Application US20210256410

QUANTUM READOUT ERROR MITIGATION BY STOCHASTIC MATRIX INVERSION
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US20210256410

1. A method of mitigating quantum readout errors by stochastic matrix inversion, comprising: (8) (5)

performing a plurality of quantum measurements on a plurality of qubits having predetermined plurality of states to obtain a plurality of measurement outputs;

selecting a model for a matrix linking the predetermined plurality of states to the plurality of measurement outputs, the model having a plurality of model parameters, wherein a number of the plurality of model parameters grows less than exponentially with a number of the plurality of qubits;

training the plurality of model parameters to minimize a loss function that compares predictions of the model with the matrix;

computing an inverse of the model representing an inverse of the matrix based on the trained model parameters; and

providing the computed inverse of the model to a noise prone quantum readout of the plurality of qubits to obtain a substantially noise free quantum readout.

2. The method according to claim 1, wherein selecting the model comprises selecting a Tensor Product (TP) noise model, and the plurality of model parameters include error rates of independent transitions from state 0 to state 1 and probabilities of independent transitions from state 1 to state 0. (1) (0)

4. The method according to claim 1, wherein selecting the model comprises selecting a Continuous Time Markov Process (CTMP) noise model, and the plurality of model parameters include atomic generator elements G_iand transition rates r_i, where i represents a qubit i in the plurality of qubits. (1) (0)

5. The method according to claim 4, wherein the model for the matrix A is such that (1) (2)

A=exp(G)

wherein model parameter generator matrix G is equal to a sum of products of atomic generator elements G_iby transition time-independent rates r_iover all qubits i as follows:

6. The method according to claim 5, wherein the atomic generator elements G_iinclude: (1) (4)

element G₁corresponding to a transition from state 0 to state 1 of a first qubit in the plurality of qubits,

element G₂corresponding to a transition from state 1 to state 0 of the first qubit in the plurality of qubits,

element G₃corresponding to a transition from state 0 to state 1 of a second qubit in the plurality of qubits, and

element G₄corresponding to a transition from state 1 to state 0 of the second qubit in the plurality of qubits.

7. The method according to claim 6, wherein the atomic generator elements G_ifurther include: (0) (2)

8. The method according to claim 1, (1) (2)

10. The method according to claim 1, wherein the number of the plurality of model parameters grows linearly with the number of the plurality of states. (0)

11. The method according to claim 1, wherein providing the computed inverse of the model to the noise prone quantum readout of the plurality of qubits comprises applying the computed inverse of the model to the noise prone quantum readout of the plurality of qubits to substantially correct the noise prone quantum readout so as to substantially remove noise in the noise prone quantum readout. (0)

12. The method according to claim 1, further comprising constructing the matrix, the matrix having a plurality of matrix elements, each element of the matrix associates each of the pre-determined states of the plurality of qubits with a corresponding each of the plurality of measurement outputs. (1) (0)

14. The method according to claim 1, wherein training the plurality of model parameters to minimize a loss function that compares predictions of the model with the matrix comprises finding the plurality of model parameters that substantially fit the matrix. (0)

24. The computer readable medium according to claim 1, wherein training the plurality of model parameters to minimize a loss function that compares predictions of the model with the matrix comprises finding the plurality of model parameters that substantially fit the matrix. (0)

15. A computer readable medium on which is stored non-transitory computer-executable code, which when executed by a classical computer causes a quantum computer to: (4) (5)

perform a plurality of quantum measurements on plurality of qubits having predetermined plurality of states to obtain a plurality of measurement outputs;

select a model for a matrix linking the predetermined plurality of states to the plurality of measurement outputs, the model having a plurality of model parameters, wherein a number of the plurality of model parameters grows less than exponentially with a number of the plurality of states;

train the plurality of model parameters to minimize a loss function that compares predictions of the model with the matrix;

compute an inverse of the model representing an inverse of the matrix based on the trained model parameters; and

apply the computed inverse of the model to a noise prone quantum readout of the plurality of qubits of the quantum computer to obtain a substantially noise free quantum readout from the quantum computer.

16. The computer readable medium according to claim 15, wherein the model for the matrix is a Tensor Product (TP) noise model, and the plurality of model parameters include error rates of independent transitions from state 0 to state 1 and probabilities of independent transitions from state 1 to state 0. (2) (0)

17. The computer readable medium according to claim 16, wherein the model for the matrix is such that the matrix is a product of a plurality of qubit matrices, each qubit matrix representing a state of a given qubit j in the plurality of qubits, the matrix being expressed as: (0) (2)

18. The computer readable medium according to claim 16, wherein the model for the matrix is a Continuous Time Markov Process (CTMP) noise model, and the plurality of model parameters include atomic generator elements G_iand transition rates r_i, where i represents a qubit i in the plurality of qubits. (1) (0)

20. The computer readable medium according to claim 15, (1) (2)

22. The computer readable medium according to claim 15, wherein the number of the plurality of model parameters grows linearly with the number of the plurality of states. (0)

23. The computer readable medium according to claim 15, wherein applying the computed inverse of the model to the noise prone quantum readout of the plurality of qubits comprises applying the computed inverse of the model to the noise prone quantum readout of the plurality of qubits to substantially correct the noise prone quantum readout so as to substantially remove noise in the noise prone quantum readout. (0)

25. A classical computer configured to execute a non-transitory computer-executable code, the code when executed by the classical computer causes a quantum computer to: (0) (5)

perform a plurality of quantum measurements on plurality of qubits having predetermined plurality of states to obtain a plurality of measurement outputs;

train the plurality of model parameters to minimize a loss function that compares predictions of the model with the matrix;

compute an inverse of the model representing an inverse of the matrix based on the trained model parameters; and

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Application US20210256410

QUANTUM READOUT ERROR MITIGATION BY STOCHASTIC MATRIX INVERSION

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