Questions tagged [circuit-construction]

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

18 questions
53 views

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". ...
47 views

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 ...
30 views

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 ...
130 views

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.
49 views

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 ...
239 views

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 ...
98 views

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 ...
108 views

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 ...
56 views

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\...