[nexuist]

Preface: I know nothing about quantum computing.

What exactly is a qubit? I'm not asking what does it mean, because I know there's superpositions and all that jazz, but as in...like, in an electronic circuit, what is a qubit? Is it made out of logic gates? Which ones?

If we can make one qubit, can't we just make a bunch of them by copy and pasting circuits similar to how we used vacuum tubes in the 60s and 70s? How come our current limit is only around 54 or so?

Are qubits, and quantum computers by extension, not even electronic circuits? If so...what the hell are they?

[itcrowd]

Essentially, they use superconducting electronics to create a quantum circuit. It's not the same logic gates as a traditional computer chip and not based on the same physics. The details are difficult & messy.

There are several reasons it doesn't scale easily to more qubits, but you can imagine that you don't want the chip to be large (must be cooled to 25mK!) but the qubits should be spaced quite far apart so they don't influence each other. Also, it's not a very simple circuit, so the layout of the transmission lines ("wire on a chip") becomes difficult to manage. The last problem also scales badly with the number of qubits (the middle qubit becomes progressively harder to reach).

There is a paragraph in the (leaked) paper that describes their chip:

> In a superconducting circuit, conduction electrons condense into a macroscopic quantum state, such that currents and voltages behave quantum mechanically [2, 30]. Our processor uses transmon qubits [6], which can be thought of as nonlinear superconducting resonators at 5 to 7 GHz. The qubit is encoded as the two lowest quantum eigenstates of the resonant circuit. Each transmon has two controls: a microwave drive to excite the qubit, and a magnetic flux control to tune the frequency. Each qubit is connected to a linear resonator used to read out the qubit state [5].

If you want a physical picture, check out [6]: https://arxiv.org/abs/cond-mat/0703002

edit: source [6] is more appropriate and open to access

[outworlder]

Holy hell.

> > In a superconducting circuit, conduction electrons condense into a macroscopic quantum state, such that currents and voltages behave quantum mechanically [2, 30]. Our processor uses transmon qubits [6], which can be thought of as nonlinear superconducting resonators at 5 to 7 GHz. The qubit is encoded as the two lowest quantum eigenstates of the resonant circuit. Each transmon has two controls: a microwave drive to excite the qubit, and a magnetic flux control to tune the frequency. Each qubit is connected to a linear resonator used to read out the qubit state [5].

I understand most of the words in isolation – and I know that they are valid, even if combining them in a useful manner to understand exactly what they are describing is eluding me.

But if there was ever a paragraph that sounded like pure technobabble, this is it. Replace the technobabble found in the star trek matter transporter with quantum lingo, and it would sound very similar.

[galonk]

"For a number of years now, work has been proceeding in order to bring perfection to the crudely conceived idea of a transmission that would not only supply inverse reactive current for use in unilateral phase detractors, but would also be capable of automatically synchronizing cardinal grammeters..."

[AndrewKemendo]

Honestly, this is how I read every quantum thing. Not because I don't believe it's real, it's just so far outside of my area of education that it might as well be describing the turbo encabulator.

[aphyr]

So I'm not super familiar with quantum computation, but I did do my undergrad research in QM (specifically, how chaotic behavior depends on the scale of nonlinear quantum systems) and I can take some informed guesses about what these words mean. It's actually super cool!

In a superconducting circuit

A circuit is a loop of something. Probably a solid material, like a metal or carbon, though it could be something more exotic. A superconducting circuit means the electrons in that material move without any resistance. This tells us the circuit is probably very cold--superconductors tend to break down at warm temperatures, like the ones in your house.

conduction electrons

Conductors have electrons in them. Some are "stuck" to atoms, others get to move around. Conduction electrons are the ones that move.

condense into a macroscopic quantum state

Macroscopic means "big", and for QM, "big" means, like, more than a handful of atoms or particles. At least as far as QM is concerned, everything--rocks, electrons, photons, people, etc., has a quantum state, but we use the phrase "quantum state" to mean a state that's, like, WEIRDLY QUANTUM. For instance, a pencil sitting on your desk is normal. A pencil that's like, half on your desk and half on mine is "quantum". Condensing means the electrons are going to change from doing normal individual electron things into acting like some sort of Big But Weirdly Quantum system, likely as a group. Like a crowd becoming a flash mob, they might do some sort of synchronized dance, only except the dance involves, say, every dancer doing two or three or ten dance moves at the same time.

such that currents and voltages behave quantum mechanically [2, 30].

Specifically, we're gonna be able to see quantum effects like superposition in Big Things like "current" and "voltage". The circuit might be in a combination of 3 volts and 5 volts at the same time. Also some of those voltages might be partly real and partly imaginary. Long story.

Our processor uses transmon

What the fuck is a transmon? I had to look this one up; it's a way of making these qubits less sensitive to voltage fluctuations.

qubits [6]

Qubits are quantum bits. A bit can be either 0 or 1. A qubit can be 0 or 1 or (and this is the quantum part) any state in between. Let's call the 0 state |0>, and the 1 state |1>. A qubit can be |1>, but it could also be (1/sqrt(2) |0>) + (1/sqrt(2) |1>). We call that a "cat" state, incidentally, because it's "half 1, half 0"--like Schroedinger's Cat, half alive and half dead. Again, the coefficients here are, in general, complex numbers, but we're gonna gloss over that.

which can be thought of as nonlinear

Nonlinear means they don't respond linearly to some input. Ever had someone do a series of small, mildly annoying things, and at some point you snapped and yelled at them? That's called "going nonlinear".

superconducting resonators

Oscillators are things that vibrate, like strings. Resonators have preferred frequencies to vibrate at. I don't exactly know what this means in this context, though. I'm guessing the circuit has some preferred frequencies it really likes to oscillate at.

at 5 to 7 GHz.

Voltages or currents or whatever are gonna go back and forth 5-7 billion times a second. That's about the same frequency as wifi signals, or microwaves.

The qubit is encoded

A qubit is an abstract thing on a whiteboard. There lots of ways we could actually make a thing that looks like a qubit. "Encoded", here, means "turned into an actual machine you can build in a lab".

as the two lowest quantum eigenstates of the resonant circuit.

An eigenstate, loosely speaking, is a state that has nothing in common with any other eigenstate. For instance, if we wanted to measure a particle's position on a line, we could take x=0 as one eigenstate, x=1 as another, x=2.5 as yet another, etc etc. An infinite number of eigenstates. Quantum systems can be in any (well, normalized) sum of eigenstates. My cat loves being inside and outside at the same time, so they're always trying to occupy 0.2|x=0> + 0.6|x=4> + 0.2|x=5>.

An operator is a thing you can do to a quantum state. Think of operators like functions on values, if you're a programmer, or like matrices that can be applied to state vectors, if you know linear algebra. For instance, I might have a measurement operator, which I use to look at my cat. There's also a special operator called the Hamiltonian, which (loosely) tells you what a state will look like after an infinitely small step in time.

Each operators has associated eigenstates, and those eigenstates have a magic property: if you apply that operator to one of its eigenstates, you get back the exact same state, times some complex number, which we call an eigenvalue. This means eigenstates for the Hamiltonian are, in a sense, stable in time. When we talk about the eigenstates of a system, we usually mean the eigenstates of the Hamiltonian. They could also be talking about measurement eigenstates--I'm not sure.

For the Hamiltonian, eigenvalues are, for Really Fucking Cool Reasons, energies. When we talk about "the two lowest quantum eigenstates", we mean the two states with the lowest energy. So maybe the circuit's eigenstates are, I dunno, 5 Ghz, 6 Ghz, 7 Ghz, etc. We'd take 5 and 6 as our |1> and |0> states.

Each transmon has two controls

A control is a thing we can use to change the transmon.

a microwave drive

Something like the microwave in your kitchen, but very small, and probably expensive.

to excite the qubit

This probably means changing the qubit from |0> to |1>. Microwaves carry energy, right? That's how they heat food. If they microwave the circuit at the right frequency, that microwave energy probably helps it jump from a lower frequency/energy to a higher one.

and a magnetic flux control

This feels like something specific to transmons. Flux has to do with the density of stuff moving through a surface. Magnetic flux probably has to do with how strong and close field lines are in some part of the transmon machinery.

to tune the frequency.

How fast the circuit wobbles depends on a magnetic field, I guess?

Each qubit is connected to a linear resonator

Huh. So we've got nonlinear resonators (the qubits) connected to linear resonators (some sort of measurement device?)

used to read out the qubit state

We need a way to actually look at the qubits, and I guess the linear resonator does that. I assume that the linear resonator is isolated from the qubit during computation, and once the computation is over, it gets connected somehow, and vibrates at the same frequency as the qubit. That process probably "spreads out" the quantum state of the system, pushing it REAL CLOSE to an actual eigenstate of the measurement system, which looks like a probabilistic measurement of the actual qubit state.

Like... my cat could be 3/4 inside and 1/4 outside, so long as the room is really dark. If I turn on the light, suddenly my cat is coupled to a MUCH BIGGER system--the room, and that "quantum" state gets diffused into that larger system, in what looks like a measurement like "cat definitely inside". I don't know a simple way to explain decoherence, haha, but if you like math, try Percival's "Quantum State Diffusion".

Hope this helps, and I also hope I got at least some of this right. Maybe someone with a better/more recent command of QM can step in here.

[galaxyLogic]

Very good explanation. Even if it would not be 100% correct, and I can not say yes or no, it gives a good overall introduction to the concepts involved.

[QuinnWilton]

I'm not a quantum physicist either, but I did study quantum mechanics in college for a bit!

> A qubit can be |1>, but it could also be (1/sqrt(2) |0>) + (1/sqrt(2) |1>). We call that a "cat" state, incidentally, because it's "half 1, half 0"--like Schroedinger's Cat, half alive and half dead. Again, the coefficients here are, in general, complex numbers, but we're gonna gloss over that.

In case anyone is interested in not glossing over this part, this [0] lecture by Scott Aaronson is an excellent introduction to the crazy world of complex probability amplitudes. It doesn't assume much more than some basic linear algebra, and does a good job of developing at least a little bit of an intuition for some of the concepts in Aphyr's comment.

[0] https://www.scottaaronson.com/democritus/lec9.html

[viraptor]

At the extreme, it approaches art: https://www.reddit.com/r/VXJunkies/

[tagrun]

We do want the chip to be "large" eventually. The scalability doesn't have anything with those, however. Refrigerators are pretty large and these devices are really really tiny; also qubits shouldn't be spaced "far" apart, this would kill all the (controllable) couplings.

[itcrowd]

I was a little too fast and loose in my previous post. You are correct that we want a large [number of qubits] on a chip eventually. The chips are tiny and the fridges large enough for now (50 qubits). It's not clear to me that they can handle thousands of qubits as imagined. The cryostat will undoubtedly be able to house the chip, but the extra electronics / cables must run in there as well. With 1000 qubits and 2 cables per qubit this will be a major challenge.

You are correct about the coupling of the qubits, I was simplifying too strongly there.

I do stand by my scaling point (center qubits harder to reach) but I'm open for counter arguments.

Thanks.

[tagrun]

There is a scalability problem but due to different reasons. See my other comment in this thread for details.

Classical circuitry is an issue, but not as much as you think. What happened is Martinis' group and others moved forward with a quick & dirty design which worked well for their device but can't be scaled (they basically didn't have the expertise like silicon people had). Nevertheless, it's not a fundamental problem, the circuitry for silicon based spin qubits never had this problem for example and xmons won't either, they just keep reiterating as the number of qubits increase, it's the least of their worries regarding scalability. There are far bigger problems regarding the scalability.

[itcrowd]

I agree on your other points and trust that you are more qualified to judge what the biggest obstacles are.

Do you have a paper I can look into that goes into the chip architectures in more detail (not specifically for this new device)? Otherwise I'll await the science / nature paper of this demonstration.

The classical circuit is mostly outside the cryo I assume since it's GHz's and LNAs are available. Do you know if the microwave readout signal is frequency multiplexed to reduce cables?

[tagrun]

When you say chip architecture, I assume you mean how to assemble together qubits like an integrated circuit. Here's one proposal for silicon based qubits: https://www.nature.com/articles/s41467-017-01905-6

Microwave signals are typically used for control rather than readout. I don't know if this experiment does it or not, and I am not an experimentalist. Multiplexing is more typically required for reducing timing errors of simultaneously driven signals (for better synchronization) and it really depends on the device and the mode of operation, plus whether the experiment they're doing needs it or not. The same experimental group sometimes do it one experiment and not do it in another, despite using the same device.

[3PS]

Short answer, a qubit is a unit vector in a 2D complex Hilbert space. Now, that doesn't actually say much about why we care or how they're useful. In practical terms, you can think of qubits as complex unit vectors along two axes, with one axis corresponding to |0⟩ (the zero qubit) and one axis corresponding to |1⟩, or the one qubit. So for example, you could have a qubit called |+⟩, which is just shorthand for (|0⟩ + |1⟩)/sqrt(2).

Measuring a qubit in a basis collapses it to one of the basis vectors (e.g Schrödinger's cat must be alive or dead once we open the box) with probability equal to its inner product with that basis vector. This is why we need a Hilbert space and not just any old vector space.

Finally, to answer your question about gates, a quantum gate is basically a unitary matrix, i.e. a matrix that preserves the norm of its inputs. You can feed qubits into these matrices by themselves or, more often, many at once, by using something called the tensor product of the qubits - this is where the math gets slightly more involved.

The long and short of it is that we can induce correlation patterns between qubits using these gates (aka quantum entanglement) and orchestrate circuits of interference patterns where the wrong answers cancel each other out and the right answer gets reinforced so that we measure it at the end - unfortunately, this is where my knowledge breaks down as a beginner. My apologies if I accidentally handwaved anything important but hopefully you get the gist.

[tagrun]

This is like saying that voltage is a scalar real number, which explains nothing about the physics of electromagnetism, and in my opinion is probably the worst way to explain physics of anything. It especially tells nothing useful given the question is about the stuff that a qubit is made of (which is different from "how do you mathematically represent an ideal qubit on paper?").

And going beyond that, as Peres puts it, "Quantum phenomena do not occur in a Hilbert space. They occur in a laboratory."

[galaxyLogic]

> Schrödinger's cat must be alive or dead once we open the box

I recently had a conversation about this in another thread. It seems to me, and nobody tried to convince me otherwise, that the Cat would be the Observer. Therefore it would be dead, NOT dead AND alive, as soon as it observes the poisonous gas in its box.

[3PS]

So this is a little nuanced. It's true that quantum systems collapse on "observation", but that doesn't actually mean "observation by a sentient entity". It could really just be any interaction with the outside environment. (This is why qubits have to be kept incredibly well-isolated.) We don't really fully know exactly how this collapse works, and related speculation is generally classified under the measurement problem [1]. But it's true that one of the key points of Schrödinger when proposing his thought experiment was that the notion of measurement or observation was not fully defined under the Copenhagen interpretation.

Side note, it's not that the cat is observing poisonous gas, but rather, that a Geiger counter is set to detect whether a radioactive atom decays or not and triggers the release of some poisonous gas if so. So, classically, Schrödinger's cat would be either alive or dead 50% of the time, not 100% dead. There are plenty of alternative ways to reconcile this classical view with quantum mechanics. Perhaps the simplest and most well-known is the many-worlds interpretation [2], which states that both events occur, just in different timelines, and we don't know what timeline we ended up in until we open the box. (Of course, it is ridiculous to speculate as to which timeline "we" end up in before the experiment is carried out, because the people in both timelines would still be "us" - this can get awkward to think about.)

[1] https://en.wikipedia.org/wiki/Measurement_problem

[2] https://en.wikipedia.org/wiki/Many-worlds_interpretation

[tagrun]

That version of the though experiment is known as "quantum suicide": https://en.wikipedia.org/wiki/Quantum_suicide_and_immortalit...

[russdill]

The point of the thought experiment was to highlight the measurement problem in QM interpretations and the difficulty in defining the observer.

[empath75]

sure but that’s still all one quantum system from the perspective of any other observer outside of the box, including other cats.

[freeone3000]

You can do it with electron spin or photon polarization or by any number of properties, but it's the state of a fundamental particle.

It's an entirely new type of computing apparatus, using the fundamental state of particles. No electron circuits, those won't work.

And it's expensive because of the above. These things are massive, have to be kept at cyrogenic temperature, and isolation gets harder the more particles you have.

[drdeca]

I thought a qubit could also be implemented with current going around a superconductor loop. Is that incorrect?

[ben_w]

You can implement them like that. Anything that has a quantum state that doesn’t decohere too fast will work. The hard part thus far has been that almost everything does decohere too fast.

[Denvercoder9]

No, that's indeed a quite popular approach.

[grumpy8]

Extremely simplified:

>> in an electronic circuit, what is a qubit?

It's not an electronic circuit, it literally is an electron or a photon. And it's using that particle's properties to do "superposition and all that jazz".

You can't put too many next to each others because they start interacting together because that's what electrons do when they get close.

[sundarurfriend]

Quantum computing for the very curious [1] has been very useful to me, for getting at least a basic idea as to what exactly a quantum computer is, what a qubit is, and how they are manipulated.

[1] https://quantum.country/qcvc

[tagrun]

Physicists here. In practice, a qubit is a two-level physical system. It can be spin state of an electron, polarization of a photon, lowest two energy states of an atom or an electron in quantum dot/well trap potential, the charge state (called charge qubit) -- whether you have 0 or 1 electrons in it, etc etc (if you have 3 levels, it's called qutrit, and for d levels qudit). This experiment uses charge qubits (a special variant which has some robustness against charge noise by design [by operating at a voltage level which is insensitive to 1st order fluctuations in the electric field, called "sweet spot"], called transmon).

The main problem is achieving full control of these systems, which is extremely hard, because there are certain things (some random/stochastic) that you can't control at all and you have to fight+race against their influence:

- qubits are tiny, and the energy splitting between these two states are typically minuscule: this means even a small vibration from a sneeze miles away can make the qubit flip.

- qubits do not live in vacuum, they are typically hosted in solid-state systems and the qubits are coupled to their hosting environment, which have their own moving parts (two-level fluctuators which lead to charge noise, phonons which also couple to electrons typically via spin-orbit coupling, spinful defects in the material which have their own dynamics, etc etc) that you can't really control. it's extremely difficult to achieve full control of a qubit in the presence of things that you can't control and random in nature.

- if the qubit is the lowest two-levels of a system with higher energy levels, one also needs to worry leakage errors to those higher states

- there are ways of suppressing the influence of such unwanted interactions (dynamically corrected gates + quantum error correction codes) given that their strength is below certain thresholds. going below those thresholds is again an enormous engineering/material science problem (extremely low temperatures, isolation from vibrations, low/high-pass filters for the classical circuitry which is used to control/drive the qubits via electric/magnetic fields, design of the device itself which typically hosts two-level fluctuators, etc etc). this problem becomes harder in general as you increase the number of qubits though.

- to do anything non-trivial, you need to have more than one-qubit and have controllable couplings between those (so you can't put them apart too far which makes it impossible to couple them). this doesn't work perfectly in practice, you can't completely control or turn off their couplings (a problem called cross-talk) which again leads to errors. so it doesn't work quite like modular classical circuit elements which you can "copy & paste" because the abstractions from the low-level, nitty-gritty physics of the underlying material fail for all these qubits.

[tagrun]

And there's the pesky issue of readout errors, which tends to bad.

[pps]

Beautifully explained, thank you!

[rolltiide]

I'm in the same boat. A qubit can have more than the two states that a transistor can have, got it.

Okay, now what can we do with that?

"crack encryption by simulating a state!" yeah but what? is that something I should be concerned about now? "hahaha no no no silly normie we'd need two thousand qubits for that, this machine only has 53!" oooookay, and you did that number in your head, how??? "we just solved the first unsolvable problem that a mere bit bound supercomputer couldn't solve, look at this math formula!" but that didn't explain "we are celebrating, are you not celebrating"

There just seems to be a lack of non-introductory but non-PhD level information. Where is the "explain it like I've been accepted into college at all".

[rmidthun]

Since we're looking at Scott Aaronson, you might want to check out "Quantum Computing Since Democritus". It gives a good explanation of the math behind qubits and how they can be used. Best intro I know of.

[rolltiide]

thank you for that and not trying to explain it in an additional convoluted way

[rini17]

Schrodinger's cat in unopened box is 1 qubit = it's alive and dead at the same time. When the box is opened to observe the result, the quantum state "decoheres" - decays to 1 bit result.

Now imagine 53 such boxes, interconnected by quantum gates. The 53 qubits combined are in all of 2^53 states at once. The gates can be set up such that some combinations like "cat 1 alive", "cat 2 dead", etc. are much more likely result than others, after the boxes are opened. And all this computation is done in one step, whereby the classical computer must do 2^53 steps to get the same result.

To have 53 cats all undisturbed in these dead/alive states so that computation is done without errors is very technically challenging :)

[drdeca]

I don’t think the cat thing helps to explain this, especially with the finality association of “dead”.

[rini17]

It can't really be explained, we kind of accept it works like it has been in both states at once until the box was opened. Similarly, we don't really know how to explain how particles travel by both slits at once in the double-slit experiment.

[drdeca]

Idk, it seems to me like https://www.smbc-comics.com/comic/the-talk-3 is a pretty good explanation.

“A new ontological category”.

What’s the problem?

[rolltiide]

satire and educational

this has been the best thing I've seen so far

[buboard]

Here .. finding the circuit that saves more cats from death is already a useful thing. Of course, i dont see an obvious algorithm to search for that circuit so it would have to be brute force. but now this computer makes even brute force possible

[drdeca]

Do you know linear algebra?

If you have a collection of n qubits, the state of those corresponds to a unit vector in a 2^n dimensional space over the field of complex numbers.

You can do certain linear operations (iirc, only unitary ones. I wouldn’t claim all unitary ones either) to change the state. You can also do a measurement, which has a random outcome, following the Born rule.

So, it isn’t really just “each of them has more than 2 possible states”. That can be the case with something classical, and has been done before (there have been ternary computers. Binary computers won out. Ternary computers (or quaternary, etc. etc.) wouldn’t be particularly special.)

You can’t just think of each of the qubits as having a state always entirely independent of the rest of the qubits.

[diegoperini]

> What exactly is a qubit?

A bit is like a boolean type, has the values of true and false. Or you treat those values as 0 or 1, then gather a bunch of bits to build useful numbers.

A qubit is like a pair<number, number> such that these numbers MUST satisfy the following constraints:

    pair.left^2 + pair.right^2 = 1
    pair.left and pair.right can be any complex number

Why such a composite type with weird constraints you may ask? Because that's how properties of really small particles behave in the real world. So the hope is, maybe if we can build our software using this weird data type called qubit, we can implement computation on quantum hardware without abstracting every problem using a dump type like a boolean or its aliases/collections.

Remember that classical computers use a clock to flip bits over time.

A similar quantum computer would manipulate qubits instead.

A bit has the storage capacity of 2 distinct bits of information.

A qubit has the storage capacity of 2 complex numbers, which corresponds to 4 floats, which is at least 16*8 bits of information if we are conservative about our assumptions.

> Is it made out of logic gates?

Kind of. Most of the current logic gates are built with semiconductors. It means by applying different voltages/currents/flux etc to different parts of a solid material, we can alter what we measure in some other part of the same material.

A quantum logic gate uses the same principle but in order to achieve the desired speed and storage advantages, it uses an object with a measurable property that at least approximately behaves like a quantum mechanical object. Common semiconductors are too crowded of atoms in terms of their body parts to make good quantum materials. They touch to each other and are almost always exposed to air. Their running temperatures are undesirably high.

A really dark (literally without a single photon) vacuum chamber that holds a really small amount of floating matter in the middle, frozen with lasers up to 0.000...1 Kelvin would make a good example of a stable but expensive qubit. We can measure this qubit by destroying its state, i.e by applying a magnetic field and measuring the emitted photon's location, polarization or frequency. The problem is, copy pasting this device to build a circuit is really hard due to logistics and auxiliary machinery required to keep all the state stable.

> How come our current limit is only around 54 or so?

That's not a fundamental limit but an engineering one, due the issues I mentioned above. The bigger the device gets, the harder to maintain its stable state. The method currently used for reaching this limit really looks like what is used in the 60s. History is repeating itself with a small twist, the running temperature is extremely low this time. Not liquid nitrogen low, but compressing atoms by sniping them from distance via laser on multiple directions low.

There is also one more problem that is unique to quantum computers. You have to measure the same qubit multiple times to be able to read those complex numbers since their values are determined statistically. You either represent a qubit with multiple qubit like devices or you use the same device to try your measurement repeatedly. Each approach comes with its own drawbacks.

> Are qubits, and quantum computers by extension, not even electronic circuits?

Even today, non quantum circuits are sometimes non electronic in some of their parts. Fiber optics, supersonic emitters/receivers and photoelectric sensors are good examples.

To this day, it is not clear whether the first consumer quantum CPU will be entirely electronic or not.

[AgentME]

>A bit has the storage capacity of 2 distinct bits of information. A qubit has the storage capacity of 2 complex numbers, which corresponds to 4 floats, which is at least 16*8 bits of information if we are conservative about our assumptions.

This whole explanation makes qubits sound just like a combo-pack of bits, or like something you'd find in an analog computer. They're much more powerful than that because they can be put into superpositions and entangled together while you continue to do calculations with them. Using superpositions and entanglement across qubits can let you solve some problems with lower-complexity algorithms than you could with classical computers.

It's like saying a car is defined by four tires being in close proximity, while skipping the fact that the usefulness of a car comes from the tires being connected together and steered which lets you do things that no amount of unconnected tires could do.

[OscarCunningham]

And also, qubits can't be used as compressed data storage. Despite the fact that it takes two real numbers to specify the state of a qubit, you only get one bit out when you measure it, with the rest of the information being destroyed.

[diegoperini]

The whole point of Quantum Supremacy test is to show that qubits can in fact store distributions in their state which is another way of saying some carefully crafted equations are storable inside qubits as long as you are interested in an approximate and numeric output. One can argue a MIDI audio or a SVG graphic is exactly that, a carefully crafted equation which even in its lossy form (mp3, jpg) is able to convey meaning.

[recursive]

> A qubit has the storage capacity of 2 complex numbers, which corresponds to 4 floats, which is at least 16*8 bits of information if we are conservative about our assumptions.

The fourth float would seem to be almost totally determined by the first three. If I'm visualizing correctly, there are at most 2 values it could possibly be.

[diegoperini]

Yes, the constraints reduce the capacity from the ideal limit of 4 real numbers.

(a + bi) type of complex numbers are indistinguishable from (b + ai) ones. Deciding the value of b immediately reduces the number of possible values for a to 2, which is a and -a respectively. Luckily, the real number line is continuous. We can accept such sacrifices without too much precision loss.

Also I should note that my calculations assumed a pair of maximally entangled particles per quantum circuit element since that's the most straightforward way to harvest quantum information with minimum number of objects.

[blattimwind]

> Kind of. Most of the current logic gates are built with semiconductors. It means by applying different voltages/currents/flux etc to different parts of a solid material, we can alter what we measure in some other part of the same material.

This kinda sounds like translinear circuits, except a couple orders of magnitude more boutique.

[buboard]

for example an electron or a polarized photon. they can take the value 0 and 1 when measured but when not measured they can be in superposition states. Quantum physics forbids copying a qubit to create another, but you can initialize them en masse to to be in a superposition state. Those things are too tiny to be easily manipulated so 53 is quite an accomplishment.

[AgentME]

>>If we can make one qubit, can't we just make a bunch of them by copy and pasting circuits similar to how we used vacuum tubes in the 60s and 70s? How come our current limit is only around 54 or so?

>Quantum physics forbids copying a qubit to create another, but you can initialize them en masse to to be in a superposition state. Those things are too tiny to be easily manipulated so 53 is quite an accomplishment.

Quantum physics forbids copying the value of a qubit, but the poster was asking why we couldn't just make more of the device that implements a qubit. The big issue is that you want the qubits to be entangled together and it's hard to prevent decoherence as you make a larger device with more qubits.

[justinpombrio]

> If we can make one qubit, can't we just make a bunch of them by copy and pasting circuits similar to how we used vacuum tubes in the 60s and 70s? How come our current limit is only around 54 or so?

This is a very good question! And as far as I can tell, no one has actually answered it yet.

In classical physics, which suffices to explain circuits made of vacuum tubes, the state of a system is fully captured by the states of its parts. Like, if you want to know the state of three bits, I just have to tell you what the first bit is (0 or 1), and the second bit, and the third one. Basically everything we interact with has this property: if you fully describe the state of each part of a thing, you have described the state of the whole thing.

But quantum mechanics is... weirder than this. In quantum mechanics, to describe the state of a system you have to give one complex number per classical state, such that the sum of the squares of the absolute values of the complex numbers adds up to 1. These complex numbers roughly correspond to the "probability" that the system is in that state (but not quite, it's more complicated than that).

So in quantum mechanics, to describe the state of three bits, you have to give eight complex numbers n1,n2,...,n8, one for each of the classical states of the bits 000, 001, 010, 011, 100, 101, 110, 111, where the sum of the squares of the absolutely values of n1,...,n8 add up to 1. That's a lot more information than 3 bits. (Imaging if you had 54 bits... you'd need 2^54 ~= 10^17 complex numbers to describe them.)

Technically, everything in the whole world, including you, is described by the laws of quantum mechanics. So why don't we see weird quantum effects all of the time? Quantum systems are very fragile: whenever they interact with the outside world (say a photon from the air bounces off of something in the system), the system "collapses", and then behaves as classical physics would predict. (Note that this is in accordance with the quantum prediction. The system goes from "only describable using difficult quantum mechanics" to "describable using quantum mechanics, but it'll just say the same thing as classical physics, and classical physics is simpler so you should just use that".)

So here's what a qbit is: it's just a regular bit that has been so insulated from the outside world that classical physics doesn't suffice to describe it. You won't find qbits on a regular circuit board, though, because they'll interact with the circuit board in any way whatsoever and then you're done.

And this is why making a 54-qbit quantum computer is so hard. You need to keep all of the qbits isolated, because if any of them interact with the outside world (think the air in the room, or a single photon, or the substrate that the qbits are on), then the whole system "collapses".

[tzs]

> If we can make one qubit, can't we just make a bunch of them by copy and pasting circuits similar to how we used vacuum tubes in the 60s and 70s? How come our current limit is only around 54 or so?

(I'm not an expert in this area, so the following may not be incomplete or limited to only certain kinds of quantum computation, or worse).

The kinds of computation that qubits can beat a classical computer on require that the qubits be entangled. If the qubits are not entangled, you can't do better than regular bits.

Briefly, if two (or more) quantum systems are entangled, and you make certain measurements that have a random outcome on one of the systems, and then measure the same property on the other system(s), there will be correlations that you would not get if the systems were not entangled. The entangled systems act is if whenever you measure one and it randomly chooses a value for the property you measured, that result is somehow communicated to the other entangled systems, and they make sure them that when they are measured they will give results with the appropriate correlation.

You might think that this could be explained if the systems had some internal variables that were set when they became entangled that determined what "random" values they would pick when later measured, but there are experiments that have shown that this is not so. The systems are truly making their random choice at the time of measurement as far as we can determine.

This happens even if after you entangled the systems, you separate them by a great distance--so far that between the time you do the measurements on the separate systems there is no time for any communication between the systems (or, rather, no time for any communication limited by the speed of light--I believe there have been experiments showing that IF there is communication, it is at more than 10000 times the speed of light). (This communication, or whatever it is, cannot be used to send messages faster than light. All it can do is make the correlations work out for entangled systems).

Anyway, the thing about entangled systems is that as soon as you make a measurement of the entangled property, you lose the entanglement. Your particle that had entangled spin, say, with another particle and that was 50/50 whether it was spin up or spin down becomes, once you actually measure spin, a non-entangled particle whose spin is a concrete value, either up or down. Measure it again, and you get the same value.

When I say "you make a measurement", I don't specifically mean you, or any other human, or any human instruments. For purposes of quantum mechanics, a measurement is anything that makes the system reveal a value. So if you have a particle with entangled spin with some other particle, and some random passing particle happens to interact with yours in a way that depends on the spin of your particle--that's a measurement and you've lost your entanglement. (Your particle might now be entangled with that random passing particle, but it is no longer entangled with the particle you intended it to be entangled with).

If you are trying to do a quantum computation on 50 qubits, you have to get them all entangled, and then you have to keep them from interacting with anything that might inadvertently do a measurements long enough for them to do their quantum computation, where you can then measure the result (which finally ends the entanglement).

This turns out to be hard, because there are a lot of things in the universe that want to effectively do a measurement. Any random particle bumping into one of yours with too much energy can do it. Some random passing electromagnetic wave can do it. The more things you need to entangled and keep entangled, the hard this is, and 50ish is the current limit.

[cdumler]

TL;DR: A quantum computer is a device that uses the measurement of quantum properties to do computation. There are many ways to implement one depending on the type of entangled particles being used, from crystals to make entangled photons and superconducting mounds to entangle electrons. This is the same for binary computers, which can made from electrical devices (transistors), values with air pressure or balls falling down wooden ramps.

Longer version

An observation about quantum behavior is that there are only certain properties that you can measure for the really, really small. These include things like mass (total energy), charge (intrinsic amount of electromagnetic strength), and spin (willingness to change direction in the presence of an electromagnetic field). It turns out that when you measure these properties, the measurements behave in non-intuitive ways.

The act of measuring the spin of a particle (which could be in any direction) is really the act of asking, "is this particle aligned with my detector?" The result will always be either aligned up or aligned down. It will be randomly about 50/50 up and down, also. This is not that surprising because the spin must align one direction or the other. The crazy part comes with the fact that you can entangle two particles.

Entangle particles can be sent off through different detectors and one thing will always be true: while any particular outcome is random, the detectors will always generated opposite results. The temptation is to say, "well, they were generated from the same source, so they have just opposite starting positions." Long story short, this has been proven not possible. Instead, there is some fundamental behavior is quantum mechanics that says that there are certain types of activities with entangles particles that have a correlation that is true as long as the entangle particles are not disrupted. In this case, particles sent to separate detectors will always have opposite results.

A quantum computer uses these correlation truths about measurements to do computations. A qubit is the concept of a quantum bit: an entity that represents one unit of entanglement. Just like a bit, quantum computers have many different ways to implement entanglement. You can entangle photons, electrons, and whole atoms. Each of these systems require specific implementations to achieve, like like electronic or mechanical computers.

Remember that one detail about "if they are not disrupted?" Yeah, turns out that it takes a hell of a lot to create an environment that doesn't destroy the coherence of the entanglement. You have to design something that allows you to setup the particles into starting state, be able to hold those particles in an entangled state with no disruptions and have a detector to determine the final state. Quantum mechanically, these are generally opposite goals.

[Analemma_]

Just like a bit, a qubit is an abstract representation of information, which can be physically instantiated in different ways.

[raincom]

"[T]hose believing that a QC can manipulate or maintain huge objects "free of cost" (i.e., at unit cost) should provide a convincing explanation to this fantastic speculation. Being skeptic of this (rather over-simplified and counter-intuitive) speculation seems to be the default and natural position." (From http://www.wisdom.weizmann.ac.il/~oded/on-qc.html )