Share Your Experience: Take the 2024 Developer Survey

# 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.

215 questions
Filter by
Sorted by
Tagged with
60 views

### Better constant for linear depth incrementers

Currently working on some quantum arithmetic and was wondering if we have a better constant factor for a linear depth incrementer. As an example (and the best I could currently find), Craig Gidney ...
• 53
44 views

### Calculating number of CNOT gates in Pauli evolution gate

How to calculate the number of CNOT gates for a Pauli exponentiation for given time? I am performing Trotterization which involves performing Pauli evolution ...
• 391
27 views

### BQSkit Selecting Starting Circuit Structure

Background On the BQSKit repository, there is a nice example of using the qfactor algorithm to instantiate a 3-qubit Toffoli circuit. For this to work, however, it is first necessary to specify an ...
• 197
110 views

### $U_1\oplus U_2$ decomposable into $I\oplus U$ and 1-qubit gates?

TL;DR Let $U_1, U_2, U$ be arbitrary 1-qubit quantum gates. Can 2-qubit gates of the form $U_1\oplus U_2$ always be decomposed into a combination of controlled gates ($I\oplus U$) and single qubit ...
• 269
1 vote
68 views

### How many gates are necessary to implement an arbitrary n-qubit permutation unitary?

How many gates are necessary to implement an arbitrary n-qubit permutation unitary, using only 1- and 2-qubit gates? An n-qubit permutation unitary is a $2^n$ x $2^n$ unitary matrix where each entry ...
• 181
85 views

### How to retrieve a phase gate from a circuit made out of $CX$ and $T$

The extract below comes from this paper. It is an example that shows a basic phase polynomial, related to the $CCZ$ gate. It can also be written with $CX$ and $T$ gates. I can't find the connection ...
• 1,958
1 vote
88 views

### Is it possible to decompose a controlled gate with control qubit in the $|+\rangle$ state?

$\newcommand{\ket}[1]{\vert#1\rangle}\newcommand{\bra}[1]{\langle#1\vert}$ Given a quantum circuit with 2 qubits that executes a controlled gate $CU$ where the control qubit is in the $\ket{+}$ state, ...
• 269
52 views

1 vote
78 views

• 159
276 views

### How to construct solution based on the Schrödinger equation and split it into gates?

To the best of my knowledge, the gate notation forms the quantum programming. For instance, I use qiskit, pennylane, etc. products to see how the algorithms do their job. At the same time the "...
57 views

### How to implement the cross term (multi-qubit) in the square of the finite difference operator?

I am trying to simulate the Hamiltonian evolution of the 1+1D $\lambda\phi^4$ scalar field theory by digitising it and encoding on a quantum computer. The process of digitising is taken from this ...
• 57
1 vote
67 views

### Non-local $CNOT$ By means of Ising gates

Consider the circuit below. This is almost the same as the standard protocol to perform a non-local $CNOT_{0,3}$. The only difference is that I decomposed the upper local $CNOT_{0,1}$ into one Ising ...
• 1,958
74 views

### Transforming an unkown phase into unkown bit values on bell states

Consider the state $|\Psi^\pm\rangle = \frac{1}{\sqrt{2}}(|01\rangle \pm |10\rangle)$. The $|\Psi^\pm\rangle$ state is a bell state up to an unkown phase. I am looking for a sequence of single-qubit ...
• 1,958
177 views

### What is the minimum number of non-Clifford gates does it take to prepare a superposition over all "two-hot" basis vectors?

The generalized W state: $$W_n=\frac{1}{\sqrt{n}}(|100\cdots 0\rangle + |010\cdots 0\rangle + \ldots + |00\cdots 01\rangle)$$ is often thought of as the uniform superposition over all "one-hot&...
• 12.6k
1 vote
855 views

### 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 ...
• 113
269 views

### Shortest depth on Clifford+T to decompose a Toffoli

I am looking for a reference providing a circuit that has the smallest possible depth, without ancilla, once the Toffoli has been decomposed on Clifford+T gateset, where Clifford is generate by cNOT, ...
• 1,596
149 views

### Implementing controlled rotation for FRQI by using controlled Ry and NOT Gate

I was reading about Flexible Representation of Quantum Images (FRQI) encoding in Qiskit textbook. It says that, given $$\{\theta_0, \theta_1, ..., \theta_{4^{n}-1}\} \quad (\theta_i \in [0,\pi/2])$$ ...
1 vote
808 views

### qiskit : can you get circuit from unitary matrix?

In qiskit you can get a unitary matrix from a circuit (circuit to unitary matrix example). Is the opposite direction possible? Can you input a unitary matrix and have qiskit come up with a circuit? If ...
• 2,207
367 views

### What's the most efficient decomposition in terms of T-count of the 4-qubit Toffoli with 1 ancilla?

When decomposing the 4-qubit Toffoli in the Clifford+T universal gate set with 1 ancilla qubit, what is the most efficient implementation one can get in terms of T-count? I can only find papers that ...
• 93