High-Temperature Superconductors in Quantum Computers
What does a room-temperature superconductor mean for quantum computers?
The recent interest in LK-99, an alleged high-temperature superconductor, has been electrifying, especially for a discovery in experimental physics announced in a pre-print, that is, without peer review or replication by independent labs. If true, it is nothing short of a breakthrough. But what would it mean for quantum computing?
Superconductors
Superconductors have a few unique properties that emerge when they are cooled below a critical temperature \(T_{\mathrm{c}} > 0\) that is different for each superconducting material. At that critical temperature, the material undergoes a phase transition, not unlike water turning into ice at 0°C (32°F) when it suddenly solidifies. But instead of turning into a solid, a superconductor becomes a perfect conductor of electricity in that its resistance vanishes completely.
In such a state, the superconductor can carry an electric current in a loop forever, without any external power source. And without any resistance, the material does not dissipate heat to its environment.
The so-called Meissner effect accompanies this transition, in which any magnetic field is completely ejected from the material. Normally, magnetic fields penetrate materials, and above the critical temperature that is also what happens with superconductors. Below the critical temperature, however, no magnetic field can enter the superconducting material, and it therefore has to bend around the material itself, which can lead to the levitation of a magnet above the superconductor.
For most superconductors discovered so far, the critical temperature is well below 77 K at ambient pressure. Above 77 K live the high-temperature superconductors, although that threshold is still more than 220 K below room temperature. Many of the high-temperature superconductors discovered up to now have required immense pressure. If the superconductivity of LK-99 can be replicated, it would come with a critical temperature of 400 K at ambient pressure.
So, what are superconductors good for? Because superconducting magnets are powerful electromagnets, they are used in MRI machines in hospitals and in certain types of maglev trains. Superconductors are also used in Josephson junctions, from which highly sensitive magnetometers are made (a.k.a. SQUIDs). And superconductors are of course used in quantum computers.
Superconducting Qubits
Superconducting qubits are the most common modality today. The essence of every qubit is that you need to engineer a two-level system, unless you already have one, such as electron spins in quantum dots or nitrogen vacancies in diamond.
Why two levels? Because qubits need to represent two logic states: \(|0\rangle\) and \(|1\rangle\).
In multi-level systems, you typically encode the ground state as \(|0\rangle\) and the first excited state as \(|1\rangle\). Transitions from one state to another come with the exchange of energy: absorption of energy to move up to a higher excitation or the release of energy to fall back down to the ground state. For qubits, you need \(|0\rangle\) and \(|1\rangle\) states you can rely on. This means that all higher excited states must be excluded from participating, lest they ruin the qubit’s purity.
If the energy levels are evenly spaced, we can inadvertently excite higher energy levels, because the same amounts of energy can be absorbed and subsequently released back to the environment by any excitation. With uneven energy levels, it is much easier to confine the system to only two levels, as desired.
For atomic energy levels, nature provides the constraints, but if we choose to build a tiny circuit with a capacitor and an inductor, all made from superconducting materials, we have a multi-level system we can tweak. The only problem is that the energy levels of such a system are uniform. That’s where the Josephson junction comes in.
A Josephson junction is a sandwich of two superconductors with a thin slice of an insulator in-between. A (super)current can flow across the junction because pairs of electrons can ‘tunnel’ across. Yes, a charge runs through such an insulator, courtesy of quantum mechanics!
If instead of an inductor we use a Josephson junction, the energy levels are spread non-uniformly, and that spread can be tuned. Such a circuit dissipates virtually no heat, which is exactly what we want. Thermal energy from the circuit itself could excite the qubits, but of course the same goes for ambient ‘noise’ from the environment, or plain ol’ heat from the room.
And that is why quantum computers based on superconductors need to be cooled down to extremely low temperatures: to minimize the influence of thermal energy. Yes, they also need to be cooled down to below the critical temperature, but that is typically a few orders of magnitude above the actual temperature of a quantum computer.
For instance, a niobium superconductor has a critical temperature of 9.2 K. But that temperature is much higher than what is needed to operate a quantum computer with superconducting niobium qubits (< 15 mK). The photon frequency corresponding to the relevant energy levels is around 5 GHz. For thermal noise (E = kT) to be of the same energy as the difference between the ground and first excited states (E = hν), we get a temperature of T = hν/k = 240 mK, where h is Planck's constant, k Boltzmann's constant, and ν the frequency of the photon.
A Bit of a Temperature
But we can tweak the energy levels, right? Let’s assume we have a room-temperature superconductor that we can use to build a quantum computer with. Let’s also assume we intend to run it at 5 K, which is cold, but it would not require dilution refrigerators, which only have a cooling power in the mW range. Cryocoolers in that temperature range have a much higher cooling power, which makes it easier to scale up quantum chip designs.
Now, to minimize the effect of ambient noise exciting the qubits, the thermal energy must be at least an order of magnitude smaller than the energy between the energy levels, which means we land in the THz range. In that range, not a lot of commercial electronic equipment is available, which is known as the ‘terahertz gap’ between microwave electronics and infrared optics. That makes it tricky to manipulate the qubits.
More accurately, to break up the electron (a.k.a. Cooper) pairs in a superconductor and with it its superconductivity, an energy of at least 2Δ(T) is required, where Δ(T) is the energy gap at the temperature T. This break-up energy has an upper limit given by 3.528 kTc when the temperature is at absolute zero. It decreases up to the critical temperature, where it becomes zero, because at that temperature the superconductivity vanishes. If LK-99 turns out to be a veritable high-temperature superconductor, we find the energy to be around 29 THz. The same terahertz gap ballpark as before. So, tweaking the energy levels to be spaced further apart only helps us if at the same time we have equipment to initialize, manipulate, and measure the qubits, which we do not at present.
Conclusion
So, are room-temperature superconductors relevant to quantum computers made from superconducting qubits? With current qubit designs and electronics, no. While we can tweak the energy levels and with it the operating temperature to some extent, we are currently limited by the electronics available to manipulate the qubits at such frequencies.
That said, decoherence is more worrisome than induced relaxation or inadvertent excitation from environmental noise, which is what I have focussed on up to now. Decoherence has two components: dephasing, in which qubits lose track of their exact phase, and phase breaking, in which they lose their superposition altogether. To protect superconducting qubits against decoherence we must isolate them from their environment… by means of extremely low temperatures.