[Cryptography] Some quantum computers might need more power than supercomputers

[Jan Dušátko]

Dne 09. 01. 26 v 9:15 Peter Gutmann via cryptography napsal(a):
> Jon Callas<jon at callas.org> writes:
>
>> Some quantum computers might need more power than supercomputers
> The German government (via the BSI) wrote a report on this and estimated that
> it would take 100 days and €4M in electricity to recover a single 2048-bit key
> on a quantum computer that doesn’t exist.  That's one single key.  There are 7
> trillion keys negotiated each year just for TLS web connections.
>
> Oh, and that's for integer factorisation, not (EC)DLP, so not actually useful
> for attacking the shopping list of common crypto protocols I mentioned
> earlier.
>
> Peter.
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Some information, which may could be useful.

If I consider a quantum computer as a refrigerator and it behaves as an 
absolute black body, I am talking about the necessary cooling power to 
maintain this radiation from environment, which could be 460W/m^2 
(environment with temperature 20˚C). But this is an ideal condition, 
there will be also heat transfers through supports, cable lines and 
other parts of the overall structure. More, any energy provided to 
system needs to be appropriately cooled also.

The question is what will be the construction of a quantum computer. All 
the power that is sent to the chips (light or microwave pulses and 
others) needs to be cooled again. Due to the efficiency of cooling under 
normal conditions, at least half as much cooling power is needed for 
each input power. At temperatures close to absolute zero, the cooling 
efficiency is reduced to hundredths per thousand. At absolute zero, the 
efficiency is zero - it would take infinite work to remove the finite 
heat. Therefore, I would simplify it to reach a temperature in certain 
orders.

If I take the cooling of an absolutely black body with an area of ​​1m^2 
from 20˚C to mK and μK, then I have some heat flow characteristics. But 
if I take the Carnot machine calculation, then the worst possible 
scenario produce list of needs. For cooling an absolutely black body 
with a surface area of 1m^2 that means:
- To a temperature of 1K requires an input of 122KW
- To a temperature of 0.1K requires an input of 1.22MW
- To a temperature of 0.01K requires an input of 12.2MW
- To a temperature in mK requires an input of 122MW
- To a temperature in μK requires an input of 122GW

To cool the delivered 1W (Carnot cooling, the best possible option and 
optimistic attitude) for perfectly insulated body, we need the following 
cooling device power:
- To a temperature of 1K requires an input of 293W
- To a temperature of 0.1K requires an input of 2.93kW
- To a temperature of 0.01 K requires an input of 29.3 kW
- To a temperature of 1mK requires an input of 293W
- To a temperature of 1μK requires an input of 293MW

For my surprise, the possible heat conductivity by construction is very 
low, about 2,0-2,2W. I estimated rod with a circular cross-section of 
diameter 18,3mm. I choose it because QC in ball of surface 
are 1m^2 probably cannot be heavier than iron ball. But radiation could 
make things worse than thermal conductivity. This is a reason why I did 
not count that.

So two parameters are needed:
- the outer surface of the quantum computer where, according to the 
cooling system, it is possible to think with pessimistic estimates
- the energy input of a quantum computer (problems with the efficiency 
of real devices, it is advisable to multiply at least 1.5 times the 
value of Carnot cooling. I do not have enough knowledge)

Based on that result, we need QC which will be able to work in 
temperature of degrees or tenth of degrees of K. Anything else is ... 
expensive refrigerator and physical experiment, not sustainable quantum 
computer.

Technology;Operating temperature;Computer power;Cooling power;System 
power;Volume;Number of qbits
Superconducting qubits (IBM, Google);10-20 mK;~mW;15-25 kW;15-25 kW;~1-2 
m^3 (cryostat + electronics);50-127 qubits
Trapped ions (IonQ, Honeywell); μK; few mW; ~20 kW (lasers + vacuum); 
~25 kW; ~1 m^3; 10-32 qubits
Neutral atoms / optical traps; μK; few mW; 5–10 kW (lasers, vacuum); 
5–10 kW; <1 m^3; 50–200 qbits
Photonic qubits; room temperature; few mW; 0.5-1 kW (detectors, optics); 
4-5 kW; <1 m^3; 50-200 qubits
Spin qubits in semiconductors (Si, SiGe); 10–100 mK; few mW; 10–20 kW; 
<1 m^3; 10–50

Jan

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