# Questions tagged [gate-synthesis]

For questions about finding (short) gate sequences to implement a specific unitary operation, for example decomposing a complicated multi-qubit gate into a sequence of basic gates. It might apply to optimizing circuits with respect to length or depth or finding gate sequences to implement an algorithm.

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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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### Cost of controlled-$U_i$

What is the cost (number of gates) of $\sum_{i=0}^{N-1}| i \rangle \langle i|\otimes U_i$ in terms of $N$ and the costs of the unitaries $U_i$? Say the gate set consists of arbitrary one-qubit gates ...
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### Representation of multiple qubit matrices in Dirac notation

Imagine one wants to represent the and function for any number of qubits in Dirac notation. The and gate flips the target qubit if all the control qubits are in state 1. This is its matrix ...
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### Decompose Toffoli gate with minimum cost for IBM quantum computer

The known decomposition of toffoli gate that can be used on IBM quantum computer is : I want to know any other Toffoli gate decompositions that can be used on IBM quantum computer and have a cost ...
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### How can I prove the universality of this set of gates?

I was reading this article. A brief explanation: Here we have a circuit, the registers are a stepfunction state, an single photon state and a function state. The first two have position operators $X$ ...
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### How to implement controlled u3 gate from Qiskit using simpler gates?

I am trying to implement the u3 controlled gate (able to rotate the qubit in any specified direction in 3 dimensions if the control is 1, for two qubits) using simpler gates. The simpler gates ...
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### 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 ...
181 views

### Transferring classical OR gate in a quantum gate

I would be interested to know how to transform the classic OR gate into a quantum gate. I thought a little about myself. The OR gate can also be rewritten as a NAND gate: So, I have now tried to ...
In article A controlled-NOT gate for frequency-bin qubits, the authors built a passage matrix acting on the states $T_0$, $T_1$, $C_0$, $C_1$ and then they infered the famous two qubit matrix notation....