# Questions tagged [circuit-construction]

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

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• 559
1 vote
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### An equivalent classical circuit for Hadamard gate

In principle, we can simulate any Quantum circuit via a classical circuit. However, this simulation could be inefficient. (Church-Turing thesis) Together, Hadamard and Toffolli are universal gate sets ...
• 763
1 vote
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### Highly-efficient $n(n+1)$?

Appendix G of this paper provides a highly-efficient way of squaring integer numbers. (LMK if anything more advanced is already available.) I'm wondering if this approach can be easily modified to ...
• 1,991
1 vote
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### A maximally distant unitary from a parameterized circuit

I have a parameterized circuit that includes a certain number of rotation gates, each parameterized by an angle. By sampling over these angles, I can obtain various unitaries. What are the unitaries ...
• 141
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### Showing the Toffoli gate can be constructed from one-qubit gates using computer matrix multiplication

I need help coming up with the code that I can use in a computer algebra system like Sage, Python, or Mathematica that can evaluate the circuit. I am not a programmer and used ChatGPT to try to help ...
• 351
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### How can I find out how compatible a quantum circuit is to a backend without executing the circuit

Say I have multiple backends, I need a score to determine how well a backend is suitable for that particular circuit, I have it's noise model too, I tried transpiling the circuit and calculating noise ...
1 vote
55 views

### Quantum circuit of stateful oracle

Suppose I have operator $U_f$ that maps state $|x\rangle|y\rangle|0\rangle$ to another state $|x\rangle|y\rangle|f(x, y)\rangle$. The function $f$ has its internal state, that changes on each ...
1 vote
73 views

### How cat state is constructed?

Context: On Wikipedia, a cat state (2-component) is defined as $$|\text{cat}_+\rangle = C_+(|\alpha\rangle + |-\alpha\rangle)$$ $$|\text{cat}_-\rangle = C_-(|\alpha\rangle - |-\alpha\rangle),$$ ...
• 14.7k
952 views

### Does the Quantum Fourier Transform require universality?

Background: In most setups of fault-tolerant quantum computation, universality is achieved using Clifford gates such as $(S, H, \text{CNOT})$ and the $T$-gate. The Eastin-Knill theorem can be ...
273 views

### How to simulate low-rank hamiltonian?

I want to implement a unitary $U\,,$ $$U=\text{exp}(-it|u\rangle\langle u|)\,,$$ where $|u\rangle$ is a known state. Are there any methods to do this efficiently?
• 115
1 vote
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• 239
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### Is it possible to modify the QFT circuit to use only 1-qubit gates?

[Measured Quantum Fourier Transform] I've recently learned the Quantum Fourier Transform, and was shown its circuit. The circuit I've seen is composed of Hadamard gates and controlled Rotation gates. ...
• 239
106 views

### How does one create a long range CNOT gate on a square grid of qubits using constant depth circuits?

In this talk, the speaker shows a bunch of data qubits on the top and ancilla qubits at the bottom that need to be linked by CNOT gates. The grid here is $n\times n$. The procedure is to swap the ...
• 3,117
1 vote
37 views

### What is the explicit action of the following circuit?

Would somebody please be able to explain the action of this circuit to me? (Taken from Arthur Pesah's blog post "Computing with Quantum Codes using Transversal Gates") I understand overall ...
• 641
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### Implementing cphase gate on IonQ through Amazon Braket

I am implementing a VQE algorithm where I need controlled phase gate as part of ansatz circuit. I am using Amazon Braket service. Ionq processor however does not support c-phase gate or phase gate. ...
• 35
1 vote
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### How to make sense of Pauli observables in the gate cutting code here?

I am following the tutorial mentioned in the circuit-knitting-toolbox. This tutorial explains how you can replace non-local gates with local operations in the superoperator representations and ...
1 vote
61 views

I want to decompose a two-qubit unitary gate $U$, $$U = e^{-i \cdot \frac{t}{2} \cdot Z_1 \cdot Z_2}\,,$$ where $t$ is an angle. I already know the right decomposition but Qiskit gives me an ...
44 views

### Does delaying measurements change the complexity of the circuit?

It's often said that for any quantum circuit with intermediate measurements, there exists an equivalent circuit where all measurements are at the end of the circuit. Is anything ever argued about the ...
• 61
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### How to find a quantum circuit to generate a target state?

I am starting in Quantum Computing, but I am pretty lost, sorry... let's say I need to design a quantum circuit to generate some given quantum states in Dirac's notation, as in the following example, ...
• 123
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### Use of $X$ gates in creating probability distribution in a quantum circuit

I have been trying to understand the Grover-Rudolph scheme for loading a probability distribution into a quantum circuit. This article gives a demonstration of this scheme by creating a probability ...
• 31
163 views

### How to implement the modular exponentiation implementation in Shor's algorithm?

I am trying to implement Shor's algorithm using modular exponentiation as described in this paper: https://arxiv.org/abs/quant-ph/0205095 The issue is found when trying to implement CMULT($a^{-1}$)mod(...
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• 451
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### Qiskit reverse_bits is not equivalent to swapping qubits

For three qubits, I thought swapping the first and third qubit is equivalent to vertically flipping the circuit. However, performing one and then the other in Qiskit returns two different operators, ...
187 views

### Adding a phase to a circuit using standard gates

How do I add an arbitrary overall phase to the circuit using standard gates? Yes, I know that the overall phase it irrelevant, yet this is only true until you control the circuit on extra qubits. Yes, ...
• 1,991
Is it possible to decompose an $n$-controlled Toffoli into $O(n)$ CNOTs without extra working qubits? If so, is such an decomposition currently available in Qiskit or any other (preferably Python and ...