For questions about finding (short) gate sequences to implement a specific unitary operation, for example decomposing a complicated multi-qubit gate into a sequence of basic gates. It might apply to optimizing circuits with respect to length or depth or finding gate sequences to implement an ...
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55 views
Arbitrary powers of NOT and SWAP
The square-root of not and square-root of swap gates are often singled out for discussion of gates displaying important properties relating to quantum computers.
How do I define arbitrary (non-...
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1answer
69 views
Doing maths with controlled-half NOTs
In Quantum Computation with the simplest maths possible there is a section titled "Doing maths with a controlled-half NOT" which covers a reversible-(N)AND circuit with controlled-half NOTs.
What ...
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1answer
133 views
Basic approximation in Solovay-Kitaev algorithm
I read the Solovay-Kitaev algorithm for approximation of arbitrary single-qubit unitaries. However, while implementing the algorithm, I got stuck with the basic approximation of depth 0 of the ...
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1answer
66 views
Square root of not as a time-dependent unitary matrix
I want to express the square root of NOT as a time-dependent unitary matrix such that each $n$ units of time, the square root of NOT is produced.
More precisely, I want to find a $U(t_0,t_1)$ such ...
3
votes
2answers
96 views
Components for realizing a photonic CNOT gate
In Realization of a photonic CNOT gate sufficient for quantum computation FIG. 1 there is a "scheme to obtain a photonic realization of a CNOT gate with two independent qubits."
What components are ...
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2answers
146 views
Expressing “Square root of Swap” gate in terms of CNOT
How could a $\sqrt{SWAP}$ circuit be expressed in terms of CNOT gates & single qubit rotations?
CNOT & $\sqrt{SWAP}$ Gates
Any quantum circuit can be simulated to an arbitrary degree of ...
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1answer
276 views
Implementing a CCCNOT gate using only Toffoli gates
A CCCNOT gate is a four-bit reversible gate that flips its fourth bit if and only if the first three bits are all in the state $1$.
How would I implement a CCCNOT gate using Toffoli gates? Assume ...
6
votes
1answer
161 views
Quantum XOR Linked List Construction
After getting help here with XNOR & RCA gates I decided to dive into XOR Swaps & XOR linked lists. I was able to find this explanation for quantum XOR Swapping which seems sufficient for the ...
6
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1answer
93 views
Quantum Ripple Carry Adder Construction
There is an excellent answer to How do I add 1+1 using a quantum computer? that shows constructions of the half and full adders. In the answer, there is a source for the QRCA. I have also looked at ...
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2answers
172 views
Quantum XNOR Gate Construction
Tried asking here first, since a similar question had been asked on that site. Seems more relevant for this site however.
It is my current understanding that a quantum XOR gate is the CNOT gate. Is ...
6
votes
1answer
196 views
Implementation of the oracle of Grover's algorithm on IBM Q using three qubits
I am trying to get used to IBM Q by implementing three qubits Grover's algorithm but having difficulty to implement the oracle.
Could you show how to do that or suggest some good resources to get ...
8
votes
2answers
97 views
Why is the decomposition of a qubit-qutrit Hamiltonian in terms of Pauli and Gell-Mann matrices not unique?
If I have the $X$ gate acting on a qubit and the $\lambda_6$ gate acting on a qutrit, where $\lambda_6$ is a Gell-Mann matrix, the system is subjected to the Hamiltonian:
$\lambda_6X=
\begin{pmatrix}...
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1answer
84 views
How can a controlled-Ry be made from cnots and rotations?
I want to be able to applied controlled versions of the $R_y$ gate (rotation around the Y axis) for real devices on the IBM Q Experience. Can this be done? If so, how?
8
votes
2answers
172 views
Shortest sequence of universal quantum gates that correspond to a given unitary
Question: Given a unitary matrix acting on $n$ qubits, can we find the shortest sequence of Clifford + T gates that correspond to that unitary?
For background on the question, two important ...
10
votes
1answer
189 views
Obtaining gate $e^{-i\Delta t Z}$ from elementary gates
I am currently reading "Quantum Computation and Quantum Information" by Nielsen and Chuang. In the section about Quantum Simulation, they give an illustrative example (section 4.7.3), which I don't ...
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2answers
152 views
Circuit of controlled-Unitary gate
Suppose we have a circuit decomposition of a unitary $U$ using some universal gate set (for example CNOT-gates and single qubit unitaries). Is there a direct way to write down the circuit of the ...
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votes
2answers
230 views
What is the mathematical justification for the “universality” of the universal set of quantum gates (CNOT, H, Z, X and π/8)?
In this answer I mentioned that the CNOT, H, X, Z and $\pi/8$ gates form a universal set of gates, which given in sufficient number of gates can get arbitrarily close to replicating any unitary ...
10
votes
1answer
110 views
How are quantum gates realised, in terms of the dynamic?
When expressing computations in terms of a quantum circuit, one makes use of gates, that is, (typically) unitary evolutions.
In some sense, these are rather mysterious objects, in that they perform "...
12
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1answer
83 views
How does approximating gates via universal gates scale with the length of the computation?
I understand that there is a constructive proof that arbitrary gates can be approximated by a finite universal gate set, which is the Solovay–Kitaev Theorem.
However, the approximation introduces an ...
