# 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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### How to create a gate with functionality CCX(a,b,b)?

Can we create a Controlled gate with below functionality? if {a==|1> && b==|1>} then {qc.x(b)} Basically, a CCX gate but the output Qubit is actually one of the input Qubits. Apparently, ...
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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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### CNOT expressed with CZ and H gates by taking into account HZH =X

From this link: Where equation 1 is: I can probably brute-force this by explicitly calculating this quantum circuit's effective 4x4 matrix and seeing that its equivalent to this teleportation ...
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### How to code a projector operator in qiskit?

I'm new to qiskit and I want to know how do I define a projector operator in qiskit? Specifically, I have prepared a 3 qubit system, and after applying a whole lot of gates and measuring it in a state ...
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### Decomposing a controlled phase gate into CNOTs

I'm trying to understand the following derivation of decomposing a controlled $R_k$ (phase) gate into a combination of CNOTs and single qubit gates, but there's one main thing about the process that ...
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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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### control gate with 3 inputs, two control and rotation gate

My question is about if there is any way to represent a circuit that take 3 inputs and applies a rotation gate on the third qubit if the first two qubits is similar (has the same state)?
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### Efficient implementation of exponential of projector

If I have an $n$ qubit system and a projector $P$ such as $P_0 = \left|0\right>^{\otimes n}\left<0\right|^{\otimes n}$ (as an example) on those qubits, is there an efficient way to implement the ...
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### Sampling random circuits vs Solovay-Kitaev compiler

Suppose I want to obtain a gate sequence representing a particular 1 qubit unitary matrix. The gate set is represented by a discrete universal set, e.g. Clifford+T gates or $\{T,H\}$ gates. A well ...
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### How are multi-qubit gates extended into larger registers? [duplicate]

Implementing a single-qubit gate in a multi-qubit register is relatively easy. For example, this gate: This is equivalent to $I \otimes H \otimes I$. If the $H$ gate was on the first bit, it would be ...
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### Implement Fredkin gate with square root of swap

I would like to implement a Fredkin gate based on square root of swap and one-qubit gates. In particular, I was hoping to find the exact gate named "?" in this circuit: In addition, I want to avoid ...
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### Rewrite circuit with measurements with unitaries

In quantum physics, because of the no-cloning theorem, lots of classical proofs of cryptographic problems cannot be turned into quantum proofs (rewinding is usually not possible quantumly). A dream ...
I need to implement a quantum comparator that, given a quantum register $a$ and a real number $b$ known at generation time (i.e. when the quantum circuit is generated), set a qubit $r$ to the boolean ...