How to understand quantum computers?

[Alex Notman]

Hi there,

I recently become interested in physics and quantum mechanics, and I was wondering if someone could suggest some readings, articles or books dedicated to quantum computers (sorry but I don't have a physics background, I'm from other worlds). I read here and here something very interesting about this topic, but I'd like to go deepen and understand the actual functioning of those machines. The only fact that the qbits could exist in multiple states is mind-blowing! many thanks for your help

 

[FactChecker]

For some light, easy, reading on quantum mechanics, I enjoyed the book "How to Teach Quantum Physics to Your Dog" by Chad Orzel. Please don't be offended by the title. It's a nice introduction for someone without a strong physics background. It does not concentrate on computers, but it will give you some understanding of the concepts of the quantum mechanics involved in the computers. And it shouldn't take long to read.

 

[.Scott]

Quantum computers take advantage of entanglement. A single bit is in one of two states. A single qubit can be a superposition of those two states. But the magic comes when you have many entangled qubits. So 10 bits will have one of 1024 states. 10 qubits can be a superposition of any combination of those 1024 states - an enormous number.

A special case of quantum computing is the quantum annealing process. Since it is not clear whether there are problems where that annealing can outpace classical computing, it has not grabbed the spot light. But it is worth noting that the "Orch Or" mechanism that Nobel Laureate Roger Penrose has proposed for some information processing in our brains looks an awful lot like a form of quantum annealing. I don't believe that Penrose ever described Orch Or as a form of "quantum annealing" - but his work predates that term.

The best reading depends on what your interest is. If you are already into software engineering, then take a close look at the wiki article on Shors Algorithm. It has gotten pretty detailed.

That algorithm is good for exercising some terminology. The algorithm itself is for factoring the product of two prime numbers. So, you might describe it as a "reverse multiply". But when manipulating qubits, that is, implementing qubit gates, you are only allowed "reversible" operations. And when many of these reversible gates are combined to form a quantum multiplication, the result is a "reversible multiplication" - which is way different that what I called a "reverse multiply". A reversible multiply means that enough "side" information (called "ancilla bits") have been stored to run the multiply backwards. This is a necessary feature of qubit logic operations. What those "ancilla bit" buy you is to have the input and output states of the multiply (or other boolean operation) to be the same quantum state. Think "if you know my work, you know me" - but in the most literal and physical sense.

Now let me switch to Grover's Algorithm. And, once again, it is to address some terminology - in particular, "oracle". If you have created a qubit computation that results in an entangled state that, when measured will yield the correct answer more often that any one incorrect answer, then you have three choices. The first is to run the computation enough times so that you can see which result gives happens with the greatest frequency - but in some cases, this may take billions or more tries. The second is good when there is some way of verifying an answer - but it can still take (depending on the problem) a huge number of tries. The third is to apply Grover's Algorithm, perhaps multiple times, before making a measurement. That algorithm makes the most likely result even more likely and it can be applied multiple times. If you read up on Grover's Algorithm, the term you will encounter is "oracle". In quantum computing, an oracle is that quantum circuit or device that creates an initial superposition. For Grover's algorithm, it is the quantum circuit or device that creates the superposition of correct and incorrect answers.

I hope this gets you started.

Scott

 

[FactChecker]

The only fact that the qbits could exist in multiple states is mind-blowing!

It's more accurate to say that a qbit has multiple possible states, 0 and 1, simultaneously. Once it collapses to a state, that is the only one it is in.

 

[PeterDonis]

It's more accurate to say that a qbit has multiple possible states, 0 and 1, simultaneously. Once it collapses to a state, that is the only one it is in.

No, this is not more accurate. A more accurate statement would be:

The state of a qubit can be expressed as a linear combination of $\ket{0}$ and $\ket{1}$, with complex coefficients. Any such linear combination is a valid state of a qubit.

When you measure a qubit's spin along the $\ket{0}$ - $\ket{1}$ axis, after the measurement, you treat the qubit, for the purpose of making predictions about future measurement results, as being in either the $\ket{0}$ state or the $\ket{1}$ state, depending on the result of the measurement. The squared moduli of the complex coefficients in the qubit's state before the measurement tell you the probabilities of getting each result. Whether the qubit is "actually" in the given state after the measurement depends on which interpretation of QM you adopt.

 

[PeterDonis]

The only fact that the qbits could exist in multiple states is mind-blowing!

That's not correct. At any given time a qubit is in exactly one state. But that state might not be the $\ket{0}$ state or the $\ket{1}$ state.

Quantum computing involves performing various operations on qubits that can change their states, i.e., they change the complex coefficients, sometimes on multiple qubits that are entangled. This can give all kinds of interesting results, but nowhere will a qubit be in "multiple states at once". The idea is simply to put qubits in states in which you can perform measurements on them that tell you things you want to know.

 

[Morbert]

Hi there,

I recently become interested in physics and quantum mechanics, and I was wondering if someone could suggest some readings, articles or books dedicated to quantum computers (sorry but I don't have a physics background, I'm from other worlds). I read here and here something very interesting about this topic, but I'd like to go deepen and understand the actual functioning of those machines. The only fact that the qbits could exist in multiple states is mind-blowing! many thanks for your help

Start with "The Talk" by Scott Aaronson
https://www.smbc-comics.com/comic/the-talk-3

 

[Alex Notman]

Many thanks for all your answers! Apparently I have a lot to study! :)

 

[HarshaVardhana]

Hi there,

I recently become interested in physics and quantum mechanics, and I was wondering if someone could suggest some readings, articles or books dedicated to quantum computers (sorry but I don't have a physics background, I'm from other worlds). I read here and here something very interesting about this topic, but I'd like to go deepen and understand the actual functioning of those machines. The only fact that the qbits could exist in multiple states is mind-blowing! many thanks for your help

Hello , I am a novice in that field and I have started learning quantum computing a little less than 6 months ago . I found it easier to first understand a classical bit and classical information and then move to qbits and quantum information . Maybe it suited me since I am an CS student . But nevertheless this method worked for me .

 

[PeterDonis]

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