# Is Quantum Computer analog?

We used to have analog computers several decades ago. Modern days computers are Digital. What about Quantum computers? Is it analog or digital? I am asking this since qubit can be many things at the same time.

• in some ways, "neither". analog computers are generally considered "classical physics" ie newtonian physics. a famous analog computer was babbages.
– vzn
Commented Mar 20, 2014 at 17:13
• I was googling "will quantum computers be analog" and came to this question. Amazing how future is approaching :) Commented Oct 12, 2016 at 10:19
• I had the same question. It is a very interesting question. My answer (with arguments similar to those already expressed) is that, NO, a QC is NOT really digital. A digital system continously projects its state on discrete levels, at every single gate. This involves a cost (dissipation) and a gain (noise immunity). Differently, a QC has to be able to exist in a continuum of states. I am not sure if quantum error correction can be considered as something mimicking digital error immunity, but QC seem pretty analog to me. The fact it uses qubits seems irrelevant here.
– Ste
Commented Mar 18, 2023 at 16:22
• Quantum Computers are generally binary, even though several bits are superimposed.
– user16034
Commented Mar 18, 2023 at 17:29

No, quantum computers are not the same as analog computers (at least in principle).

Analog computers simulate the (mathematical) problem to be solved by building a physical system that obeys the same constraints/laws as the mathematical problem. The answers are obtained by observing and measuring the behavior of the physical simulation. Its accuracy is that of the simulation (there may be parasitic effects), the accuracy of the initial conditions, the setting of problem parameters in particular, and the measurement on the result.

Accuracy may also be limited by the scale range of applicability of the phenomena used for the simulation. For example, if the answer is given by a level of water in some container, you may be limited by capillarity effects (which can be accounted for to some extent) and by the fact that measuring water level with more accurcy that the diameter of a molecule may not be very meaningful.

I used to think that a major difference is that analog computing is in principle based on the simulation of continuous laws, involving reals, while digital computing operates exclusively on countable sets. But, in the light of current knowledge in computing theory, this distinction is probably naive because I suspect that physics could be formalized as well using only computable reals, of which there is only a countable number.

Quantum computing will mainly allow you to do several digital computations in parallel (to state it simply). It is always a finite cross product of several computations, and hence stays in the countable realm. You may think of it as the cross-product construction of an automaton that simulates two or more computations of simpler automata (though it is even less general than that from what I understand of it). These finite cross product constructions never leave the countable realm.

In general, a quantum computation is thought of as a digital computation, however there is a variant of quantum computer called a "continuous variable quantum computer" or CVQC, that can be considered an analog computer. I believe they are primarily used in quantum simulation, but they are not something I have studied, so I don't know much more about them than the acronym.

With that said, there are things about "digital" quantum computers that seem very analog. For example, say you start with a quantum register in the ground state, and then you evolve the state unitarily, and finally measure the state.

In some sense, you started with a zeroed out array of classical bits, and ended with an array of classical bits which were the result of the computation, but the unitary evolutions in-between seem very analog. They must be modeled with complex matrices, and the states resulting from the unitary transformations have real amplitudes, etc. But because the output is clearly digital, we consider it a digital computation.

If we could "measure" electron spin wrt an axis (for instance) and get an arbitrary real value, then quantum computing would be analog... But then we would be living in some other universe, with even weirder physics :P

While most schemes for making quantum computers involve digital techniques, there are indeed some analog devices called adiabatic quantum computers (AQC). See Going digital may make analog quantum computer scaleable | Ars Technica for more details.

I believe I understand the basis of your question: The information encoded in one bit in an ordinary modern computer can be described by two (binary) values, commonly written as 0 or 1 or (better for the point at issue) as +1 or -1. However, if you wish, this can be depicted graphically as something being at the north pole or the south pole of an Earth-like sphere. This would be a needlessly elaborate way of depicting how a bit holds information, but it is legitimate. Would navigators bother to use an analog globe if they existed only on the two poles?

The information encoded in a quantum computer cannot be written as either a +1 or -1, fundamentally because the information encoded in a qubit (the quantum-computer equivalent of a bit) can have any value between +1 and -1. One way of depicting this is on a sphere that, like a globe, has analog latitude and longitude markings.

Such a sphere can be the Bloch sphere, a unit sphere borrowed from solid spherical geometry and trigonometry. We can give such a sphere lines of latitude and longitude. The bad new is that encoding a point between the poles now entails less familiar trig and complex numbers. The good news is that any such point can be clearly evaluated, including for describing the information encoded in a qubit. Yes, in effect this Bloch sphere resembles an obviously analog globe! In this sense I agree; quantum computers can be envisioned as relying on analog mathematical tools.

This is an interesting question. I partially agree and partially disagree with previous answers so maybe it is worth adding mine.

Of course, a QC is different from old-time analog computers, but only because of its "quantumness", which has little to do with its being analog vs digital. A QC is definitely not a digital system, in any meaningful way. It lacks all the fundamental characteristics that I would say characterize a digital system:

1. Differently from an analog system, a digital one partitions the continuum of possible configurations in a set of discrete ranges (or logic levels if you like to think about 0s and 1s);
2. The computing system continuously projects its configuration on one of the conventional discrete ones. This happens at every single logic gate. Take the NOT gate, whenever the input voltage is above V_IH, the gate interprets the input as "1" and projects the output to the conventional "0";
3. The crucial benefit (why do digital systems exist, in the end?) of this whole procedure is noise immunity, and one cost is dissipation.

A QC does not fit well in any of these points. Forget about the existence of qubits: this is about irrelevant. The fact that the wavefunction of a QC is given by the product of the wavefunction of many qubits simply sets the basis of the Hilbert space, but a quantum memory can (and has to be able to) exist in an uncountable number of configurations represented by all the complex amplitudes that describe its wavefunction. Take even a one-qubit memory: it can exist in an infinite number of superpositions of 0 and 1, that are on a one-to-one correspondence with the points of the surface of the Bloch sphere... which are definitely uncountable. This is very different from a bit, which can only have two configurations.

In addition, there is no projection at every quantum gate, and surely no dissipation. Quantum computing is even reversible, in principle: this is the opposite of a dissipative system. A QC indeed needs to preserve the full quantum information of its qubits, all the amplitudes, entanglements, and so on, which are pretty much continuous. It only projects its configuration on one of the classic states at the end of the calculation, at the read-out stage.

In short, a QC is a (quantum) analog computing system.

This is sometimes brought up, and summarized as "a QC somehow is performing many (digital?) computations in parallel". This is a compelling and very communicative view, but I think it easily leans toward the misconception. This is a tricky concept. A QC performs its computation on a "superposition" of configurations of a digital classic computer. First of all, this is not the superposition most people think about: this is a quantum superposition and one has no access to the results of the individual calculation... actually, the result of the individual calculation does not even exist, since during the calculation intermediate and final results will be in quantum superposition and give rise to interference... One can only interrogate (statistically) the final result, which depends on the coefficients that describe the superposition.

In my view, the only important question in the analog vs digital discussion is "how information is encoded?". In a standard computer, it is encoded in the state of the memory, which is definitely digital. My DNA also encodes information in a digital form. A QC does not. To be direct, consider an 8-qubit quantum memory. The qubits just set the basis of the Hilbert space, which will be 00000000, 00000001, and so on: a 256-dimensional Hilber space. The information contained in the memory is encoded in the density matrix, which is a 256x256 hermitian matrix, with a very large number of analog amplitudes. Not digital, those amplitudes are not segmented in any way in a discrete set of conventional intervals.

In the end, if a QC were digital, people would not fight so much with error correction. Noise immunity is the main reason for the existence of digital systems.

relating to or using signals or information represented by a continuously variable physical quantity such as spatial position, voltage, etc.
"analog signals"
(of a clock or watch) showing the time by means of hands rather than displayed digits.
not involving or relating to the use of computer technology, as a contrast to a digital counterpart.
"old-school analog paper map skills"


noun noun: analogue; plural noun: analogues; noun: analog; plural noun: analogs

a person or thing seen as comparable to another.
"an interior analogue of the exterior world"
Chemistry
a compound with a molecular structure closely similar to that of another.
"thioacids are sulfur analogues of oxyacids"


When we look at the meaning of analog, then when we apply it to computing, it just means using something analogous to the real world. Or a model. And as many have said, the model may have flaws, or not account for certain unknown aspects of reality.

That being said, I recall reading in a magazine called Analog Computing in the 80's, that a true analog computer would be able to make use of the entire EM spectrum as inputs and outputs. I don't think we are there yet by that definition, but that may be a pipe dream.