Comparing Digital and Quantum Computers, Part 7: Power estimation

Everyone in the IT world is wondering how big a threat quantum computers pose to cryptography and how to deal with the problem. This series of articles tries to explain the problem in a popular way. After introduction to Shor's algorithm we can estimate power requirements for solution, using that algorithm.

Estimated power consumption of quantum computers

From the point of view of creating a cryptographically relevant computer, the question is not only when it will be created, but also what its power requirements will be. This subsequently allows us to estimate the necessary investments, but also operating costs. It is a very interesting problem to estimate the properties of something that does not actually exist yet. High school physics can help us with this, but certainly not Moore's law. Again, the estimate given in this article corresponds to current knowledge and may not fully correspond to future reality. As they say, no theory survives the collision with reality.

A quantum computer should operate with almost zero power consumption. Almost zero means that there must be some power consumption. But is that really the case? At temperatures close to absolute zero, resistance drops, and at least some materials become superconductive (have zero resistance). The closer we get to zero, the better for us. Other quantum computers must be able to operate at room temperature. But most people would feel really cold at that temperature, and room temperature is a physical term. That is, easy cooling, for example, using liquid nitrogen. What does this actually mean for us?

If I think of a quantum computer as a refrigerator, heat flows into the refrigerator from the surroundings. In physics, there is something called a black body. That is, an ideal object capable of absorbing radiation of all wavelengths. This is exactly the same case where such a body absorbs all radiation from the surroundings, absorbs heat. But how much heat can be absorbed through radiation?

The following procedure can be used to receive energy by radiation. Based on the Stefan-Bolzmann law, $Q = \epsilon\sigma A\left( {T^{4}}_{\mathit{environment}} - {T^{4}}_{\mathit{device}} \right)$the intensity of radiation increases with the fourth power of the body temperature. If the area of a completely black body is $A = 1m^{2}$, the emissivity $\varepsilon = 1$(for a completely black body) and $\sigma = {5,670374419 \bullet 10}^{- 8}\ {Wm}^{- 2}K^{- 4}$ are the Stefan-Bolzmann constant, it is possible to consider an ambient temperature of 20˚C (293.15˚K) and a body temperature of 1˚K, the heat received by radiation from the environment is about ${460\ Wm}^{- 2}$. This means almost half a kW.

But we also know from practice that heat is transferred through conductors, using supports, cables and other parts of the overall structure. But this also means dealing with the cross-section of the conductor, which must be as small as possible to limit the transfer. So how do we calculate the requirements for the structure? Let's start with an estimate. We can consider a quantum computer with a density of iron, which is about 3 times lighter than the heaviest known element, osmium. I doubt that any quantum computer will have such a density, but this creates some reserve. So we have a steel ball with an area of $1m^{2}$. The corresponding beam would have to have a diameter of 6.1mm, and with about a threefold safety margin we can consider a beam with a diameter of about 18mm. Now what about thermal conductivity, which also decreases with decreasing temperature? Fortunately, it is possible to use cryogenic tables, for example, on the NIST website. Based on the calculation, it is possible to obtain a heat transfer of about 2.2W for such a beam. Given the ratio to the temperature received by radiation from the environment, we can neglect this value.

This calculation is quite pessimistic, because a black body is a physical construct that has the greatest possible energy intake from the environment. It is therefore possible to work with the given values further, for example by selecting suitable materials. There are several types of insulation, from ceramics to vacuum, some aerogels, for example, have low thermal conductivity and are at the same time impermeable to certain types of radiation.

In reality, due to the layering of protections, there is a significant reduction in radiation transmission. Where each additional individual layer can reduce the transmission to 3% - 5% of the original flux. In an ideal state, two layers with attenuation to 5% of the original flux should give a total attenuation of 0.25%. However, no structure is perfect, so in reality we can get values corresponding to more than one formula $q \approx \frac{1}{N + 1}$. In such a case, somewhere around 50 layers, the main heat transfer should be the structure.

How to determine the required power of a given cooling system? Most quantum computers, at least for now, remain a large refrigerator. Either the system for calculations or at least the detection systems are cooled. At temperatures close to absolute zero, the cooling performance decreases significantly, and at absolute zero the efficiency is zero – infinite work would be needed to remove the final heat. Therefore, a simplification is given to achieve temperatures in certain orders of magnitude. For the calculation, it is necessary to use the formula of the Carnot engine, a kind of perfect heat pump.

So, it is the ratio of the heat that we have to remove from the cooled system $Q_{c}$and the work supplied by cooling $P_{cooling}$. This can be converted to the ratio of the temperature of the cooled system $T_{c}\$to the difference in ambient temperature and the cooled system $T_{h} - T_{c}$. Based on the Carnot engine calculation, we obtain $1m^{2}$ the results in the following table for cooling an absolutely black body with an area of . Each layer of insulation should reduce radiation to 5%, i.e. the first 5%, the second 0.25%, but this is an ideal case. In reality, more than ten layers will probably be needed for this. What can be used for insulation? Aerogels, reflective layers (foils, nanofoils), vacuum, more precisely multilayer panels containing vacuum (MLI – Multi Layer Insulation). But what are the limitations of the insulation capabilities, it will depend on the design. The theoretical limit of insulation should be able to limit the radiation flux from 460W to 4.6µW, but there will always be some radiation flux. The above limitations are given by the physical properties of the material and quantum phenomena.

This gives us an idea of the cooling power required for a device of a certain volume. But that's not all. It is important to remember that a quantum computer consumes energy, depending on its design. First, it is the operating temperature, and second, all the power is sent to the chips. Light or microwave pulses for operating or manipulating qubits, maintaining states, reading or writing them, all the power again needs to be cooled. This is an energy input into the system that can significantly affect the thermal balance. As a result, such a computer could stop working if there is insufficient cooling. Therefore, it is necessary to use the calculation for Carnot cooling again. Since this is ideal cooling, the question is whether such efficiency can be achieved. In this case, we are looking for the optimal cooling efficiency of a perfectly insulated body of a certain temperature, to which 1W of energy (power input) is supplied.

So for a rough calculation we need three parameters:

• The outer surface of a quantum computer. This is the volume in which the core of the system can be enclosed. Depending on the cooling system, pessimistic estimates can be considered. As they say, it can't get any worse. Miniaturization brings significant advantages here, which is why there is an effort to make quantum chips as small as possible. Similarly, choosing the right insulation brings significant savings.

• The energy input of a quantum computer, where unfortunately we are talking about optimal cooling, which depends on the efficiency of the system. It is necessary to have the lowest possible energy input for the calculation. The calculation itself will generate heat at least thanks to the Landauer limit. Additional heat will be generated by technologies for manipulating qubits and reading their state.

• The operating temperature of the core of a quantum computer. On the contrary, it must be as high as possible, ideally in units or tens of degrees K. The lower we are, the more energy-intensive the cooling is.

The qubits themselves have negligible power consumption from a physical point of view. For superconducting and spin qubits, as well as ion traps, the "consumption" is in the order of pW to fW. The same applies to manipulation using microwaves, we are moving in the same order of magnitude on the qubit or on the gate. The problem is the power of lasers for manipulating ion traps, where the power per qbit is in the range of nW to µW, i.e. 6-9 orders of magnitude more. Furthermore, when measuring the output of quantum circuits, the actual measurement loads the system with units of mW for each qbit. By far the biggest problem is the cabling. Each line contributes to the system with a thermal load of µW to mW, the lines mediate, for example, the dissemination of information and other support. All received energy must then be pumped out of the system, which is energy-intensive.

To be continued in the next section Quantum Computer Technology Overview (March 30th 2026)

Autor článku:

Jan Dušátko

Jan Dušátko has been working with computers and computer security for almost a quarter of a century. In the field of cryptography, he has cooperated with leading experts such as Vlastimil Klíma or Tomáš Rosa. Currently he works as a security consultant, his main focus is on topics related to cryptography, security, e-mail communication and Linux systems.