Introduction to Quantum Computing with Qiskit (with IBM Quantum)

1. 00:00Hi everyone! Welcome back to this very last video of our course.
2. 00:04So, in this video I'm gonna talk about
3. 00:07measurement error mitigation and as the name suggests,
4. 00:10the goal is to mitigate some measurement errors.
5. 00:12So, to correct for errors that happened during the measurement,
6. 00:16I will show you how to do so with Qiskit by actually
7. 00:19going through the examples that we have been running in before,
8. 00:23like the
9. 00:24circuit the Grover's, a circuit, all the measurement outcomes that we got there.
10. 00:27I will show you how we can improve them when correcting for these errors.
11. 00:32So, first of all we import our standard Qiskit libraries
12. 00:37and then we actually have to, especially have
13. 00:41to create what we call the calibration job.
14. 00:44So, for that there's a premade Qiskit function which is
15. 00:47called complete measurement collaboration where we feed the number of qubits
16. 00:51and we also when run that, we need to give our layout,
17. 00:55the layout that we have used.
18. 00:56Or ideally we don't have to give it but we
19. 00:58get much better results if we feed the layout that we
20. 01:01have used when we run a specific job, so that we
21. 01:03can also correct for errors that are correlated and stuff.
22. 01:08So,
23. 01:10the way the function works is we prepare all
24. 01:13basis states, so all 2^n different states
25. 01:17and then we measure them all.
26. 01:18And ideally of course it would just measure whatever we have prepared.
27. 01:21However, due to our noise,
28. 01:24we will not always measure exactly the state with
29. 01:27probability one but we might have a probability of 99%
30. 01:31to measure the state that we have prepared and
31. 01:33some very small probabilities to measure some other states.
32. 01:36However, all these smaller probabilities add up.
33. 01:39So, that's why we want to correct for them.
34. 01:40And so what we do is we create this matrix,
35. 01:42the so called calibration matrix, in which we
36. 01:46note all these, in which we denote all
37. 01:50these probabilities to then be able to correct for them.
38. 01:54So, let us prepare the calibration shop.
39. 01:58We again as always give our provider
40. 02:01and now we executed this function measurement calibrations
41. 02:05using the complete measurement calibration function from Qiskit
42. 02:08with our backend which is well,
43. 02:10the one here used the
44. 02:11Hanoi device, because that's the one I've used for running Grover and Deutsch-Jozsa
45. 02:15before. We feed the layout and determine the number of shots.
46. 02:22Now, of course I ran it before so we don't have to wait again
47. 02:26and here we can see.
48. 02:28So, we will get from these calibration results.
49. 02:30We will apply the complete measurement fitter function on that, on these results.
50. 02:35And given the state labels which is just which states have prepared.
51. 02:38So, in the case of three qubits, it's 000 001 010 and so on.
52. 02:45We apply the filter, for we create the filter function then to filter later on
53. 02:49the noisy measurement results and I will show you how the matrix looks like now.
54. 02:55So, this is the matrix we got for the Hanoi device and we can see for example
55. 03:00if I've prepared the state 000 there's a 91
56. 03:03or 92% chance to actually measure that state.
57. 03:07Well, they're smaller probabilities to measure other states.
58. 03:09So, on the diagonal elements here are those that
59. 03:13should ideally be as close as possible to one.
60. 03:16But for example on this diagonal that would mean that all bits flipped.
61. 03:21And of course that probability is actually the smallest.
62. 03:23So, here you have the smallest number even in zero.
63. 03:27Now what we can do is we can look at how
64. 03:33this matrix looks like in a more illustrative way here
65. 03:37you can see the prepared state and the measured state.
66. 03:39So, as before you can see the probabilities of the dark
67. 03:43head is the closer it is to one, looks now as
68. 03:45if it would be almost one and well it is almost
69. 03:48one is like what 90 between 91 and 94% or something.
70. 03:54But then we also see here there's some higher probability that for example the
71. 03:59second qubit flips rather than that the first qubit or last qubit flips
72. 04:04and so on. So this is just an illustrative way of seeing it.
73. 04:07But one thing I actually want to notice now here, we see there's
74. 04:10a warning which is deprecation warning, because
75. 04:13the Qiskit Ignis package is deprecated.
76. 04:16So, the function that I've used just for this illustration
77. 04:19now might not be available anymore in a few weeks.
78. 04:23So, this just reminds me that I wanted to give you
79. 04:25this general warning that of course Qiskit, it's being continuously developed.
80. 04:30So, all the functions that you see now hopefully
81. 04:32they will still be available in a few weeks,
82. 04:35months, years.
83. 04:36But sometimes they change a bit they might need or they might have
84. 04:39additional functionalities and then you might need to give them another argument.
85. 04:43They might require one more argument or something.
86. 04:45So, if you try to run these functions one by one and something doesn't work maybe just
87. 04:49check whether, checking the documentation of Qiskit, whether by
88. 04:52now it needs one additional argument for example.
89. 04:57So, now we can have a look at the Grover's job that I ran
90. 05:00before and see then how we how the measurement error mitigation affects that.
91. 05:06So, we call our backend and the old job by good that I saved the job ID
92. 05:12here, then we look at the counts which are now called the
93. 05:15noise counts which are the counts we got before, that I showed you before
94. 05:20and we can now, once we are given the noise counts we can
95. 05:23just calculate the mitigated counts, mitigated results
96. 05:27by applying the measure the measurement filter.
97. 05:32This way, so we apply the measurement filter and then get these mitigated
98. 05:35counts and now we can plot both the noise counts and the mitigated counts
99. 05:40and let's see how that looks like.
100. 05:43So, here we can see it's not a huge advantage.
101. 05:47It's not going from like 29% to 50% which would be the theoretical result.
102. 05:51But we can still see that the two elements that we're looking for
103. 05:55in the grover algorithm 001 and 010 those to get a small,
104. 06:01we get a higher chance now, while all the others, here's a
105. 06:05small exception, but in general they all have a lower probability.
106. 06:08So, the red ones are the mitigated results.
107. 06:11So, for the Deutsch-Jozsa algorithm that we ran before, let us look how they
108. 06:17mitigated results look in that case.
109. 06:20So, first here we can see the results of the very last job that we ran on Deutsch-Jozsa.
110. 06:24So, the one where we created our oracle ourselves with all the CNOT gates.
111. 06:29So, we only only had this 58% chance probability to get the correct result.
112. 06:36Now we get 62%.
113. 06:38So, again it's still not going up to one.
114. 06:40But of course the problem is that most of the errors here
115. 06:43came from the CNOT rates, from the
116. 06:46CNOT error rates and not from the measurement.
117. 06:50That's why we, so we only correct and correct for the measurement of course.
118. 06:53And then we can see still all the other errors decrease.
119. 06:57But so, what happens if we look at one of the results where we had a constant oracle.
120. 07:05In this case for the constant oracle,
121. 07:07we did not have to apply any CNOT gates and the circuit depth was very short.
122. 07:11So, in the end we basically have no other errors but almost all
123. 07:15errors just that we had just came from the measurement error mitigation.
124. 07:20So, in this case here we can see that from 96%,
125. 07:23our measurement error mitigation brings us to 100%.
126. 07:28And all these blue small errors that are here,
127. 07:31they all disappear in the mitigated version or at least they
128. 07:34become so small that we can't see them anymore on the Histogram.
129. 07:38You can also check for the other oracles, because that oracle was now
130. 07:44constant.
131. 07:47Now we have another mitigated one, but the two,
132. 07:49now we can look at the other two oracles that were given by Qiskit
133. 07:52or at least we have a higher probability before. So, here we can see from 84 it goes to 91.
134. 07:58And in the very last one,
135. 08:04we can see that it goes from 92-99.
136. 08:07So you can see this,
137. 08:09this oracle was also implemented in a way that probably
138. 08:13did not require a lot of gates but was quite efficient in
139. 08:17or efficient, well as we want to call,
140. 08:19it would definitely be just easier implemented to create this balanced function.
141. 08:26Yes,
142. 08:27so with this was actually the last video of our
143. 08:30course, so I really hope you have enjoyed all these videos.
144. 08:34I wish you good luck for your final exam and I hope to see you in
145. 08:37future videos from IBM, where they talk about getting more insights on how to use Qiskit.

To enable the transcript, please select a language in the video player settings menu.