# Questions tagged [circuit-construction]

For questions about the construction of complex circuits using elementary quantum gates.

18 questions
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### Quantum Fourier Transform without SWAPs

The Quantum Fourier Transform from Nielsen and Chuang chapter 5 is pictured here: In the textbook the author refers to "swap gates at the end of the circuit which reverse the order of the qubits". ...
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### Quantum operation in blocks

I have $n$ states in superposition $|A\rangle=\dfrac{1}{2^{l/2}}\sum_{i=0}^{2^l-1}\sum_{j=0}^{2^l-1}|0\rangle^{\otimes q}|i\rangle^{\otimes l}|j\rangle^{\otimes l}$. Now I have to apply the transform ...
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### Sequential circuit using quantum gates

Without feedback/loop how can we build a sequential circuit? The basic feature of sequential circuit is that is depends not only on the current inputs but also on the previous inputs/outputs. I've ...
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### Circuit construction for Hamiltonian simulation

I would like to know how to design a quantum circuit that given a Hermitian matrix $\hat{H}$ and time $t$, maps $|\psi\rangle$ to $e^{i\hat{H}t} |\psi\rangle$. Thank you for your answer.
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### Correspondence between the Topological model and Quantum Circuit model

For example, given the $R$ & $F$ gates and Toric codes for a given problem, how to convert this code into the conventional circuit model and vice versa. From the literature developed, it seems ...
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### Error: Simulation of “Quantum algorithm for linear systems of equations” for $4\times 4$ systems on Quirk (without SWAP) - Global phase

Following @DaftWullie's answer I tried to simulate the circuit given in Fig. 4 of the paper (arXiv pre-print): Quantum circuit design for solving linear systems of equations (Cao et al, 2012), on ...
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### How exactly is the stated composite state of the two registers being produced using the $R_{zz}$ controlled rotations?

This is a sequel to How are two different registers being used as "control"? I found the following quantum circuit given in Fig 5 (page 6) of the same paper i.e. Quantum Circuit Design for ...
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### How to build a quantum circuit representing the Ising Model?

Can someone explain to me how to build a quantum circuit representing the Ising Model? I just want to understand how to represent the Ising Model for the purposes of quantum state label classification....
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### Can anybody explain or suggest a good reference on how to make a modular exponentiation circuit for N=15 with any coprime base?

I have read many papers related to it but in every paper, they just show the circuit of order finding algorithm for N=15, but did not explain what is the procedure to make it. It will be great if ...
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### How to implement the mixed quantum state fidelity in a quantum circuit?

Suppose we use Uhlmann-Josza fidelity $F(\rho, \sigma):=(\mathrm{tr}\sqrt{\sqrt{\rho}\sigma\sqrt{\rho}})^2$, can we construct a quantum circuit that help us to calculate the fidelity of two mixed ...
Let me first tell my problem statement. Suppose I have a uniform superposition of states $$|A\rangle=\dfrac{1}{2^{9}}\sum_{i,j,k=0}^{2^6-1}|0\rangle^{\otimes 8}|i\rangle|j\rangle|k\rangle,$$ where $|0\... 0answers 51 views ### Tensorial notation for this quantum XOR circuit Suppose I have this quantum XOR circuit; this is a quantum circuit for the classical XOR operation$$\begin{eqnarray*} x_1'= x_1\oplus x_2\oplus x_3\oplus x_4,\\ x_2'=x_2\oplus x_3\oplus x_4\oplus x_5,... 0answers 45 views ### N&C quantum circuit for Grover's algorithm In the chapter about the Grover algorithm, it is suggested that the gate which executes the phase shift is given in the following form: Now I have looked at this gate in detail and come to the ... 0answers 39 views ### How to simulate a simple circuit to add two numbers in Quirk? I am new and I don't understand where I should give the input and where I should get the output. Please explain with an example of a circuit run on the Quirk simulator. How to add two numbers? 0answers 48 views ### Implement a circuit as a matrix in ProjectQ Suppose a have a circuit coded up in ProjectQ, suppose also it is that large to be hard enough to write it down as a unitary matrix by hands (e.g. order-finding, which is rather standard, but turns ... 0answers 19 views ### Controlled controlled adder gates involved Let's say I have a circuit that given in the figure As we can see that this circuit consists of$2$-Toffoli gates and$4$C-NOT gates, and to construct this entire circuit using only single qubit ... 0answers 53 views ### Quantum operation involving permutation Suppose I have the state$\frac{1}{2^l/2}\sum_{i=0}^{2^l-1}|0\rangle^{\otimes q}\otimes |i\rangle^{\otimes}|0\rangle_i^{\otimes l}$. I perform some unitary transformation between the registers$|i\...
I have 4 states say $|00\rangle, |01\rangle,|10\rangle, |11\rangle$. I want to add the states in a manner such that $|a\rangle=|00\rangle\otimes|01\rangle\to |00\rangle\otimes|01\rangle$ and \$|b\...