Can qubit be represented in Boolean?

Question

A bit can have only two states: true and false. In quantum computing, the qubit, or quantum bit, in which you can assume true and false simultaneously. How this is represented in boolean form?

Or rather, it is possible to represent a boolean value with quantum programming?

operation boolParaQubit (q : bool) (Qubit) {
    body {
        let valorBooleano = q;
        using (registrador = Qubit[1]) {
             X(registrador(valorBooleano));
             return M(registrador[0]);
        }
    }
}

When calling this procedure, the output is: boolParaQubit(true) -> One. How would it look if this Qubit did not assume Zero or One?

Answer 1

While electrons or photons are often used to represent qubits, I prefer to use another fundamental particle of nature. The cat.

Let’s take, then, a 3 qubits cat system. Each cat, in order to function properly as qubit, needs to be isolated from the world. If it is somehow noticeable around the world, any exchange of quantum information (through bosons) will cause the cat’s wave function to collapse and it will stop behaving as qubit to behave as bit. So we need to put him inside an electromagnetically opaque box.

Now, how do I do the qubit 1 or 0 reading? Well, we need to have two distinct cat states. With electrons, this measurement can be the direction of the spin. But cats have a very difficult spin to measure, so we need another state.

Alive and dead, however, it is easier to measure. But, how to do this? Put in some enriched uranium, a Geiger counter and a vial of cyanide; if the Geiger counter senses the radioactive emission from this uranium source, it will trigger a system that will release the cyanide and the cat will die immediately. We’ll put enough uranium in there to, given the one-hour window, the possibility of radioactive decay will be 50%. So, every hour, our cat will have the same chance of being dead or alive.

According to the interpretation of Copenhagen, this means that, for the outside world, the qubit of our cat will be in an overlap of states of alive and dead at the same time. In the interpretation of pilot wave (defended by de Broglie), however, it is impossible to determine externally whether the cat is alive or dead, but it will be, deterministically, through some hidden variable, only alive or just dead.

The pilot wave theory was supposedly already falsified, but I don’t have the reference. However, several experiments that demonstrate the absence of hidden variables have been performed, and also have a experiment performed which only makes sense in the Copenhagen interpretation.

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So, let’s create our random number generation algorithm using 3 qubits of live cats. We will take into account 1 as being the cat dead and 0 as being the cat alive. By measuring exactly one hour after the algorithm starts, each cat will have a 50% chance of being dead.

Initially we are in the following state:

q0           ; q1          ; q2
1|0> + 0|1>  ; 1|0> + 0|1> ; 1|0> + 0|1>

To be in the following state after one hour:

q0                           ; q1                          ; q2
sqrt(2)/2|0> + sqrt(2)/2|1>  ; sqrt(2)/2|0> + sqrt(2)/2|1> ; sqrt(2)/2|0> + sqrt(2)/2|1>

And after another hour, I’d be in the next state:

q0                     ; q1                    ; q2
1/2|0> + sqrt(3)/2|1>  ; 1/2|0> + sqrt(3)/2|1> ; 1/2|0> + sqrt(3)/2|1>

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What we just put together was a quantum random number generation algorithm. When, by chance, a classical system is to measure the state of the system, the function will collapse and it will be in only one deterministic state. For example, if after 1 step of quantum processing, we take the 3 qubits, we could take the number 010 as likely to find 001 or 000. However, after 2 steps of quantum processing, the chance to find 001 is much smaller than 111.

Each quantum "step" usually takes another name: quantum gate (in the same direction as gates of logic circuits, such as the AND port or the OR port). The function of a quantum gate, as well as the traditional logic gate, is to take various inputs and return outputs that depend on these inputs. The difference between a classical gate and a quantum gate is that the classical one will perform deterministic processing, while the quantum gate will pick up overlapping inputs (remembering that 1|0> + 0|1> is a valid overlap where it is only possible to observe 0 when measuring the value of qubit) and will return outputs also in overlap.

Our quantum door, in this case of random number generation, was the passage of time. Not that that’s very helpful, but it’s what I was able to do using cats, uranium and cyanide. In the case of quantum systems where you need to retrieve this information and use it in another calculation (whether quantum or classical), these gates usually involve things that interact with photons/electrons.

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Qubit can be represented in Boolean?

According to the Copenhagen interpretation, what we know as a boolean is a qubit that is constantly collapsing to the state 1> or 0>. When we can stop observing this variable and put it in a quantum stochastic environment, it starts to assume the multiple values of the overlap until it is again observed.

So a boolean is a specific case of a qubit. And a qubit is an overlay of necessarily boolean.

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You can see more of quantum states/quantum computation in the following videos:

• The Quantum Experiment that Broke Reality - PBS Space Time
• Why Quantum Computing Requires Quantum Cryptography - PBS Space Time
• The Quantum Internet - PBS Space Time
• Hacking at Quantum Speed with Shor’s Algorithm - PBS Infinite Series
• The Mathematics of Quantum Computers - PBS Infinite Series
• How Quantum Computers Break Encryption | Shor’s Algorithm Explained - minutephysics
• How to Teleport Schrödinger’s Cat - minutephysics
• Hardy’s Paradox | Quantum Double Double Slit Experiment - minutephysics
• The No Cloning Theorem - minutephysics
• Bell’s Theorem: The Quantum Venn Diagram Paradox - minutephysics
• Some light quantum Mechanics (with minutephysics) - 3Blue1Brown
• Quantum Cryptography in 6 Minutes - Up and Atom
• Superposition of Quantum States - Up and Atom
• How Does a Quantum Computer Work? - Veritasium
• How To Make a Quantum Bit - Veritasium
• Single Photon Interference - Veritasium