The quantum mechanics we learn in undergrad and even grad level classes often does not tell us much about the physics of what we actually observe in the laboratory. But why? Well for one thing, idealized quantum mechanics doesn't deal with open quantum systems, those that interact with the actual environment—and this changes everything. Quantum mechanical states are so delicate that unless we are very careful about how we interact with them, they can easily disperse the the information they contain into the environment.
That's a challenge for us physicists, since the information that these states store is what we use to perform quantum computations. For the past 6 years I spent doing my PhD in quantum computing, I worked on figuring out how to best measure superconducting quantum bits, the nanoscale objects that store quantum information, in our world of open quantum systems—without destroying them. So, how do we do it?
Injection and output lines inside an IBM dilution refrigerator which houses the quantum processors, amplifiers, and all cryogenic hardware components.
The common method for reading out superconducting qubits is with Quantum Non-Demolition (QND) measurements. These are a class of measurements, where, once you measure the quantum state and it collapses into one of the classical states, |0> or |1>, making further measurements on the same system won't change the result (unlike, say, position and momentum, where measuring one randomizes subsequent measurements of the other). To achieve this, we send a very weak signal consisting of only a few microwave photons to the qubit, which is coupled to a microwave resonator. When the signal reaches the resonator its phase will shift slightly, depending on whether the qubit state is 0 or 1, then the signal leaves the processor and travels back up to our room-temperature electronics. However, this microwave signal is extremely weak, only about 10^-16 W—ten times weaker than the most sensitive signal that an FM radio antenna can pick up. It would be impossible to see such a low power signal without the aid of an amplifier.
The first type of amplifier we introduce to combat this problem is called the HEMT (High Electron Mobility Transistor), capable of adding around 40 decibels (dB) of power, where decibels are a logarithmic unit used to compare signal strengths. A 3 dB increase equates to doubling the power, a 10 dB increase is 10 times the power, and a 40 dB increase is 10*10*10*10 = 10,000 times the power. However, these HEMTs are commercial components and add a lot of extra noise to the signal. It's possible to read out the state of a transmon qubit with a HEMT, but this usually requires measuring the state thousands of times and averaging the results. (For more information on why you might want to run many trials, or shots, of the same experiment, check out the IQX docs here). But if we hope to run a quantum algorithm, we need single-shot measurement capability; that is, we need to be able to read out a qubit's final state after running an algorithm only once, no averaging allowed.
We fix this by adding a component between the qubit and the HEMT that does an initial bout of amplifying without adding thermal noise, so that the signal is then strong enough for the HEMT to amplify more easily. This component is called a quantum-limited amplifier (QLA). The QLA amplifies just 20 dB, or 100 times, to give the boost that the HEMT needs to finish the job. But, in doing so, A QLA adds only minimum amount of noise possible based on the rules of quantum mechanics. The Heisenberg uncertainty principle puts a maximum precision on simultaneous measurement's of specific pairs of properties in a system like its position and momentum, and this idea works the exact same way. In microwave measurement, we usually measure two components of the signal, called its In-phase (I) and Quadrature-phase (Q) component, which are essentially just the real and imaginary part of a signal tone. However, like measuring something's position and momentum, measuring both I and Q perfectly is not possible. Instead, it is mathematically required to add at least the energy of half of a photon's worth of noise, on average, to the signal. QLAs are the only amplifiers today capable of approaching this quantum noise limit. You can learn more about two types of QLAs, the Traveling Wave Parametric Amplifier (TWPA) and the Josephson Parametric Converter (JPC), in a recent research blog post here.
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| A) visual representation on the difficulties of reading out a qubit with a HEMT amplifier alone. The HEMT adds so much additional noise that the signals (which leave the qubit now phase-shifted--blue for ground and red for excited states) are very hard to discern without many averages. (B) shows the readout chain with the addition of a Quantum-Limited Amplifier. The QLA acts as the first amplifier in the readout chain, providing modest gain with the minimum possible noise. The quantum noise is now the dominant noise in the system, so now when signal passes through the HEMT amplifier, the added thermal noise doesn't destroy it. The result is capable of single-shot measurement. |
Reading out a qubit takes more than just amplifying a signal, however. In order to complete the readout sequence, other pieces of hardware must be introduced; cryogenic isolators and circulators, in order to fix issues caused by the QLAs. One type of QLA, the Josephson Parametric Converters (JPCs), tend to amplify signal in reflection, meaning a large tone would be sent backwards towards the qubit, which is bad because it will disrupt the fragile quantum state. But the other popular QLA, the Traveling Wave Parametric Amplifiers (TWPA) introduces difficulties as signals try to flow over their thousands of Josephson junctions, also creating some spurious reflections. In order to direct these reflections away from the qubits, we place cryogenic isolators and/or circulators between the qubit chips and the QLAs.
Isolators and circulators use a magnetic material called a ferrite to cancel any waves propagating over incorrect paths. The two are basically the same, and both can be thought of as a three port device, but the circulator can be made into an isolator by blocking off one port.
Isolators are extremely useful, but as you might have guessed, they too have their downsides. They are large and bulky components that must fit into the dilution fridge, and they introduce additional signal loss into the system as some photons always leak out when you add new components. On-chip isolators and circulators are also an interesting area of superconducting quantum information research <https://arxiv.org/abs/2006.01918>, as we try to find ways to reduce this loss and make components that take up less space in the fridge.
There are still many more subtleties underlying the physics of using microwaves to read out qubits. For instance, with some highly engineered systems, it is actually possible to attain good measurement fidelity without a QLA using a technique called Excited State Promoted (ESP) readout. This takes advantage of the fact that qubits are not truly 2-level systems; they have higher energy excited states than the |1> state we use for calculations that we usually do our best to ignore (basically, instead of just a 0 and 1 like in a regular bit, there's also 2, 3, etc). If we push excited state qubits to these higher states before readout, the separation between these and the ground state qubits becomes more obvious. We used this technique in order to achieve a Quantum Volume of 64 on one of our devices. <https://arxiv.org/pdf/2008.08571.pdf.>
ESP readout can't replace QLAs, though. ESP readout sometimes introduce non-computational errors of its own, such as when it comes to implementing measurement with that requires feedback, like error correction. In these cases, we need the measurements to be non-perturbative, meaning the measurement itself does not disrupt the quantum state, because later parts of the algorithm are based on the currently measured state. QLAs reduce the drive strength of the pulse used for readout by a factor of 10, which makes the measurement far less likely to disturb the qubits by measuring them.
We generally want to have the measurement pulses be as short as possible, as this minimizes read out errors where the qubit spontaneously flips its state and is less likely to effect other qubits nearby. But in order to shorten the pulse time, the strength of the pulse (i.e. number of microwave photons) needs to increase. Yet stronger pulses tend to exacerbate these spontaneous errors, making them non-QND. It's sort of a Catch-22. Furthermore, the field is still lacking qualitative agreement between observed phenomenon and theoretical models relating non-QND effects to measurement fidelity. For instance, in a recent paper, a group led by Ioan Pop at the Karlsruhe Institute of Technology was able to create QND measurements using a fairly strong microwave pulse that one might think should be destructive <https://arxiv.org/pdf/2009.14785.pdf>. They attribute this to using granular aluminum, among other things. The physics of measurement and their effect on the qubits, what we refer to as back-action, remain a mysterious and intriguing area of research. We take for granted the QND nature of typical dispersive measurement in superconducting qubits, but should we?
Harnessing the power of measurement is a key component to building a quantum computer. The engineering required for a fault-tolerant quantum computer is often focused on the processors themselves, with good reason. But there is still much more work to be done outside the chip as well, and as this blog grows, we will take deep dives into all aspects of quantum hardware. We hope you’ll continue reading!