# Questions tagged [circuit-construction]

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

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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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### 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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### Reducing the depth of quantum circuits with ancilla qubits

This question is two-fold and considers general $n$-qubit operations on a quantum computer. First, can a general $n$-qubit operation be implemented on a quantum computer without the use of ancilla ...
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### Equivalence checking of quantum circuits up to error

Suppose you are given two circuit descriptions $A$ and $B$ where by a circuit description I mean a sequence of gates (in the order they are applied) and the qubits they are applied on. (For the sake ...
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### Stabilizer circuit synthesis via Clifford gates

I have been working with stabilizer codes and I understand the mathematical way that they are described and how to simulate such in a classical computer in order to check their performance. However, ...
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### 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?
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### 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 ...
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### Simple Quantum Circuit to calculate sum of input states $|a\rangle + |b\rangle$

What is the simplest quantum circuit which takes states $|a\rangle$ and $|b\rangle$ as its input, and outputs their (normalized) sum $|a\rangle+|b\rangle$? Cross-posted on Physics.SE
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### Repeating Quantum Phase Estimation algorithm

In the Quantum Recommendation Systems paper, the authors use the Quantum Phase Estimation algorithm in a way that is slightly different from what I've seen so far. This is how it is described: The ...
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### Primer for Quantum Circuits and Optimization

I am interested in studying physical systems and trying to build circuits to simulate them. Now, of course, all the systems I could try to work with at simple, toy, systems - and that's fine. ...
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### Methods for encoding non-linear probabilities as data

I am working on translating a computing method I developed to model complex non-linear systems with classical computational methods into a form that is natural to quantum computing. The technique ...
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### Ansatz Techniques to Multi-Body Physics Problems

I have been reading this paper: https://arxiv.org/abs/1906.01563v1. I am wondering: is it possible to use the idea behind quantum circuits to build classical Hamiltonians represented in the same way?...
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 ...
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\...