# Thermal Limits of Quantum Compting

Sun, Dec 25, 2022 tags: [ physics optics photonics ]

Disclaimer: I have little knowledge about the details of quantum computing! Neither do you need any to understand this short article.

I am working on my master’s thesis these days, or more specifically the research that will hopefully lead to having something to write about. While I cannot go into details due to my host institutes customs on intellectual property etc. – the world will have to wait for my thesis to be published – I am fortunately allowed to talk about the context and the problem. Later on, I hope to write a few more articles on the specific technologies I am using, while remaining at a high enough abstraction level to not violate any rules. I also won’t go into extreme details: for that you will have to wait for my master’s thesis.

Most of what I’ve learned can also be found in the papers, 1, 2, 3.

At this point, what’s most interesting is the context: Controlling quantum computers with light. To see why that’s an interesting approach, it’s important to first look at how today’s quantum computing platforms work, and how qubits inside them are controlled and read:

## The Problem

What almost all (if not all) quantum computing platforms of today have in comon is their requirement for extremely low temperatures, using a cryogenic dilution fridge. This cooler uses different helium isotopes to reach temperatures of far below 1 K, usually below 20 mK (milli-kelvin). That’s because the current qubit implementations - whether superconducting, spin, atomic, … - use quantum states, usually two of them corresponding to the qubit values |0> and |1>, that are separated by a very low energy difference. This energy difference must be higher than the thermal fluctuations of the environment; otherwise the fluctuations would be enough to signficantly interfere with the qubit before any useful work could be done. As an aside, a useful rule of thumb is that thermal energy fluctuations at temperature $T$ are on the order of $\Delta E \approx k_B T$, where $k_B = 1.38 \cdot 10^{-23} \mathrm{J/K}$ is the Boltzmann constant.

To make this work, multiple stages within a cryostat are required; see for example (2) for how to build a modern quantum computer’s cryogenic environment. Here, the team uses five(!) stages, at temperatures of 35K, 3K, 0.9K, 0.1K, and finally 0.01K - that’s 10 milli-kelvin. A massive problem at this point is the cooling: the colder your devices are, the harder it is to cool them even further. After all, you need to extract energy out of the system, and this is obviously very difficult if there is already very little energy left to extract. As an example, the article gives a cooling power of 30 Watts, that’s about four bright LED lightbulbs, at $T = 45\mathrm{K}$. This is quite a bit, and notably the cooling power in excess of the so-called passive load of the cryostat, i.e. the heat passing through the insulation layers. However, the cooling power drops to 40 mW (0.04 W) at 1.2 K, 200 µW (0.0002 W) at 140 mK, and finally only 20 µW (0.00002 W) at the final stage of 6 mK.

That’s alright for a steady state, passive system. But in a quantum computer, the qubits are supposed to solve problems. And such calculations imply at least some activity, which in turn comes with energy consumption and thus energy dissipation. Specifically, in a quantum computer based on e.g. superconducting qubits (“transmons”, for example), the qubits are controlled and read by microwave signals travelling through coaxial cables into the cold area.

This works fairly well, except for two issues: First, the cables are very expensive (confirmed to me as a top pain point by a professor who has spent years on quantum computing), and secondly: they conduct heat. The first point is painful but tolerable as long as there is enough funding. The second point is much more physical, in contrast.

There are two issues with the heat conduction of the commonly used coaxial cables: First the passive heat load, or the fact that the metallic cables simply conduct heat. This is caused by the same mechanisms (electron conduction) that makes them conduct signals very well. That means: one could use cables that conduct less heat, but also have worse performance conducting the actual signals. Another mechanism of heat conduction besides just the bulk metallic conductivity is the coupling of heat radiation into the cables. At room temperature (300 K), everything emits a lot of infrared radiation; this radiation can enter the coaxial cables and will be conducted into the heart of the quantum computer, if no measures are taken. In addition, the cable’s own material is radiating too. This all becomes worse with the number of qubits, as each qubit needs a certain number of lines feeding into/out of it, and each signal path needs its own cable.

The second aspect is closely related: the active heat load. In order to attenuate the heat radiation conducted by these cables, common platforms today apply a combined attenuation of -60 dB: that is a reduction of power by a factor of one million! This ensures that very little of the initial heat radiation is left at the critical stages; however, attenuation of radiation comes with dissipation of its energy as heat. And that heat is dissipated in the cryogenic cooler (though not in the most critical stages). The signal must be comparatively strong to survive this attenuation.

## A Solution?

A very basic idea would be to instead take the microwave (or “RF”) signals, and instead of transmitting them directly, modulate them onto an optical signal. This is very similar to how radio works: an acoustic wave is modulated onto a radiofrequency carrier wave of a much higher frequency than the signal itself.

Why is this attractive?

For once, a single optical signal can, due to its high frequency (or “bandwidth”) carry many more than just one RF signal. This means that many (for a value of “many” between eight and 64) conventional cables can be replaced by one fiber.

a modulated signal (slow oscillations) on a carrier signal (frequent oscillations)

Then, fiber is very cheap compared to high-tech coaxial cables. And it is made not from metal, but glass, and from very thin glass at that - meaning that the passive heat load is greatly reduced (by about 100x, according to some estimates from the cited papers).

And finally, fibers emit very little infrared (heat) radiation themselves, and any conducted radiation can be filtered comparatively easily.

The big challenges remaining to be solved are now:

1. Reliably modulate and demodulate RF signals at room temperature or cryogenic temperatures (around 4K) from light. The technology exists, and has been proved to work for individual qubits - even with commercially available modulators and photodiodes.
2. Reliably multiplex and demultiplex multiple signals onto and out of one fiber. This is the center pillar of my master’s thesis, and is relatively challenging; building good multiplexers (low crosstalk, low loss) is difficult. Especially if a system is very sensitive to crosstalk, as qubits likely are.
3. Ensure that an optical system including its active component actually does impose a lower heat load than a conventional control bus. Processing optical signals and converting them from and into RF signals comes with inherent energy use and needs to be implemented carefully.
4. Make this whole system not much more expensive than what is possible today. The lack of expensive RF cables helps, but the additional conversion steps don’t come for free.

And with all of that, pure performance for controlling qubits should obviously be at a comparable level - that on its own is likely already a big task!