# 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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### Solving variables in symbolic unitary to get a desired real-valued unitary using qiskit or qympy, qiskit-symb/pytket

I am trying to decompose a 4x4 unitary into 2 qubit circuit using U3 and CNOT gates but the circuit implementation qiskit gives me is not optimized. So I started looking at qiskit-symb and qympy to ...
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### Is there a tool to decompose 4-Qubit unitaries (aka 16x16 matrices)?

I was wondering if there is a tool that can decompose such a matrix in gates on 4 qubits? I found one for 3-qubit gates (9x9 matrices) in Cirq but nothing for bigger matrices. (The matrix is not ...
1 vote
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### Constructing a controlled phase gate from given gates

As part of a project in a quantum computing course we were asked to classically simulate the quantum phase estimation algorithm, which has inverse QFT as one of its components. On the Wikipedia page ...
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1 vote
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### Global (Ising) Gates and ZX-calculus representation

I could find from this source -- but also from other works on ZX-calculus -- the following extract: This looks to me as a generalisation of a 2-qubit Ising gate to an $n$-qubit global Ising gate. ...
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### How to find the canonical form (i.e., phase-free representation) of a unitary matrix?

While reading Weiden and others' recent paper: Improving Quantum Circuit Synthesis with Machine Learning, I came across the notion of canonically representing a unitary matrix. More precisely, two ...
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### Exact synthesis of Toffoli gate from CNOT and rational single-qubit gates?

Is it possible to implement a Toffoli gate exactly using just CNOT gates and single qubit complex rational gates (i.e. with entries in $\mathbb{Q}(i)$), possibly with ancillas? I know this works with ...
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### Gate synthesis with parametrised precision

I am wondering whether Qiskit (or other quantum program language) can perform gate synthesis with parametrised precision. I tried with ...
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1 vote
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### How can I simulate the following 2×2 Hamiltonian $e^{i\begin{bmatrix} 8 & 6+i \\ 6-i & -1\end{bmatrix}}$?

How can I simulate the following 2×2 Hamiltonian $$e^{i\begin{bmatrix} 8 & 6+i \\ 6-i & -1\end{bmatrix}}|\Psi\rangle$$ ie. how to rewrite that matrix exponential in terms of other, well-used ...
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### Is there a matrix exponential $e^{iA}$ gate in IBM Quantum Experience?

Is there a gate that can perform the matrix exponential operation $$e^{iA}|\Psi\rangle$$ in IBM quantum experience API? What is the name and symbol for this type of gate (or some other gates that can ...
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### Computing the Bloch sphere representation of an arbitrary operator in $U(2)$

Computing the Matsumoto-Amano normal form of an operator in $U(2)$ involves finding the Bloch sphere representation of said operator, see Remarks on Matsumoto and Amano’s normal form for single-qubit ...
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### How many two-qubit controlled gates do you need to simulate any CU gates where U is a diagonal matrix?

Assuming we have n qubit, the first qubit is a control qubit, and the rest are the targets of $U$. If $U$ is a diagonal matrix, is there any theory to find the minimum number of two-qubit controlled ...
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### Brute force gate decomposition of (specific) 4 qubit unitary matrix

I have a specific 4-qubit 16x16 unitary matrix $U$ with $9$ parameters. My goal is to find a gate decomposition in terms of e.g. ...
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### How to construct common classical gates with CNOT circuit?

How can I construct AND, OR, NAND, NOR with CNOT gates. First off, this other question describes how to make them with matrices. Theoretically I can construct all those gates already. I know how to ...
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