Systems and methods for modeling noise sequences and calibrating quantum processors
Calibration techniques for devices of analog processors to remove time-dependent biases are described. Devices in an analog processor exhibit a noise spectrum that spans a wide range of frequencies, characterized by 1/f spectrum. Offset parameters are determined assuming only a given power spectral density. The algorithm determines a model for a measurable quantity of a device in an analog processor associated with a noise process and an offset parameter, determines the form of the spectral density of the noise process, approximates the noise spectrum by a discrete distribution via the digital processor, constructs a probability distribution of the noise process based on the discrete distribution and evaluates the probability distribution to determine optimized parameter settings to enhance computational efficiency.
1. A method of operation of a hybrid processor, the hybrid processor comprising a quantum processor and a digital processor, the quantum processor having a plurality of devices, at least one of the plurality of devices having a measurable quantity associated with a noise process and an offset parameter, the method comprising:
receiving by the digital processor a model for the measurable quantity and a form of a spectral density of the noise process;
approximating a noise spectrum of the noise process by a discrete distribution via the digital processor;
constructing a probability distribution of the noise process based on the discrete distribution via the digital processor, wherein constructing a probability distribution of the noise process includes constructing a probability distribution of the noise process on a next data point based on a probability distribution of the noise process over the frequency space derived from the spectral density of the noise process and the probability distribution of the noise process over time;
evaluating the probability distribution to determine a number of parameter settings that reduce time dependent biases in the quantum processor via the digital processor;
applying the number of parameter settings that reduce time dependent biases in the quantum processor to one or more of the plurality of devices of the quantum processor to at least partially compensate for the noise process over time; and
operating the quantum processor to solve a problem using the number of parameter settings that reduce time dependent biases in the quantum processor.
2. The method of claim 1 wherein receiving by the digital processor a model for the measurable quantity comprises determining a model for the measurable quantity via the digital processor.
3. The method of claim 2 wherein determining a model for the measurable quantity includes at least one of:
determining the spin state of a qubit in the quantum processor, the spins state linked to a flux noise and a flux offset parameter; and
determining a magnetization of a group of qubits in the quantum processor, the magnetization linked to a flux noise and a flux offset parameter.
4. The method of claim 1 wherein receiving by the digital processor a form of a spectral density of the noise process comprises determining a form of a spectral density of the noise process via the digital processor.
5. The method of claim 4 wherein determining a form of a spectral density of the noise process includes at least one of: determining the measurable quantity, and computing the form of the spectral density assuming a combination of static error, a 1/f spectrum and a white noise.
6. The method of claim 1 wherein evaluating the probability distribution to determine parameter settings that reduce time dependent biases in the quantum processor includes evaluating the probability distribution via at least one of: a Monte Carlo method, a Markov Chain Monte Carlo method, approximate sampling, a heuristic optimization method, or optimization by the quantum processor.
7. A hybrid computing system, the hybrid computing system comprising: a quantum processor and a digital processor, the quantum processor having a plurality of devices, at least one of the plurality of devices having a measurable quantity associated with a noise process and an offset parameter, the digital processor operable to:
receive a model for a measurable quantity;
receive a form of a spectral density of the noise process;
approximate a noise spectrum of the noise process by a discrete distribution;
construct a probability distribution of the noise process based on the discrete distribution on a next data point based on a probability distribution of the noise process over the frequency space derived from the spectral density of the noise process and the probability distribution of the noise process over time;
evaluate the probability distribution to determine a number of parameter settings that reduce time dependent biases in the quantum processor;
apply the parameter settings that reduce time dependent biases in the quantum processor to one or more of the plurality of devices of the quantum processor to at least partially compensate for the noise process over time; and
instruct the quantum processor to operate to solve a problem using the number of parameter settings that reduce time dependent biases in the quantum processor.
8. The hybrid computing system of claim 7 wherein the digital processor being operable to receive a model for a measurable quantity comprises the digital processor determining the model for the measurable quantity.
9. The hybrid computing system of claim 8 wherein the measurable quantity is at least one of:
a spin state of a qubit in the quantum processor, the spin state linked to a flux noise and a flux offset parameter; and
a magnetization of a group of qubits in the quantum processor, the magnetization linked to a flux noise and a flux offset parameter.
10. The hybrid computing system of claim 7 wherein the digital processor being operable to receive a form of a spectral density of the noise process comprises the digital processor determining a form of a spectral density of the noise process.
11. The hybrid computing system of claim 10 wherein the form of the spectral density of the noise process is determined by at least one of: the digital processor operable to determine the measurable quantity and the digital processor operable to compute the form of the spectral density assuming a combination of static error, 1/f spectrum and white noise.
12. The hybrid computing system of claim 7 wherein the probability distribution to determine the parameter settings that reduce time dependent biases in the quantum processor is evaluated via at least one of: Monte Carlo method, Markov Chain Monte Carlo method, a heuristic optimization method, and optimization by the quantum processor.
13. A method of operation of a hybrid processor, the hybrid processor comprising a quantum processor and a digital processor, the quantum processor having a plurality of devices, at least one of the plurality of devices having a measurable quantity associated with a noise process and an offset parameter, the method comprising:
receiving by the digital processor a model for the measurable quantity and a form of a spectral density of the noise process;
approximating a noise spectrum of the noise process by a discrete distribution via the digital processor;
constructing a probability distribution of the noise process based on the discrete distribution via the digital processor, wherein constructing a probability distribution of the noise process includes constructing a probability distribution of the noise process on a next data point based on a probability distribution of the noise process over the frequency space derived from the spectral density of the noise process and a probability distribution of the noise process over time;
evaluating the probability distribution to estimate a noise value via the digital processor;
setting a value of the offset parameter of the at least one of the plurality of devices to an opposite of the estimated noise value via the digital processor; and
operating the quantum processor to solve a problem using the value of the offset parameter of the at least one of the plurality of devices.
14. The method of claim 13 wherein evaluating the probability distribution to estimate a noise value includes evaluating the probability distribution by one of:
gradient descent or integration via Markov Chain Monte Carlo, to obtain a noise distribution, fitting the noise distribution to a Gaussian distribution and taking a maxima of the Gaussian distribution as the noise value.
15. The method of claim 13 wherein receiving by the digital processor a model for the measurable quantity comprises determining a model for the measurable quantity via the digital processor.
16. The method of claim 15 wherein determining a model for the measurable quantity includes at least one of:
determining a spin state of a qubit in the quantum processor, the spin state linked to a flux noise and a flux offset parameter; and
determining a magnetization of a group of qubits in the quantum processor, the magnetization linked to a flux noise and a flux offset parameter.
17. The method of claim 13 wherein providing a form of a spectral density of the noise process to the digital processor comprises determining a form of a spectral density of the noise process via the digital processor.
18. The method of claim 17 wherein determining a form of a spectral density of the noise process includes at least one of: determining the measurable quantity and computing the form of the spectral density assuming a combination of static error, 1/f spectrum and white noise.
19. A method of operation of a hybrid processor, the hybrid processor comprising a quantum processor and a digital processor, the quantum processor having a plurality of devices, at least one of the plurality of devices having a measurable quantity associated with a noise process and an offset parameter, the method comprising:
receiving by the digital processor a model for the measurable quantity and a form of a spectral density of the noise process;
approximating a noise spectrum of the noise process by a discrete distribution via the digital processor;
constructing a probability distribution of the noise process based on the discrete distribution via the digital processor, wherein constructing a probability distribution of the noise process includes constructing a probability distribution of the noise process on a next data point based on a probability distribution of the noise process over the frequency space derived from the spectral density of the noise process and a probability distribution of the noise process over time;
determining an iterative rule for determining a value of the offset parameter of the at least one of the plurality of devices, the rule depending on a calibration parameter α that at least partially compensates for the noise process, via the digital processor;
evaluating α via the digital processor; and
setting α as the value of the offset parameter of the at least one of the plurality of devices via the digital processor; and
operating the quantum processor to solve a problem using the value of the offset parameter of the at least one of the plurality of devices.
20. The method of claim 19 wherein evaluating α includes evaluating α as a function of the probability distribution of the noise process and the iterative rule.
21. The method of claim 19 wherein providing a model for the measurable quantity to the digital processor comprises determining a model for the measurable quantity via the digital processor.
22. The method of claim 21 wherein determining a model for the measurable quantity includes one of: determining a spin state of a qubit in the quantum processor, the spin state linked to a flux noise and a flux offset parameter; determining a magnetization of a group of qubits in the quantum processor, the magnetization linked to a flux noise and a flux offset parameter; and determining a magnetization of a group of qubits in the quantum processor, the magnetization linked to a flux noise and a flux offset parameter.
23. The method of claim 19 wherein receiving by the digital processor a form of a spectral density of the noise process comprises determining a form of a spectral density of the noise process via the digital processor.
24. The method of claim 23 wherein determining a form of a spectral density of the noise process includes at least one of: determining the measurable quantity and computing the form of the spectral density assuming a combination of static error, a 1/f spectrum and a white noise.