Introduction to Qiskit Ignis. Ignis provides tools related to noise.

1. Overview of Qiskit Ignis
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parton (Shin Nishio, B4)
Keio SFC AQUA
Struggle witherrors
2019/6/6

2. Quantum Error ?
Quantum errors(noise) on QC are caused
by physical phenomena.
• heat
• oscillation
• electromagnetic wave
etc
2
QC

3. NISQ era [Preskill2018, Quantum]
Noisy
• ibmq20_tokyo [IBM 2018, IBMQ]
• Single Qubit Gate error (10#$): 1.83
• Bi-Qubit Gate error (10#%): 8.06 (IBMQ16)
• Readout error (10#%): 8.58
• Error rate of each qubit is unequal
Intermediate Scale Quantum
• # of Qubits : 10~10$ (2019 spring: 20-72)
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[IBM 2018, IBMQ]
IBM, Quantum devices and simulators, accessed 2018/11/4
https://www.research.ibm.com/ibm-q/technology/devices/

4. NISQ era [Preskill2018, Quantum]
Noisy
• ibmq20_tokyo [IBM 2018, IBMQ]
• Single Qubit Gate error (10#$): 1.83
• Bi-Qubit Gate error (10#%): 8.06 (IBMQ16)
• Readout error (10#%): 8.58
• Error rate of each qubit is unequal
Intermediate Scale Quantum
• # of Qubits : 10~10$
4
Howcan we knowthis values ?

5. Simple Error model
1. G ■ (single qubit gate error)
2. B ■ (bi-qubit gate error)
3. SPAM ■
(state preparation and measurement)
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6. Simple Error model
1. G ■ (single qubit gate error)
2. B ■ (bi-qubit gate error)
3. SPAM ■
(state preparation and measurement)
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How many errors occur in a circuit?

7. Qiskit Ignis
• Ignis provides tools for quantum hardware
verification, noise characterization, and error
correction.
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image
https://medium.com/qiskit/qiskit-ignis-a-framework-for-characterizing-and-mitigating-noise-in-quantum-devices-691d0459cab9

8. Ignis provides…
Ignis provides tools for noise estimation
and correction.
1. Characterization experiments to
measure
2. State and Process Tomography
3. Randomized Benchmarking
4. Measurement Error Mitigation
5. Quantum Volume
8

9. 1. Characterization experiments to measure
• stochastic noise parameters such as T1 and T2
The value that was evaluated whether the
condition was maintained when left.
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image from
https://github.com/Qiskit/qiskit-tutorials/blob/master/qiskit/ignis/relaxation_and_decoherence.ipynb

10. 2. State and Process Tomography
an experimental procedure to reconstruct a
description of part of quantum system from the
measurement outcomes of a specific set of
experiments.
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Tutorial
https://github.com/Qiskit/qiskit-tutorials/blob/e32d94ec578a798acada2616032bf47a1a541c5f/community/ignis/tomography-overview.ipynb
Original paper
• State tomography
Hradil, Phys. Rev. A 55, R1561 (1997).
Banaszek et al., Phys. Rev. A 61, 010304 (R) (1999).
• Process tomography
Poyatos et al., Phys. Rev. Lett. 78, 390 (1997).
Chuang and Nielsen, J. Mod. Phys. 44, 2455 (1997).
0:
()*+, -
%
1:
(#*+, -
%

11. 2. State and Process Tomography
state tomography
• Estimate quantum states(density matrix 𝜌) by
measuring on multiple bases
𝑃 𝑥 = 𝑇3[𝜌Π6]
process tomography
• Know the details of the changes in quantum
states that occur with some operations
𝑃(𝑥) = 𝑇3[Π6 𝒢(𝜌)]
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givenestimateobservable
observable given estimate

12. 3. Randomized benchmarking
• Tools to general one- and two-qubit random
Clifford sequences in parallel
• Analysis of the data to determine average gate
error
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Original paper
J. Emerson, et al., J. Opt. B: Quantum Semiclass. Opt. 7, S447 (2005).
E. Knill, PRA 77, 012307 (2008), E. Magesan, et al., PRL 106, 180504 (2011).

13. 13
Concept
• see the frequency of noise at a lighter cost than
tomography
• use randomness for evaluate cost of whole
gate set
• separate SPAM error and gate error
• Clifford group (gate set)
𝐶< = 𝑈 𝐶< 𝑃> 𝑐<
@
∈ 𝑃<}
Small number of experiments
requires many basis for multi-qubit system
3. Randomized benchmarking
𝑃< : Pauli group
e.g. 1-qubit pauli : {±𝐼, ±𝑖𝐼, ±𝑋, ±𝑖𝑋, ±𝑌, ±𝑖𝑌, ±𝑍, ±𝑖𝑍}

14. 14
Procedure
1. Randomly select m gates from the Clifford
group and arrange them in any order.
2. Select the Clifford gate which will reverse the
operation of the entire preceding sequence
of m Clifford gates,
execute this as the m + 1th gate.
3. Randomized benchmarking
put ⟩|0 No error → get ⟩|0
error occured→ get ⟩|1

15. 15
• It is observable that noise increases as 𝑚 is
increased !
fitting function
𝐴𝑟O
+ 𝐵
Error per Clifford (EPC)
𝐸𝑃𝐶 =
2T − 1
2T (1 − r)
image from
https://github.com/Qiskit/qiskit-
tutorials/blob/master/qiskit/ignis/randomized_benchmarking.ipynb
3. Randomized benchmarking

16. 4. Measurement Error Mitigation
• Tools to generate the circuits and analysis to
construct a measurement calibration
• Filter object that can be applied to results to
mitigate measurement errors
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17. 4. Measurement Error Mitigation
• Tools to generate the circuits and analysis to
construct a measurement calibration
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e.g. calibration matrix for 2-qubit
state
image from
https://github.com/Qiskit/qiskit-
tutorials/blob/e32d94ec578a798acada2616032bf47a1a541c5f/community/ignis/measurement_error_mitigation.ipynb
The sum of the components
in each column is 1
measurement
basis
0.799 0.209
0.099 0.696
0.248 0.054
0.019 0.181
0.088 0.03
0.014 0.065
0.662 0.167
0.071 0.598
00 01 10 11
00
01
10
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2T× 2T matrix for n-qubit system

18. 4. Measurement Error Mitigation
• Filter object that can be applied to results to
mitigate measurement errors
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e.g. apply meas_filter = meas_fitter.filter to the GHZ state
image from
https://github.com/Qiskit/qiskit-tutorials/blob/master/qiskit/ignis/measurement_error_mitigation.ipynb

19. 5. quantum volume
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Quantum Volume [Lev S. Bishop et al. , 2017]
1. The number of physical qubits
2. The number of gates that can be applied before errors
make the device behave essentially classically
3. The connectivity of the device
4. The number of operations that can be run in parallel.
Tutorial
https://github.com/Qiskit/qiskit-tutorials/blob/master/qiskit/ignis/quantum_volume.ipynb

20. Conclusion
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Ignis provides tools related to noise
1. Characterization experiments to
measure Measure T1 & T2, ZZ interaction
2. State and Process Tomography 𝜌 and 𝒢
3. Randomized Benchmarking EPC
4. Measurement Error Mitigation
calibration matrix and filtered results
5. Quantum Volume Performance