WEBVTT NOTE This file was exported by MacCaption version 7.0.13 to comply with the WebVTT specification dated March 27, 2017. 00:00:05.505 --> 00:00:09.343 align:center line:-1 position:50% size:59% Before we introduce superconducting qubits and quantum processors, 00:00:09.343 --> 00:00:15.315 align:center line:-1 position:50% size:60% let's take a look at the classical architectures of computers that we use today. 00:00:15.315 --> 00:00:20.520 align:center line:-1 position:50% size:52% As you know, we represent information in a classical computer using bits 00:00:20.520 --> 00:00:23.690 align:center line:-1 position:50% size:44% that can either be in state 0 or 1. 00:00:23.690 --> 00:00:28.962 align:center line:-1 position:50% size:58% Physically, what happens inside a classical computer when we want to represent 0 or 1 00:00:28.962 --> 00:00:36.336 align:center line:-1 position:50% size:65% is that the state of a transistor switches between being on or off or at high or low voltage. 00:00:36.336 --> 00:00:42.309 align:center line:-1 position:50% size:63% We then combine bits of information using Boolean logic to perform operations on the bits 00:00:42.309 --> 00:00:45.512 align:center line:-1 position:50% size:55% in order to solve computational problems. 00:00:45.512 --> 00:00:51.718 align:center line:-1 position:50% size:52% In the table shown to the bottom left, you find the truth table for an AND gate 00:00:51.718 --> 00:00:55.722 align:center line:-1 position:50% size:61% when it is applied to two input states, A and B. 00:00:55.722 --> 00:01:04.564 align:center line:-1 position:50% size:53% For this gate, the outcome is 1 if and only if both A and B are in state 1. 00:01:04.564 --> 00:01:08.802 align:center line:-1 position:50% size:57% Now, let's consider the quantum computer. 00:01:08.802 --> 00:01:14.942 align:center line:-1 position:50% size:57% In a quantum processor, the fundamental information carrier is a quantum bit (qubit). 00:01:14.942 --> 00:01:22.249 align:center line:-1 position:50% size:61% Just like the classical bit, we encode quantum information in two basic states called 0 and 1, 00:01:22.249 --> 00:01:26.620 align:center line:-1 position:50% size:47% but we express the quantum states using the annotation you see here, 00:01:26.620 --> 00:01:30.857 align:center line:-1 position:50% size:50% which shows that it's a quantum state and not the classical one. 00:01:30.857 --> 00:01:33.860 align:center line:-1 position:50% size:50% However, contrary to the classical bit, 00:01:33.860 --> 00:01:38.231 align:center line:-1 position:50% size:39% the quantum bit is not limited to only being in state 0 or 1. 00:01:38.231 --> 00:01:42.135 align:center line:-1 position:50% size:42% It can actually be in both states at the same time. 00:01:42.135 --> 00:01:45.272 align:center line:-1 position:50% size:59% This phenomena is known as superposition, 00:01:45.272 --> 00:01:50.310 align:center line:-1 position:50% size:54% and it really reflects the statistical nature of quantum mechanics. 00:01:50.310 --> 00:01:54.648 align:center line:-1 position:50% size:63% Mathematically, we can write the quantum state in the way shown here, 00:01:54.648 --> 00:02:01.288 align:center line:-1 position:50% size:63% where the complex coefficients, CNOT and C1, describe the probability of finding a qubit 00:02:01.288 --> 00:02:04.157 align:center line:-1 position:50% size:20% in state 0 or 1. 00:02:04.157 --> 00:02:11.398 align:center line:-1 position:50% size:68% We can then visualize the quantum state as a point on a unit sphere, known as the Bloch sphere, 00:02:11.398 --> 00:02:18.472 align:center line:-1 position:50% size:67% where we find the ground state 0 on the north pole and excited state 1 on the south pole, 00:02:18.472 --> 00:02:21.375 align:center line:-1 position:50% size:43% just like you see illustrated here. 00:02:21.375 --> 00:02:27.147 align:center line:-1 position:50% size:55% Another important ingredient in a quantum processor is entanglement. 00:02:27.147 --> 00:02:30.817 align:center line:-1 position:50% size:61% This is a concept I will elaborate on a bit later, 00:02:30.817 --> 00:02:34.721 align:center line:-1 position:50% size:63% but using an analogy with a classical 2-bit gate, 00:02:34.721 --> 00:02:37.190 align:center line:-1 position:50% size:53% like the AND gate we discussed before, 00:02:37.190 --> 00:02:42.462 align:center line:-1 position:50% size:55% entanglement between two qubits can be obtained through two qubit gates. 00:02:42.462 --> 00:02:44.798 align:center line:-1 position:50% size:61% Without entanglement, the quantum computer 00:02:44.798 --> 00:02:50.270 align:center line:-1 position:50% size:57% will not have access to its powerful scaling and computational power. 00:02:50.270 --> 00:02:53.640 align:center line:-1 position:50% size:35% It's an essential ingredient in a quantum processor. 00:02:55.342 --> 00:02:59.446 align:center line:-1 position:50% size:54% In addition to superposition states, there's another very important ingredient 00:02:59.446 --> 00:03:05.185 align:center line:-1 position:50% size:55% needed to give a quantum processor its true processing power: entanglement. 00:03:05.185 --> 00:03:10.023 align:center line:-1 position:50% size:58% It is quite intuitive, that even if we have thousands of isolated qubits in a processor, 00:03:10.023 --> 00:03:12.259 align:center line:-1 position:50% size:60% we still need them to interact with each other 00:03:12.259 --> 00:03:16.463 align:center line:-1 position:50% size:49% before we can harness their combined computational power. 00:03:16.463 --> 00:03:19.800 align:center line:-1 position:50% size:47% Entanglement is a special property of quantum mechanics 00:03:19.800 --> 00:03:26.006 align:center line:-1 position:50% size:51% that allows multiple qubits to share a single-extended superposition state. 00:03:26.006 --> 00:03:33.113 align:center line:-1 position:50% size:61% We just learned that measurement of a qubit in a superposition forces it to be either 0 or 1. 00:03:33.113 --> 00:03:35.615 align:center line:-1 position:50% size:48% In the case of two entangled qubits, 00:03:35.615 --> 00:03:41.121 align:center line:-1 position:50% size:49% we make sure a single qubit forces each qubit to be either 0 or 1. 00:03:41.121 --> 00:03:45.325 align:center line:-1 position:50% size:59% To gain some insight into how entanglement benefits itself, 00:03:45.325 --> 00:03:48.128 align:center line:-1 position:50% size:48% let's consider the following example. 00:03:48.128 --> 00:03:51.431 align:center line:-1 position:50% size:51% We take two qubits and entangle them with each other. 00:03:51.431 --> 00:03:57.504 align:center line:-1 position:50% size:46% Remember, if we measure qubit 1, it can either be in state 0 or 1. 00:03:57.504 --> 00:04:00.407 align:center line:-1 position:50% size:55% If we then subsequently measure qubit 2, 00:04:00.407 --> 00:04:05.145 align:center line:-1 position:50% size:61% we find that the outcome of this measurement depends on the state of qubit 1, 00:04:05.145 --> 00:04:09.816 align:center line:-1 position:50% size:51% even if the two qubits no longer exchange information with each other. 00:04:09.816 --> 00:04:12.352 align:center line:-1 position:50% size:51% If we then look at the combined result, 00:04:12.352 --> 00:04:19.493 align:center line:-1 position:50% size:60% we find that the probability of measuring both qubits in state 0 or both qubits in state 1 00:04:19.493 --> 00:04:26.066 align:center line:-1 position:50% size:60% is much larger than measuring the two qubits in opposite states, as you can see here. 00:04:26.066 --> 00:04:30.437 align:center line:-1 position:50% size:42% This means that the qubits can, in fact, affect each other, 00:04:30.437 --> 00:04:34.441 align:center line:-1 position:50% size:69% even when they no longer exchange information. 00:04:34.441 --> 00:04:42.048 align:center line:-1 position:50% size:62% In this way, quantum interference pattern occurs between the qubit states in the register. 00:04:42.048 --> 00:04:45.218 align:center line:-1 position:50% size:36% It is this effect that we use in the quantum algorithms, 00:04:45.218 --> 00:04:47.787 align:center line:-1 position:50% size:59% where the result of the algorithm is obtained 00:04:47.787 --> 00:04:52.692 align:center line:-1 position:50% size:48% by studying the probability of finding the register in a certain given state. 00:04:54.694 --> 00:05:00.066 align:center line:-1 position:50% size:56% Ideally, we would like our quantum system to stay in the state in which it is initiated 00:05:00.066 --> 00:05:03.236 align:center line:-1 position:50% size:64% for as long as needed in the quantum algorithm. 00:05:03.236 --> 00:05:06.773 align:center line:-1 position:50% size:58% Unfortunately, however, this is not the case. 00:05:06.773 --> 00:05:14.014 align:center line:-1 position:50% size:71% When you learn about quantum systems, you often hear about the term coherence time or decoherence. 00:05:14.014 --> 00:05:19.352 align:center line:-1 position:50% size:63% This is a measure of how well the qubit manages to stay in its quantum state. 00:05:19.352 --> 00:05:22.856 align:center line:-1 position:50% size:47% As quantum engineers, it is our mission to design a system 00:05:22.856 --> 00:05:26.393 align:center line:-1 position:50% size:56% to have as long of quantum coherence times as possible, 00:05:26.393 --> 00:05:31.264 align:center line:-1 position:50% size:49% since this will allow us to run a larger and larger number of quantum gates 00:05:31.264 --> 00:05:34.534 align:center line:-1 position:50% size:62% on the system before it loses its quantumness. 00:05:35.735 --> 00:05:38.104 align:center line:-1 position:50% size:65% One way to think about quantum coherence time 00:05:38.104 --> 00:05:42.642 align:center line:-1 position:50% size:57% is in terms of how well isolated a system is from its environment. 00:05:42.642 --> 00:05:48.215 align:center line:-1 position:50% size:46% We can divide up coherence times into two characteristic time scales. 00:05:48.215 --> 00:05:52.385 align:center line:-1 position:50% size:47% First, we have T1, which is the energy relaxation time, 00:05:52.385 --> 00:05:57.757 align:center line:-1 position:50% size:53% which means the time scale after which the qubit relaxes to the ground state. 00:05:57.757 --> 00:06:01.261 align:center line:-1 position:50% size:44% This process can be represented in the animation to the left, 00:06:01.261 --> 00:06:05.632 align:center line:-1 position:50% size:52% where the qubit state relaxes from its excited state on the south pole 00:06:05.632 --> 00:06:09.903 align:center line:-1 position:50% size:55% and the Bloch sphere to the ground state in the north pole. 00:06:09.903 --> 00:06:14.407 align:center line:-1 position:50% size:55% After the system has relaxed, there's no more energy left in the system, 00:06:14.407 --> 00:06:18.278 align:center line:-1 position:50% size:58% so we will need to re-initiate the qubit state. 00:06:18.278 --> 00:06:22.415 align:center line:-1 position:50% size:53% Also note that this is only one trajectory which the qubit can relax, 00:06:22.415 --> 00:06:27.087 align:center line:-1 position:50% size:39% so it can relax from any point on the Bloch sphere. 00:06:27.087 --> 00:06:31.458 align:center line:-1 position:50% size:63% Then we have T2, which is the dephasing time, 00:06:31.458 --> 00:06:36.563 align:center line:-1 position:50% size:52% which refers to the time after which the system loses its phase information. 00:06:36.563 --> 00:06:41.001 align:center line:-1 position:50% size:60% This can be observed if we place the system on the equator of the Bloch sphere 00:06:41.001 --> 00:06:44.638 align:center line:-1 position:50% size:47% and let the state evolve for some time. 00:06:44.638 --> 00:06:47.874 align:center line:-1 position:50% size:37% This process is represented in animation to the right. 00:06:47.874 --> 00:06:50.110 align:center line:-1 position:50% size:56% As opposed to the energy relaxation time, 00:06:50.110 --> 00:06:56.816 align:center line:-1 position:50% size:58% the dephasing can, under some conditions, be reversed by apply a refocusing process. 00:06:56.816 --> 00:06:57.817 align:center line:-1 position:50% size:37% From these two animations, 00:06:57.817 --> 00:07:03.323 align:center line:-1 position:50% size:64% we can see that the impact that a certain source of noise will have on these two time scales 00:07:03.323 --> 00:07:07.727 align:center line:-1 position:50% size:50% depends on how the noise is coupled to the quantum system. 00:07:07.727 --> 00:07:13.266 align:center line:-1 position:50% size:59% Finally, let's illustrate how the computational power scales for a quantum processor 00:07:13.266 --> 00:07:17.170 align:center line:-1 position:50% size:53% as more and more qubits are entangled and added to the register. 00:07:17.170 --> 00:07:21.341 align:center line:-1 position:50% size:64% If we start with one qubit, we have already seen that we can represent the system 00:07:21.341 --> 00:07:27.347 align:center line:-1 position:50% size:58% by two complex coefficients, CNOT and C1. 00:07:27.347 --> 00:07:31.951 align:center line:-1 position:50% size:40% If we then add one more qubit and entangle the two qubits, 00:07:31.951 --> 00:07:36.956 align:center line:-1 position:50% size:46% we need four complex coefficients to describe the combined state. 00:07:36.956 --> 00:07:43.163 align:center line:-1 position:50% size:66% If we add another qubit to the register, we arrive at eight complex coefficients and so on. 00:07:43.163 --> 00:07:48.935 align:center line:-1 position:50% size:51% In conclusion, we see that the number of coefficient scales adds 2n, 00:07:48.935 --> 00:07:52.672 align:center line:-1 position:50% size:43% where n is the number of qubits. 00:07:52.672 --> 00:07:56.710 align:center line:-1 position:50% size:46% This gives the quantum processor a very large number of states. 00:07:56.710 --> 00:08:01.548 align:center line:-1 position:50% size:47% If we entangle 300 qubits, we can represent more coefficients 00:08:01.548 --> 00:08:04.684 align:center line:-1 position:50% size:65% than the number of atoms in the known universe.