Quantum Computing for Natural Sciences (with IBM Quantum)

1. 00:00Hi everyone and welcome back to our lecture series on quantum computing applications in the natural sciences.
2. 00:07This is lecture number nine and here we will be taking a look at how to improve the results of quantum computations on noisy
3. 00:14hardware through error mitigation techniques.
4. 00:19You may have heard of quantum error correction before and perhaps are wondering what is the difference between error correction
5. 00:24and error mitigation. in quantum error correction, we aim to catch and correct the error of every single instruction in a
6. 00:34quantum circuit and thus make every single circuit execution perfect.
7. 00:40On the other hand, in error mitigation, we rather aim to extract a good final result of our computation from many individual
8. 00:50runs on noisy hardware where we don't really correct the noise in the individual circuits.
9. 00:58A big difference is that error correction is believed to still be quite a bit away and require improvements both on the hardware
10. 01:07in terms of the noise level
11. 01:09And on the theory side, in terms of the complexity of the error correction code.
12. 01:15In contrast error mitigation techniques are very much something we can use today, which is where we will now dive into them
13. 01:23Let's take a look at what kind of errors we actually have in a quantum circuit, single qubit gates are the most robust operations
14. 01:31in state of the art I B M quantum superconducting devices
15. 01:35They routinely achieve an average of 99.99 gate fidelity.
16. 01:41On the other hand, two qubit gates are a little less robust and typically achieve around an order of magnitude, um less of
17. 01:50a gate fidelity and finally read out so correctly classifying a qubit as one or zero is successful with around 99% success
18. 02:02probability.
19. 02:04So all of these will make the final output of our quantum circuit noisy.
20. 02:11Let's now first take a look at how we can deal with the readout errors and look at readout error mitigation.
21. 02:20Here we prepare a set of reference states.
22. 02:23So the zero and one for our qubit and then calibrate, what results do we get
23. 02:30When we prepare those states?
24. 02:32Typically, we will get numbers such as the ones on screen where when we prepare zero, we measure zero almost all of the time
25. 02:40but not every time we can use this data to form a so called assignment matrix where our calibration data makes up the individual
26. 02:48columns of the matrix.
27. 02:51If we write our measurement probabilities as a vector P, then the assignment matrix M translates between the idealized measurement
28. 03:02probabilities and the noisy measurement probabilities that we actually measure on our device.
29. 03:09Therefore, when we invert the matrix M
30. 03:12The inverted matrix can be used to translate between a measured probability distribution to a corrected one, which represents
31. 03:23the one we perhaps would have ideally measured.
32. 03:27As you can see M to the minus one includes some negative values.
33. 03:33So the final vector of the corrected probabilities might also include small negative values, which is why it's called a quasi
34. 03:41probability.
35. 03:42This however, does not really matter for purposes such as computing expectation values.
36. 03:49In principle, we could now use this technique on every single qubit in our circuit and thus perform um a readout error
37. 03:57mitigation of a multi qubit system.
38. 04:00But it is also possible to improve this and include correlated errors on multiple qubits in a scalable way.
39. 04:08Next, I want to introduce a technique called a zero noise extrapolation which doesn't only deal with the readout but with
40. 04:15noise as a whole.
41. 04:17The idea here is that our computation gives a noisy result.
42. 04:21Unfortunately, we can't reduce the level of noise, but we can actually artificially increase the level of noise.
43. 04:29And as we then perform the computation with different noise levels, we can extrapolate our computational result to the limit
44. 04:38of no noise.
45. 04:42For example, we can increase the level of noise by stretching the duration of the pulses that actually implement the gates
46. 04:51on the hardware.
47. 04:53And here we see an example of how this was actually done in a quantum chemistry calculation to perform a VQE of a
48. 05:02lithium hydride molecule, we see on the X axis, the entire atomic distance and on the y the energy of the molecule and the
49. 05:10red data points are the unmitigated noisy results of the standard V Q E computation.
50. 05:17The other colors on top here represent the computation at increased levels of the noise.
51. 05:24And finally, the blue points denote the zero noise extrapolated limit of these data points.
52. 05:32And we see that the blue points really fit the theoretical predictions shown as a dashed line much closer than the original ones
53. 05:42So this is how zero noise extrapolation can be used to obtain an improved result from several results at different noise
54. 05:50levels.
55. 05:54A second technique I want to introduce is called probabilistic error cancellation or PEC
56. 05:59In short. Here, we assume that the noise in the device is actually known precisely.
57. 06:08So we can think of our circuit as including the gates we want to implement and some additional layers which represent
58. 06:16the noise.
59. 06:19If we could simply invert the noise channels in our circuit, for example, with these yellow boxes that represent the inverse
60. 06:28then we would recover the perfect execution of our circuit.
61. 06:33Unfortunately, typically the inverse of a noise channel will not be a physical operation that we can directly implement in
62. 06:41the hardware.
63. 06:43The core idea of PEC is however, that it's possible to cancel the noise on average with a probabilistic circuit sampling
64. 06:54technique and classical post processing for example, to correct a bit flip noise, one can with classical randomness sample
65. 07:05to either include um an identity gate or an X gate in this inverse noise layer and combine this with classical post processing
66. 07:14at a rate that is defined by the level of noise in the device.
67. 07:20With this technique, actual noise free estimators can be extracted from noisy hardware.
68. 07:27However, it's important to stress that this really relies on having a well characterized noise model on the device.
69. 07:35And it was recently demonstrated that in fact, it is possible to obtain this in a scalable way.
70. 07:41There is another price that you have to pay to use PEC which is that the variants of the estimator that you build increases
71. 07:51exponentially with the amount of noise in the system and the qubit numbers and circuit depth.
72. 07:57So the run time will scale like this where gamma is a measure of the noise in your circuit.
73. 08:03So you may wonder, well, if this scales exponentially, where is the use in that?
74. 08:09We imagine this scenario if we compare the run time with and see how it scales with the problem complexity.
75. 08:17We know that classical computers will always run into an exponential scaling which is represented by the red curve
76. 08:24So for small systems, this might be efficient and then it will grow exponentially.
77. 08:30We also know that represented as the green curve here, quantum error corrected computers will have an efficient scaling.
78. 08:39But they come at a small overhead already for small problem instances which is not yet feasible on today's hardware quantum
79. 08:49error mitigation techniques maybe
80. 08:55used to bridge the gap between these two regimes.
81. 08:59So when the noise isn't low enough, this PEC overhead will lead to an exponential scaling which is still favorable over the
82. 09:08classical computer and perhaps will lead to an advantage in between these two regimes.
83. 09:17With this, let's briefly summarize, we have seen how error mitigation techniques can enable improved results
84. 09:24Um Despite having noise present in the quantum computation,
85. 09:29the cost that we have to pay for this comes with a measurement overhead.
86. 09:34And this further stresses what we have visited in lecture number eight, which is the fact that it's important to develop
87. 09:39techniques for efficient measurement strategies,
88. 09:45the techniques that we have seen in this lecture.
89. 09:48So readout error mitigation CNE and PEC are now available to users of the Qiskit run time framework.
90. 09:57And we believe that these techniques really offer the potential to achieve a quantum advantage even in a regime where full
91. 10:05error correction is not yet available.
92. 10:10This concludes now the lecture part of our video series.
93. 10:14In the next video, we have planned something slightly different.
94. 10:17We will bring in Doctor Ivano Tavernelli as a leading expert in the field and have a little Q and A session with him
95. 10:24to take a look at the challenges and potentials of quantum computing for tasks in the natural sciences.
96. 10:33I'll see you in the next video and thank you for your attention.

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