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As we all know, quantum algorithms scale faster than classical ones (at least for certain problem clases), meaning quantum computers would require a much smaller number of logical operations for inputs above a given size.

However, it is not so commonly discussed how quantum computers compare to regular computers (a normal PC today) in terms of power consumption per logical operation. (Has this not been talked about much, because the main focus of quantum computers is how fast they can compute data?)

Can someone explain why quantum computing would be more or less power-efficient than classical computing, per logical operation?

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  • $\begingroup$ I was in a conference yesterday where the speaker gave us a concrete example. Slides will be available soon, I will give you a link to them =) Concretely, he was comparing the cost (in term of energy) of a simple operation on both a classical processor and a quantum one. I keep you up to date! $\endgroup$ – Nelimee Mar 30 '18 at 8:46
  • $\begingroup$ Considering that, past the ~50 qubit mark, you need a supercomputer to simulate a quantum processor, is generally comparing with a standard PC maybe a bit unfair? $\endgroup$ – Mithrandir24601 Apr 7 '18 at 7:11
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As usual, it is too soon to make comparisons like this. The power consumption of a device will depend strongly on the architecture it uses, for one.

However, in principle, there is no reason to suspect that quantum computers would consume more energy than classical devices performing the same operations. Indeed, one would expect the opposite, the fundamental reason being that quantum computers work (mostly) via unitary operations. A unitary operation is a reversible operation, or, in other words, an operation during which no information is lost to the environment. Such an operation is basically "perfectly" energy efficient (for one, it wouldn't produce heat).

So, in principle, the elementary operations performed in a quantum algorithm which uses unitary operations can be ideally energy efficient. This is in direct contrast with what you have with classical devices, in which the elementary operations are non-reversible, and therefore necessarily "waste" some amount of information for every operation.

Having said this, there are a million caveats to be taken into account. For example, quantum computers in the real world will have to deal with decoherence, so that the operations are not really unitary. This implies that error-correction protocols are necessary to take this into account, and one should then go and track what is the added energy consumption of this whole process. Also, while unitary operations are energy efficient, in practice when one acquires the result of the measurement, measurements have to be performed, and this are non-reversible operations which typically destroy the information. After each such measurement, one will need to generate the carriers of information again. Also, many quantum computing protocols rely on repeated measurements during the computation. One could go on for a long time, as this is very much uncharted territory.

One recent work that discusses in some measure the power consumption problem is 1610.02365, in which the authors present a method for (classical machine learning) information processing using photonic chips. One claim of the authors is that photonic chips allow to perform operations in an extremely energy efficient way, exploiting the natural evolution of coherent light. They do not demonstrate any form quantum computation, but their energy efficiency reasonings would not change much when using the same device for quantum information processing.

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The answer to the first question (why is energy efficiency in quantum vs classical not discussed as often as speed?) is: in part because the problem is less univocal and in part because the answer is less flattering.

The answer to the second question (are quantum computers more or less energetically efficient?) will change with time, since it depends on technological developments of the different architectures.

At the present time, quantum computing is obviously less energetically efficient. A minimal classical computer can be designed to be extremely cheap, also in terms of energy (e.g. 1.5 W (average when idle) to 6.7 W (maximum under stress) for a Raspberry Pi ). In contrast, today to build and operate a minimal quantum computer is an engineering feat with staggering energy cost, even if the number of qubits is well below 100 and the maximum number of operations is orders of magnitude below what is achieved in a fraction of a second by a minimal classical computer.

In the future, one can either speculate or take into account the fundamentals. Let us avoid speculation and stick to the fundamentals:

  • There is no absolute fundamental physical reason for quantum computers to be more or less energy efficient than classical ones.
  • Energy efficiency will always depend on the architecture, and thus on available technological solutions.
  • To evaluate energy consumption, it will always be important to distinguish between the idle consumption and the cost of operation.

To elaborate on the latter point, present devices, both in commercial and academic settings, are bulky. Not ENIAC-sized, but larger-than-a-large-fridge-sized. Furthermore, to be controlled they require an auxiliary classical computer. The size-per-qubit is expected to get better, the need for an auxiliary classical computer is not.

But besides direct electrical power, there are often further physical requirements which cost energy, and which are fundamentally needed to keep the device in the desired quantum regime. For example, popular architectures today include different solid-state devices that need to be kept at temperatures of the order of a few Kelvin or lower. These temperatures are achieved with the help of liquid Helium, which is energetically very costly to liquify (cryogenic gases and electricity are among the main costs in Electronic Paramagnetic Resonance laboratories such as the Electron Magnetic Resonance Facility (EMR) at the MagLab, or, closer to my experience, in the pulsed Electron Paramagnetic Resonance section at the ICMol). I have no experience with ion/atom traps, which are also popular architectures, so while they require mantaining a high-quality vacuum, for al I know it may be that these are more energy efficient.

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    $\begingroup$ Welcome to quantum computing SE! Do you have any numbers for the energy used to cool a cryostat or ion trap? Sure, it'll probably improve in the future, but it would give a reasonable baseline $\endgroup$ – Mithrandir24601 Apr 7 '18 at 7:17
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    $\begingroup$ Different machines will consume He at different rates, and I can only roughly estimate. A cryostat for a pulsed EPR machine (which of course is not really quantum computing) consumes in the order of 100L/week (wrong number but approximate order of magnitude). And according to this document, using a liquefier to recover He, 1kWh/L of liquid He is a pretty good yield. So coupling both estimates we could be talking of >1kW of consumption to keep the cryostate cold via reliquified He. $\endgroup$ – agaitaarino Apr 7 '18 at 7:41
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    $\begingroup$ @agaitaarino - Dr. Alejandro Gaita Ariño, what Mithrandir24601 is saying is that it isn't always obvious that someone is an expert in the field and has written papers or worked with / built the systems in question. There is a preferred format for answering - you are welcome to quote your own work/papers where relevant. We appreciate your visit, and the time taken to answer the question. $\endgroup$ – Rob Apr 7 '18 at 7:44
  • $\begingroup$ @Rob Thanks for the advice! To the limits of my expertise, I tried to reword my answer in terms that are more clear and easier to imagine/understand. I'd love to give better numbers, but I'm mostly a theoretical chemist so while I'm sometimes close to this kind of equipment I do not build it. $\endgroup$ – agaitaarino Apr 7 '18 at 8:10

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