I'm sure nearly everyone has by now heard that Google “proved” the D-Wave 2 they operate jointly with NASA (mainly paid for by Google) can operate “up to ∼ 10^{8} times faster”. If not, you might want to have a quick read of their paper, titled “What is the Computational Value of Finite Range Tunneling?” Even if you don't read the paper, you can be excused for wondering if “the race to a real quantum computer” (my words) is over. There is enough press around every such announcement from Google, IBM, and others that you easily can get the impression it is just down to the details now.

In fact, there are still major, fundamental challenges to be overcome and building blocks to be created. You might have heard earlier last year how IBM had solved the problem of quantum error correction. Although there was a lot of buzz about that, it is interesting to note that a month earlier, Google reported on their own blog that they had already done more or less the same thing. And so it goes. But the near-term reality could be even more interesting, especially if you are old or lucky enough to have played with analog computing.

Way back in 2013, I wrote a series of posts on the possible role of quantum computing in analog design. (see: Will Quantum Computing Enhance Analog Design? Part 1 Parts 1-3) In the introduction to that series, I provided the following diagram:

**Figure 1**

Consider if you were given the problem of making a table, sort of like a train schedule, to represent flow out of the 5 outlets versus various combinations of the inlets. To solve that problem in digital space requires a pretty good fluid dynamics simulation tool, an accurate physical model of the system translated into the input for the tool, and a fast computer. It is very doable, but pretty expensive.

Now suppose we change the problem to determine which input has the most impact on the output of the 3rd pipe from the left? You could solve that by going to the hardware store and plumbing up a simulator, which would be a version of an analog computer. Or, you could build an analog computer, and come up with models for the fittings (combinations of L, R, C circuits) then play with it. The result for any given set of inputs, once the analog computer is in hand and “programmed', is available nearly instantly, while each run of the digital simulation might take minutes or hours or days. If you think about the fittings modeled as L-R-C circuits, they capture the dynamics as well as the steady state behavior. The dynamic part can be thought of as a simulator node capable of having many possible values. And that sounds something like a qubit.

It turns out that people who actually worry about quantum computing and other problems for a living, and who talk way over my head, had thought about this aspect of an interchangeable relationship between quantum computing and analog computing long before me. In a paper published in 2010 in the Philosophical Transactions of the Royal Society A, Vivien Kendon of the University of Leeds and colleagues said “To perform a quantum simulation, the Hilbert space of the system to be simulated is mapped directly onto the Hilbert space of the (logical) qubits in the quantum computer. This type of direct correspondence is how data are encoded in a classical analogue computer.” (Also on arxiv here).

More recently, Tomi Johnson of the National University of Singapore and colleagues published a paper on arxiv “What is a quantum simulator?” in which they say “At the time of writing, astonishing levels of control in proof-of-principle experiments (cf. the above references and citations within) suggest that quantum simulation is transitioning from a theoretical dream into a credible possibility.” In other words, the initial real-world applications of quantum computing may be closer to analog computing than digital computing.

There is another, interesting, and more subtle analog approach that may also be important in the practical sense. In an article published in Quanta Magazine, Ivan Deutsch was interviewed about, among other things, analog quantum simulators. He said “with an analog quantum simulator — I use one controllable physical system to simulate another”. He goes on to mention some work at the Max Planck Institute in Germany using “an optical lattice–a super-chilled egg carton made of light” and how they were able to manipulate that to explore quantum mechanical equations of motion. Essentially if you imagine some exotic physical devices you can “program” to represent a quantum system, then you can achieve quantum computing results without an actual quantum computer, per-se.

The German work caused a (quantum) light to go off in my head, as I had read about some work right in my back yard, by JILA (Joint Institute for Laboratory Astrophysics, in Boulder; run jointly with NIST (the National Institute of Standards and Technology)). In a press release titled “It’s a Beauty: JILA’s Quantum Crystal is Now More Valuable” they describe a physical egg-crate formed of artificial molecules supercooled and manipulated by laser beams. If they can learn how to solve some real-world problems with such an egg crate, that would be beautiful indeed.

This op ed piece is commendable for providing many very interesting references to recent work in the broad – and exponentially widening – field of quantum computing. I confess to being quite unable to keep abreast of these developments. However, as for the suggested quasi-equivalence of quantum and analog computing, I feel this might be more than a bit misleading as to the important ways in which these differ.

Nevertheless, there are some intriguing similarities. Consider, for example, a fully-analog circuit of almost any complexity, existing as, let's say, a breadboard. [Young folks: this is a circuit built up from a selection of primitive elements place on the “board” – sans bread – and wired by hand. Primitives range from such basic elements as R, L and C, through discrete transistors, up to analog ICs]. Let's omit for now any energy-storage elements – principally L's and C's, but there are, of course, others – having significant effect on the circuit's time-domain behaviour. One could refine all these definitions.

But here's the similarity: When the primary source of [DC] power is applied, the circuit instantly “solves” the equations for all the elements, both individually and also as an interactive ensemble. It does not need to be “told” about the physics of these elements, using modeling equations, because

the circuit is itself a piece of the real, physical world. In this respect,it is an “analog” of nothing. Likewise, the circuit's response to any other stimuli applied to it will likewise occur without any recourse to some sort of computation. In this respect itISits“own analog computer”.Now, we may question the absolute accuracy of any “result' – say an output voltage of a simple amplifier – of this tangle. Whatever solution it happens to settle on – by the rapid conversation that occurs when any stimulus is altered – is its own “private” solution. The matter of providing

accuracynever occurs to an analog circuit. It might be quite accurate – enough for the ensemble to be used as a component in a useful [that is, high-precision] Analog Computer; but, as far as the circuit is concerned, it is simply solving its internal equations, whose accuracy in some absolute sense can range from poor to excellent.We may yet find another similarity here to quantum computing. While small ensemble of quantum elements – a few qubitsworth – may fortuitously appear to behave quite well, and very, very fast in operation, I have a hunch that

as they become larger in extent– to employing hundreds of elements – they will be prone to [at least one of] the same enemies as analog computing, namely, universal noise. Operation at low temperatures may squelch basic qunoise; but some types of circuit error – those attributable toshot noisefor example, which is not temperature dependent [at least, as generally explained and modelled, although, as an aside, there may be some errors of rigour here, as far as real devices are concerned], and even some fancy variety of 1/f noise – may eventually show up in large quantum computers yet to be designed and built.Barrie

Thanks for the interesting thoughts on noise and accuracy. There are, as I understand it techniques exist to eliminate errors in digital processing. That works well for distinguishing 1s from 0s. But as you point out, that may not work or even make sense in quantum or analog computing. Both Google and IBM say they have figured out quantum error correction. I must admit I don't understand how that works.