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Quantum Fourier Transform (QFT) Hadamard & Controlled-Phase Gate Complexity Calculator

Easily calculate and compute quantum fourier transform (qft) hadamard & controlled-phase gate complexity calculator with accurate equations, live formulas, and expert guidance.

Number of qubits in Fourier register.

Drops controlled rotations with phase angle < 2π / 2^m. Enter 0 for full exact QFT.

Calculated Result
144 gates

Total QFT Gates

Total QFT Gates

144 gates

Total Quantum Gates

144

Controlled Phase Rotations

120

Hadamard Gate Count

16

Output Swap Gate Count

8

144 — gates

Calculation Breakdown

  1. Applied FormulaCalculates the gate synthesis counts (Hadamard, Controlled-R_k, and bit-reversal SWAP gates) for exact and approximate Quantum Fourier Transforms.N_{\text{exact}} = \frac{n(n+1)}{2} + \left\lfloor \frac{n}{2} \right\rfloor, \quad N_{\text{approx}} \sim \mathcal{O}(n \log n)

QFT Gate Complexity Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.03672108144Total QFT Gates

What Is the Quantum Fourier Transform (QFT) Hadamard & Controlled-Phase Gate Complexity Calculator?

This tool computes quantum fourier transform (qft) hadamard & controlled-phase gate complexity calculator with high precision arithmetic.

How Does the Quantum Fourier Transform (QFT) Hadamard & Controlled-Phase Gate Complexity Calculator Work?

Calculates the gate synthesis counts (Hadamard, Controlled-R_k, and bit-reversal SWAP gates) for exact and approximate Quantum Fourier Transforms.

Quantum Fourier Transform (QFT) Hadamard & Controlled-Phase Gate Complexity Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

Nexact=n(n+1)2+⌊n2⌋,Napprox∼O(nlog⁡n)N_{\text{exact}} = \frac{n(n+1)}{2} + \left\lfloor \frac{n}{2} \right\rfloor, \quad N_{\text{approx}} \sim \mathcal{O}(n \log n)

Calculates the gate synthesis counts (Hadamard, Controlled-R_k, and bit-reversal SWAP gates) for exact and approximate Quantum Fourier Transforms.

How to Use the Quantum Fourier Transform (QFT) Hadamard & Controlled-Phase Gate Complexity Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Quantum Fourier Transform (QFT) Hadamard & Controlled-Phase Gate Complexity Calculator Example

Input Values:

qubitCountN:16
approximateQftCutoffM:0
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required gates.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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