# What is Quantum gates: Definition and 16 Discussions

In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits. They are the building blocks of quantum circuits, like classical logic gates are for conventional digital circuits.
Unlike many classical logic gates, quantum logic gates are reversible. However, it is possible to perform classical computing using only reversible gates. For example, the reversible Toffoli gate can implement all Boolean functions, often at the cost of having to use ancilla bits. The Toffoli gate has a direct quantum equivalent, showing that quantum circuits can perform all operations performed by classical circuits.
Quantum gates are unitary operators, and are described as unitary matrices relative to some basis. Usually we use the computational basis, which unless we compare it with something, just means that for a d-level quantum system (such as a qubit, a quantum register, or qutrits and qudits:22–23) we have labeled the orthogonal basis vectors

|

0

,

|

1

,

,

|

d

1

{\displaystyle |0\rangle ,|1\rangle ,\dots ,|d-1\rangle }
, or use binary notation.

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1. ### I Discover Beginner-Friendly Books on Quantum Information and Computation | Q&A

Hello to everyone, I would like to ask you to brief questions. The first one is whether you could recommend any pedagogical books on Quantum Information and Computation. I tried Nielsen and Chuang but I found it too dense for a beginner in the field. The second question is the following: to...
2. ### I Representing Quantum Gates in Tensor Product Space

Where do I start. I want to write the matrix form of a single or two qubit gate in the tensor product vector space of a many qubit system. Ill outline a simple example: Both qubits, ##q_0## and ##q_1## start in the ground state, ##|0 \rangle =\begin{pmatrix}1 \\ 0 \end{pmatrix}##. Then we...
3. ### How can I apply single qubit gates and CNOT to 8x1 column vectors?

I know |GHZ>=(1/sqrt(2))[1; 0; 0; 0; 0; 0; 0; 1], and |000>= the tensor product |0> x |0> x |0> = [1; 0; 0; 0; 0; 0; 0; 0]. Can I apply single qubit gates (i.e. 2x2 matrices) and CNOT (a 4x4 matrix) to 8x1 column vectors? If so, does anyone know a good starting point or a hint to get me moving...
4. ### Controlled-Z gate as a product of exponentials

I have numerous points of confusion: what does it mean that the matrices are within the exponential? How do I go about doing the matrix multiplication to prove the given form of CZ matches the common form, the 4x4 matrix? Update: using the fact that exp(At)=∑ ((t^n)/n!)*A^n, where A is a...
5. ### Projective measurements of quantum processor

Am I correct in thinking that the system measures the probability |<f|1>|^2 for some state <f|? Then the probabilities for each of the six states would be: |<0|1>|^2= 0 |<1|1>|^2= 1 |<+x|1>|^2= |(1/√2)|^2 = 1/2 |<-x|1>|^2= |(-1/√2)|^2 = 1/2 |<+y|1>|^2= |(-i/√2)|^2 = 1/2 |<-y|1>|^2= |(i/√2)|^2...
6. ### Quantum gates: what is the hardware?

In looking up "quantum gates", e.g. "Hadamard gate", all I come across is the matrix representations of the operations. But I do not see how, physically, they are achieved. (I also presume it will be different if we are talking about photons or electrons.) Could someone give me an appropriate...
7. ### Can anyone explain quantum gates

Hi I am studying Quantum computing and basically have no understanding of quantum gates and my lecturer is not very helpful. I don't understand why a 4x4 quantum gate would ever effect a two qubit system because surely that is at best only a 2x2 matrix, assuming they effect each other through...
8. ### Compute Matrix for Simple Quantum Gates

The example from my textbook shows one example of how to compute the matrix for a gate. The example is the U_CNOT operator: |00> -> |00>, |01> -> |01>; |10>->|11>; |11>->|10> Then they show that the operator is merely the sum of the outer products of these. |00><00| + |10><10| + |01><11| +...
9. ### What is the hardware for quantum gates?

I have lots of materials on the theory of quantum gates in terms of matrices, linear operators, and so forth. However, I would like to gain a basic understanding of how these matrices are achieved in practice. The difference is between knowing that a transistor acts as a switching or amplifying...
10. ### Understanding X Quantum Gate: Act on |i> State?

Hi everybody ... One of the one-qbit simple quantum gate is X which defined by: X: |0> ----- |1> |1> ----- |0> but how does this gate ( unitary operator ) act on |i> state? (i=0 or 1) I mean at first we have to measure what state is ( 0 or 1) and so flip them but after we know the...
11. ### What Does Basic Operations Mean in Quantum Gate Simulation?

Homework Statement I am actually trying to reproduce the research paper on "Elementary gates for Quantum computation". With reference to that paper, According to Corollary 7.4 - On an n-bit network(where n>=7), a lambda(n-2)[sigma x] gate can be simulated by 8(n-5) lambda(2)[sigma x] gates(3...
12. ### Rewriting quantum gates as CNOT+rotations

Homework Statement The goal is to 'decompose' common 2 qubit quantum gates such as the pi/8 gate into a sequence of CNOTS and single qubit rotations. I have the book by Nielsen and Chuang and the info is sortof in there (universality proof of CNOT), but I don't get how to apply it, i.e. how to...
13. ### Exploring Quantum Gates and Nuclear Spin

After reading Seth Lloyd's book “Programming the Universe”(only once) I came up with a few questions. The way I understand it... He describes the fabric of space-time as consisting of an endless array of casual space (wires) and matter(quantum gates). The wires tell information where to go and...
14. ### Can the Fredkin Gate be Proven to be Reversible and a Universal Classical Gate?

How do quantum gates work and how our they different than classical gates?
15. ### Can I Model Quantum Gate Operations with Excel and MathCad?

I'm taking a course that requires me to come up with a research project. I'm officially in my sophomore year and I'm a Physics Major with a fairly broad exposure to electrical eng. and some advanced math courses. That being said... I'm very interested in computer simualtion of quantum...
16. ### Can Quantum Gates Be Generalized for Higher Dimensions?

Hi i am coding a quantum computer simulator. the simulator will be able to work in dimensions other than qubits. in other words the user can select either qubits(d=2), qutrits(d= 3)...etc Obviously in this scenario one must have the generalised versions of all the gates So far i have...