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Questions tagged [circuit-construction]

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

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1answer
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Understanding the Group Leaders Optimization Algorithm

Context: I have been trying to understand the genetic algorithm discussed in the paper Decomposition of unitary matrices for finding quantum circuits: Application to molecular Hamiltonians (Daskin &...
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4answers
2k views

How do I add 1+1 using a quantum computer?

This can be seen as the software complement to How does a quantum computer do basic math at the hardware level? The question was asked by a member of the audience at the 4th network of the Spanish ...
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2answers
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How is the oracle in Grover's search algorithm implemented?

Grover's search algorithm provides a provable quadratic speed-up for unsorted database search. The algorithm is usually expressed by the following quantum circuit: In most representations, a crucial ...
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2answers
358 views

Automatic compilation of quantum circuits

A recent question here asked how to compile the 4-qubit gate CCCZ (controlled-controlled-controlled-Z) into simple 1-qubit and 2-qubit gates, and the only answer given so far requires 63 gates! The ...
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3answers
260 views

What would be the simplest addition that would make the D-Wave architecture universal?

The D-Wave system, as I understand it, allows us to program Ising models and to find their ground states. In this form, it is not universal for quantum computation: it can not simulate a circuit model ...
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1answer
185 views

SWAP gate(s) in the $R(\lambda^{-1})$ step of the HHL circuit for $4\times 4$ systems

Context: On the 5th page of the paper Quantum circuit design for solving linear systems of equations (Cao et al, 2012) there's this circuit: Schematic: A brief schematic of what's actually ...
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2answers
138 views

Topological Circuit Simulator

Does something like Quirk exist for topological (eg. braided) circuits? Alternatively, any ideas on how @CraigGidney is getting these circuits (or something similar)?
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3answers
131 views

Generalization for $n$ quantum teleportations

In Breaking Down the Quantum Swap, it is stated: Thanks to the CNOT, we can implement a xor-swap on a quantum computer. All we need to do is chain three CNOTs back and forth. In a comment to a ...
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2answers
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Why is it important to eliminate the garbage qubits?

Most reversible quantum algorithms use standard gates like Toffoli gate (CCNOT) or Fredkin gate (CSWAP). Since some operations require a constant $\left|0\right>$ as input and the number ...
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0answers
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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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1answer
92 views

How are two different registers being used as “control”?

On page 2 of the paper Quantum Circuit Design for Solving Linear Systems of Equations (Cao et al.,2012) there's this circuit: It further says: After the inverse Fourier transform is executed on ...
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2answers
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Given a decomposition for a unitary $U$, how do you decompose the corresponding controlled unitary gate $C(U)$?

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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1answer
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How exactly does Simon's algorithm solve the Simon's problem?

Problem Statement: We are given a $2-1$ function $f:\{0,1\}^{n}\to\{0,1\}^{n}$ such that: there is a secret string $s\in\{0,1\}^{n}$ such that: $f(x)=f(x\oplus s)$. Challenge: find $s$. Simon's ...
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2answers
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How can the state $\lvert0\rangle+M^{-1/2}\sum_{j=1}^M\lvert j\rangle$ be generated?

I was wondering if anybody to help me to generate the following state. It would be preferable if you use only Hadamard, CNOT and T-gates, on $\lceil\log_2(M+1)\rceil$ qubits: $$|\psi\rangle = \frac{1}{...
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1answer
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How to construct a quantum circuit for the following state transformation?

I have a certain transformations that goes as follows: Given $A=|abc\rangle$, $B=|xyz\rangle$, now I have cases as: $$\text{if }c=1,z=1, b\oplus y=1 \implies \text{flip}(x)$$ $$\text{if }c=1, z=1 \...