Quantum readout error mitigation by stochastic matrix inversion

Patent metadata

Field	Value
Publication number	US-11537927-B2
Application number	US-202016791367-A
Country	US
Kind code	B2
Filing date	Feb 14, 2020
Priority date	Feb 14, 2020
Publication date	Dec 27, 2022
Grant date	Dec 27, 2022

Abstract

A method of mitigating quantum readout errors by stochastic matrix inversion includes 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 model parameters to minimize a loss function that compares predictions of the model with the matrix; computing an inverse of the model 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.

First claim

We claim:

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

3. The method according to claim 2 , 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:

A
=

[

1
-

ϵ
1

η
1

ϵ
1

1
-

η
1

]

⊗

⁢
…
⁢

⊗

[

1
-

ϵ
n

η
n

ϵ
n

1
-

η
n

]

,

wherein ∈ j are error rates describing transition from state 0 to state 1 for qubit j (j=1 . . . n), and
wherein η j (j=1 . . . n) are error rates describing transition from state 1 to state 0 for qubit j (j=1 . . . n).

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 i and transition rates r i , where i represents a qubit i in the plurality of qubits.

5. The method according to claim 4 , wherein the model for the matrix A is such that
A =exp( G )
wherein model parameter generator matrix G is equal to a sum of products of atomic generator elements G i by transition time-independent rates r i over all qubits i as follows:

G
=

∑
i

⁢

G
i

⁢

r
i

.

6. The method according to claim 5 , wherein the atomic generator elements G i include:
element G 1 corresponding to a transition from state 0 to state 1 of a first qubit in the plurality of qubits,
element G 2 corresponding to a transition from state 1 to state 0 of the first qubit in the plurality of qubits,
element G 3 corresponding to a transition from state 0 to state 1 of a second qubit in the plurality of qubits, and
element G 4 corresponding 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 i further include:
element G 5 corresponding to transition from state 01 to state 11 of neighboring first and second qubits, and
element G 6 corresponding to a transition from state 10 to state 11 of the neighboring first and second qubits.

8. The method according to claim 1 ,
wherein the model approximates the matrix as an exponential of a model parameter generator matrix G, wherein the model parameter generator matrix G is equal to a sum of products of atomic generator elements G i by transition time-independent rates r i over all qubits i,
wherein the atomic generator elements G i of the model parameter generator matrix G generates a transition from a bit string a i to another bit string b i on a subset of bits C i , wherein a i and b i are either state 0 or state 1 of qubit i.

9. The method according to claim 8 , wherein computing the inverse of the model representing the inverse of the matrix based on the trained model parameters comprises computing the exponential of negative model parameter generator matrix G.

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.

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 quant

Assignees

• IBM

Inventors

• Bravyi Sergey
• Gambetta Jay M
• Mckay David C
• Sheldon Sarah E

Classifications

• G06N7/08

  using chaos models or non-linear system models · CPC title

• G06N7/01

  Probabilistic graphical models, e.g. probabilistic networks · CPC title

• G06F17/16

  Matrix or vector computation {, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization (matrix transposition G06F7/78)} · CPC title

• G06N10/60

  Quantum algorithms, e.g. based on quantum optimisation, quantum Fourier or Hadamard transforms · CPC title

• G06F17/18 Primary

  for evaluating statistical data {, e.g. average values, frequency distributions, probability functions, regression analysis (forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04)} · CPC title