# Questions tagged [circuit-construction]

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

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### Simulating Clifford + few-T circuits

I want to simulate large stabilizer circuits (H/S/CNOT/MEASURE/feedforward) with a small number of T gates mixed in. How can I do this in a way that scales exponentially only in the number of T gates? ...
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### Quantum Fourier Transform without SWAPs

The Quantum Fourier Transform from Nielsen and Chuang chapter 5 is pictured here: In the textbook the author refers to "swap gates at the end of the circuit which reverse the order of the qubits". ...
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### Quantum operation in blocks

I have $n$ states in superposition $|A\rangle=\dfrac{1}{2^{l/2}}\sum_{i=0}^{2^l-1}\sum_{j=0}^{2^l-1}|0\rangle^{\otimes q}|i\rangle^{\otimes l}|j\rangle^{\otimes l}$. Now I have to apply the transform ...
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### Ansatz Techniques to Multi-Body Physics Problems

I have been reading this paper: https://arxiv.org/abs/1906.01563v1. I am wondering: is it possible to use the idea behind quantum circuits to build classical Hamiltonians represented in the same way?...
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### How do I get out 2 measurements from the same execution on Qiskit?

Here's my circuit, trying to checkout the effect of measurement on the IBM Q circuit. Here you can see I do 2 different measurement at different time, and I hope to be able to see both results. ...
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### How many two-qubit gates required for general N-qubit unitary?

Is there a known formula or a scaling behaviour for how many two-qubit gates are required to construct a general N-qubit unitary? I suppose there are several cases to consider: Exact representation ...
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### What implementation changes should be done in maxcut code using VQE?

In the paper, "Quantum algorithm implementations for beginners" in the section XVII. QUANTUM SIMULATION OF THE TRANSVERSE ISING MODEL (page 54-58), the authors have plotted energy $E$ vs magnetic ...
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### Using Quantum Fourier Transform in adding two 2-bit numbers

I am trying to use Qiskit to write a code that uses QFT to add 2 numbers. I am referring to this paper: https://iopscience.iop.org/article/10.1088/1742-6596/735/1/012083 I have a few questions: 1) Is ...
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### Quantum Optimization via Quantum Label Classification in Quantum Circuits

I have been reading Farhi and Neven's paper on quantum neural networks on quantum circuits. I also found an example - albeit not ideal as pointed out by a couple of users - thank you - in here. ...
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### Coding an oracle for Simon's algorithm

I am trying to implement Simon's algorithm which calls for a 2-to-1 mapping function that satisfies $f(x) = f(x⊕s)$. I am looking for a simple way to code the oracle (using $H$, $Cx$, and $R$ gates), ...
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### How to derive a circuit from given equations?

I was reading a paper on Quantum Neural Networks where the authors discussed a new back propagation algorithm. They shared a schematic of the circuit. However, I am unable to understand how the ...
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### There seems to be a problem with the implementation of identity gates on Qiskit as compared to the circuit composer

I have been experimenting with slowing down the decay of qubits, and as a control, I implemented a circuit with just identity gates for comparison. However, when I implement such circuits in Qiskit, ...
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### N-Toffoli on Cirq

I am looking for guidance in more generally how to developed n-bit gates in Cirq. I am working on a QNN paper and I need to develop a n-controlled gate to be able to measure the cost function of the ...
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### Measuring the expected energy of a quantum circuit

I implemented the following circuit: I am interested in measuring the expected energy of the circuit. I am using Cirq. I am wondering what are the next steps. Sorry if the question seems very basic, ...
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### Understanding CNOT gate for indirect measurement

I am trying to write a simple circuit to understand the process of finding the set of parameters such that the cost function of that circuit in question is minimized. For that I understand one has to ...
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### Implementing a complex circuit for a Szegedy quantum walk in qiskit

Problem definition I'm implementing a quantum circuit in qiskit for a Szegedy quantum walk, (reference, Fig 21.). It uses two registers of dimension $N$ ($N=3$) each one. The challenges I'm facing ...
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I'm trying to program a controlled gate as the figure below in Qiskit. Should it be sufficient to separate and control individually the Hadamard gates?
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### Simulating a 3-local Hamiltonian Term

This may be a fairly basic question, but in Nielsen & Chuang, the following circuit is given for simulating $\exp\left(-i\Delta t Z_1 \otimes Z_2 \otimes Z_3\right)$: which uses an ancilla qubit ...
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### Can anybody explain or suggest a good reference on how to make a modular exponentiation circuit for N=15 with any coprime base?

I have read many papers related to it but in every paper, they just show the circuit of order finding algorithm for N=15, but did not explain what is the procedure to make it. It will be great if ...
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### Sequential circuit using quantum gates

Without feedback/loop how can we build a sequential circuit? The basic feature of sequential circuit is that is depends not only on the current inputs but also on the previous inputs/outputs. I've ...
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### Primer for learning about quantum circuits simulating systems

I am interested in a couple of books or arXiv links to learn how to develop quantum circuits for the purpose of simulating quantum multi-body systems. Moreover, I am interested in learning how to ...
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### Quantum gate teleportation T gate

I am faced with the problem of teleporting certain gates using modified Bell states. For example, I have solved the problem with the $S$ gate, which is defined as following: Alice and Bob share a ...
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### Most efficient way for general state generation

Assume we are given an $n$-qubit system and complex numbers $a_0, \ldots, a_{m-1}$ with $m = 2^n$. Assume further we start with the initial state $|0 \ldots 0\rangle$ and want to make the ...