

### Claim 5 (depends on 2)

The method of claim 2, wherein performing a multi-qubit optimization routine to obtain initial qubit operation frequency values comprises:
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.

### Claim 6 (depends on 2)

The method of claim 2, wherein the qubit operation frequency values comprise qubit idling frequencies and qubit interaction frequencies.

### Claim 7 (depends on 2)

The method of claim 2, further comprising identifying multiple idling frequency arrangements for the grid, comprising:
defining an idling frequency splitting pattern for the grid; and
bounding the range over which the 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.

### Claim 8 (depends on 7)

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

### Claim 9 (depends on 6)

The method of claim 6, 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 the mean value of the 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 idling frequency for each qubit pair as the coarse-grained initial two-qubit interaction frequency for that pair.

### Claim 10 (depends on 9)

The method of claim 9, 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.

### Claim 11 (depends on 10)

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

### Claim 12 (depends on 10)

The method of claim 10, 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.

### Claim 13 (depends on 12)

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

### Claim 14 (depends on 7)

The method of claim 7, further comprising iteratively identifying multiple idling frequency arrangements for the grid until third termination criteria are met.

### Claim 15 (depends on 1)

The method of claim 1, further comprising 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.

### Claim 16 (depends on 1)

The method of claim 1, wherein the first and/or 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, and/or ii) low adjacent qubit detuning; and
an interaction cost term that penalizes i) low qubit relaxation time interaction frequencies and/or 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.

### Claim 17 (depends on 1)

The method of claim 1, wherein the one or more constraints incorporate knowledge of the physics and/or engineering constraints of the quantum computing device.

### Claim 18 (depends on 1)

The method of claim 1, 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.

### Claim 19 (depends on 1)

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 comprising the method of claim 1.

### Claim 20 (depends on 1)

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 comprising the method of claim 1.