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In the recent Question "Is Quantum Computing just Pie in the Sky" there are many responses regarding the improvements in quantum capabilities, however all are focussed on the current 'digital' computing view of the world.

Analog computers of old could simulate and compute many complex problems that fitted their operating modes that were not suitable for digital computing for many many years (and some are still 'difficult'). Before the wars (~I & II) everything was considered to be 'clockwork' with mechanical Turk brains. Have we fallen into the same 'everything digital' bandwagon trap that keeps recurring (there are no tags related to 'analog')?

What work has been done on the mapping of quantum phenomena to analog computing, and learning from that analogy? Or is it all a problem of folk having no real idea how to program the beasts.

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  • $\begingroup$ I asked a similarish question: quantumcomputing.stackexchange.com/questions/2595/… $\endgroup$
    – Steven Sagona
    Jul 7, 2018 at 19:16
  • $\begingroup$ I just want to clarify that their is the potential distinction between Network based analog computers where connections are bi-directional, and Amplifier based analog computers where there was feedback (slow & sluggish..) based connections. It is the speed around the nodes, and the floor 'noise' that drives the interconnected nodes to their final state. It just feels like 'Quantum' is just a method of miniaturisation and speed up... $\endgroup$
    – Philip Oakley
    Nov 25, 2019 at 14:44

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Here is a quick list of notable differences between analog and quantum computers:

  1. Analog computers can't pass Bell tests.

  2. The state space of an analog computer with N sliders is N dimensional. The state space of a quantum computer with N qubits is $2^N$ dimensional.

  3. Error correct an analog computer and what you've got is a digital computer (i.e. not fundamentally analog anymore). Quantum computers are still quantum after being error corrected.

  4. Analog computers aren't sensitive to decoherence errors. They don't break if you make accidental copies of the data. Quantum computations do break if that happens.

  5. Analog computers can't (efficiently) run Shor's algorithm. Or Grover's algorithm. Or basically any other quantum algorithm.

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    $\begingroup$ This is confusing to me. You seem to suggest that "analog" and "quantum" are two different things, but in reality they are not mutually exclusive: You have have (1) analog-classical (2) analog-quantum (3) digital-classical (4) digital-quantum. So for example, "analog computers" can pass Bell tests if they are analog quantum computers. Same goes for the rest of your points. $\endgroup$
    – user1271772
    Jul 10, 2018 at 21:03
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    $\begingroup$ @user1271772 In the context of the question, it is clear that I am referring to classical analog computers. $\endgroup$
    – Craig Gidney
    Jul 10, 2018 at 23:08
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What work has been done on the mapping of quantum phenomena to analog computing, and learning from that analogy?

A starting place (with a lot of good references) to learn about analog quantum computing (also known as "quantum analogue computing" and "continuous variable quantum computing") is here. Note that analog classical computing is not as powerful as analog quantum computing, for a reason similar to what I explained in my answer to this question: quantum computers (whether digital or analog) can take advantage of quantum entanglement.

Have we fallen into the same 'everything digital' bandwagon trap that keeps recurring (there are no tags related to 'analog')?

A lot of people unfortunately have, and this might be part of the reason why "adiabatic quantum computing" struggled to get the respect it deserved in its early years (and even now). Adiabatic quantum computing is a specific type of analog quantum computing which certainly does have a tag on this Stack Exchange and a fair number of questions (but not enough, in my opinion). It has been proven that "adiabatic quantum computing", which is completely analog and does not involve any gates, can do anything that a digital quantum computer can do with the same computational efficiency, so while it is true that many people in quantum computing have fallen into the 'everything digital' bandwagon trap, there are some people that appreciate analog quantum computing (for example adiabatic quantum computing).

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  • $\begingroup$ Thanks for the extra tags, the links and the terminology clarification. For myself, I was comparing electrical mesh networks to quantum networks, where historically the electronic networks were 'instant', just as quantum is now, and both have similar physics on their side. $\endgroup$
    – Philip Oakley
    Jul 10, 2018 at 13:21
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Are quantum computers just a variant on Analog computers of the 50's & 60's that many have never seen nor used?

No, they are not.

The digital vs analog factor is not the point here, the difference between quantum and classical devices lies at a more fundamental level.

A quantum device cannot, in general, be simulated efficiently by a classical device, be it "analog" or "digital" (or at least, this is strongly believed to be the case). In this sense, quantum computers are really radically different from any variation of classical analog computers, or other forms of classical computing for that matter.

Indeed, the most popularized architectures for quantum computing, those operating on sets of "qubits", are the quantum counterparts of digital classical computers. Analog devices also have their quantum counterparts (see for example continuous-variable quantum information).

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  • $\begingroup$ The aspect I had in mind was the way interactions are seen. In digital there is a presumed certainty, while in analog there is 'noise' (fluctuation, probability, ..). It's the latter that Quantum tends to be presented as, hence the suggestion of my Q (plus there are few left who really remember such analog methods!) $\endgroup$
    – Philip Oakley
    Jul 10, 2018 at 16:33
  • $\begingroup$ @PhilipOakley I'm not sure I understand. It's the latter that Quantum tends to be presented as <- I don't understand this sentence $\endgroup$
    – glS ♦
    Jul 10, 2018 at 16:40
  • $\begingroup$ The 'latter' (for QM) being "probability distributions" and the like. So noise in an analog system is a multi-dimensional probability problem (as per Shannon) and Qubits would appear to be a similar multi-dimensional probability problem, hence the similarity of the conceptual abstractions. One key difference is the spatial extent such that old fashion analog networks rarely got to a MHz BW, and millisecond responses over cm, but QM hopes for much much higher frequencies over microns and less. $\endgroup$
    – Philip Oakley
    Jul 10, 2018 at 16:49
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    $\begingroup$ Qubits would appear to be a similar multi-dimensional probability problem: but they are not really, or at least, not the same way the classical analog devices are. A qubit can be in a continuum of states, that's true, but every time you measure it you always observe it in one of two positions, so it's something fundamentally different than what you have classically. $\endgroup$
    – glS ♦
    Jul 10, 2018 at 16:56
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Have we fallen into the same 'everything digital' bandwagon trap that keeps recurring?

What I have noticed is more the 'everything binary' bandwagon trap; which reminds me of the Grandma's cooking secret:

Once upon a time, a mother was teaching her daughter the family recipe for making a whole baked ham. It was the very best ham anybody had ever had so they always followed that recipe carefully.

They prepared the marinade, scored the skin, put in the cloves, and then came a step the daughter didn't understand.

"Why do we cut off the ends of the ham?" she said. "Doesn't that make it dry out?"

"You know, I don't know," said the mother. "That's just the way grandma taught me. We should call grandma and ask."

So they called grandma and asked, "why do we cut off the ends of the ham? Is it to let the marinade in, or what?"

"No," said Grandma. "To be honest, I cut the ends off because that's how my mother taught me. I added the marinade step later, because I was worried about the ham drying out. Let's call great grandma and ask her."

So they called the assisted living facility where great grandma was living, and the old woman listend to their questions, and then said.

"Oh, for land sakes! I cut off the ends because I didn't have a pan big enough for a whole ham!"

I was recently thinking about qubytes & wondering if they really needed to be defined as 8 qubits. An 8-level quantum system (qunit) would have an 8 dimensional space & could in theory encode a byte (8 bits). Is this a better definition of a qubyte (quantum byte)?

Or is it all a problem of folk having no real idea how to program the beasts.

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    $\begingroup$ I'd agree that the "everything binary/digital" has become a mantra that many are embedded within (that then being above). We explain brains and everything as if it's like a computer. There was a period in the early electronics days where its theories/techniques could be applied to big analog issues, such as resistive (impedance) meshes. It's mostly the same old Maxwell, apart from the mistaken(?;-) Gibbs formulation, that QM uses, so a bit of provocation about a bit of lateral thinking is in order, maybe. For the 'byte', have a look at baud rate, which is not bit rate. $\endgroup$
    – Philip Oakley
    Jul 10, 2018 at 16:40
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    $\begingroup$ 'Symbol rates' - nice! I think the binary issue predates everything as a computer. See: the tree of knowledge of good & evil ;P $\endgroup$
    – user820789
    Jul 10, 2018 at 17:41
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    $\begingroup$ for the 8d space, have a look at C Furey's PhD "Standard model physics from an algebra?", and the 2 minute YouTube lectures. Has a lot of plausibility relative to our need for a mathematics to represent science .. (can't let things become voodoo maths/science - other theologies available) $\endgroup$
    – Philip Oakley
    Jun 5, 2019 at 14:55

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