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Questions tagged [matrix-representation]

For questions about matrix representations of quantum gates.

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6
votes
1answer
773 views

What are theta, phi and lambda in cu1(theta, ctl, tgt) and cu3(theta, phi, lam, ctl, tgt)? What are the rotation matrices being used?

I was reading the documentation for qiskit.QuantumCircuit and came across the functions cu1(theta, ctl, tgt) and ...
3
votes
1answer
513 views

Nielsen & Chuang Exercise 2.2 - “Matrix representations: example” [closed]

Reproduced from Exercise 2.2 of Nielsen & Chuang's Quantum Computation and Quantum Information (10th Anniversary Edition): Suppose $V$ is a vector space with basis vectors $|0\rangle$ and $|1\...
5
votes
3answers
1k views

How to construct matrix of regular and “flipped” 2-qubit CNOT?

When constructing the matrices for the two CNOT based on the target and control qubit, I can use reasoning: "If $q_0$==$|0\rangle$, everything simply passes through", resulting in an Identity matrix ...
3
votes
2answers
696 views

Difference between 3 qubits, 2 qutrits & 1 six level qunit

What is the difference between 3 qubits, 2 qutrits and a 6th level qunit? Are they equivalent? Why / why not? Can 6 classical bits be super-densely coded into each?
10
votes
1answer
218 views

Advantage of simulating sparse Hamiltonians

In @DaftWullie's answer to this question he showed how to represent in terms of quantum gates the matrix used as example in this article. However, I believe it to be unlikely to have such well ...
4
votes
1answer
121 views

What applications does the quantum gate [(i,1),(1,i)] have?

I've been working through the great introduction to quantum computing on Quantum Country. One exercise there is to find a possible quantum gate matrix that is not the $X,I$ or $H$ matrix. I thought ...
1
vote
1answer
219 views

Matrix representation and CX gate [duplicate]

I am having hard time figuring out how the CX (controlled-NOT) gate is represented in the matrix representation. I understood that tensor product and the identity matrix are the keys, and I ...
4
votes
0answers
99 views

Clock matrix vs matrix clock

In the process of research leading up to my previous question, I found out about matrix, vector & logical clocks. The citation in the aforementioned question mentions clock and shift matrices. ...
4
votes
3answers
219 views

Simple proof that $(U \otimes V)(|x\rangle \otimes |y\rangle) = U|x\rangle \otimes V|y\rangle$?

This transformation comes up a lot during symbolic manipulation of quantum operations on state vectors. It's the reason why, for instance, $(X\otimes \mathbb{I}_2)|00\rangle = |10\rangle$ - it lets us ...