# Questions tagged [circuit-construction]

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

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### How can I build up an arbitrary quantum circuit given a certain unitary matrix operation?

Suppose I want to put a qubit whose initial state is $|0\rangle$ to the final state $\frac{1}{\sqrt{3}}|0\rangle + \sqrt{\frac{2}{3}}|1\rangle$. Well, in that case, the unitary matrix that performs ...
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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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### Simulation for the [5,1,3] stabilizer code in Qiskit

Sorry that I keep asking questions for the same subject. It is driving me crazy. I have followed the [5,1,3] stabilizer code circuit designed by Gottesman in page 35 in his paper (also illustrated in ...
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### Why is implementation of controlled Hadamard on IBM Q so complex?

With reference to question how to implement CCH gate I easily realized that CH gate can be implemented with $\mathrm{Ry}$ gates and $\mathrm{CNOT}$ followingly: Note $\theta = \frac{\pi}{4}$ for ...
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### How to implement the CCH gate in quantum computers available in clouds?

How to implement CCH gate in quantum computers available in clouds? If there is not any gate directly available for it, what are the possible ways to represent CCH?
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### Uncomputation in quantum implementation of a classical algorithm

In Nielsens and Chuangs book, they present a way to implement a reversible version of any classical algorithm (section 3.2.5). In short, they use Fredkin and other simple reversible gates to ...
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### Decomposing a $(w+1)$-qubit permutation gate into $w$-qubit permutation gates, SWAPs and NOTs

Say I have a quantum circuit of $w+1$ qubits with a permutation gate (mapping computational basis states to computational basis states) that does the permutation $(i, i+1)(i+4, i+5)$ on $w+1$ qubits ...
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### How to implement a Fredkin gate using Toffoli and CNOTs?

Inspired by a question Toffoli using Fredkin, I tried to do "inverse" task, i.e. to implement Fredkin gate (or controlled swap). In the end I implemented it with three Toffoli gates. Firstly, I ...
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### Can a Toffoli gate be implemented using Fredkin gates?

Even though this seems to be a much asked basic question, I couldn't find a reputed answer to this: Implement a 3-qubit Toffoli gate using 3-qubit Fredkin gates. The best I could do was using 4 ...
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### Computing circuit depth in Cirq

I ran into a problem of how to extract circuit depth from Cirq circuit object. In Cirq circuits consist of a list of Moments. Number of moments is not equal to the circuit depth in general case. I ...
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### Compiling the Pauli-Z operator to the Rz operator for Hamiltonian simulation

I saw a tutorial on this long ago, but lost it. I know that the Pauli-Z operator compiles to Rz, but how? Here are the steps I remember: First, we have to solve for $U(t)$ in the Schrodinger equation ...
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### How to transform e.g., a 4 by 4 unitary matrix into a quantum circuit

I am new to Quantum Computing. I would really appreciate if some one could offer me some ideas, suggestions and/or useful references to solve the following problem about realizing an arbitrary ...
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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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### Quantum circuit for a three-qubit bit-flip code

I know a three-qubit bit-flip code has a common encoding circuit as follows, Further, as in page 35 in Gottesman's paper, the encoding circuit can also be constructed through stabilizer generators. ...
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### How are physical quantum chips made?

So this might be a dumb question, but I have trouble finding any information on the physical aspect of quantum computers. Online you can find only pictures of big bulky things said to be quantum ...
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### Is this interpretation of quantum circuits right?

Just need some clarification: Results derived as the output of "running" a "quantum circuit" constructed from "quantum gates" are distributed in a certain way, based on the design, and the multiple ...
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### How is inner product addition performed?

The Swap test proof on page 8 of https://sites.cs.ucsb.edu/~vandam/teaching/S05_CS290/week9.pdf ends with this derivation: How you add those inner products to get from \$\frac{1}{4}(2 + \langle \Psi, \...