Quantum Computing Qubit Stability Calculator

Estimate qubit coherence time (T2) based on temperature, magnetic field noise, and qubit type.

Cryogenic temperature in millikelvin
Environmental magnetic field fluctuations
Type of qubit with baseline coherence time

Formulas Used

The coherence time (T2) is estimated by adjusting the baseline coherence time of the qubit type based on environmental factors (temperature and magnetic noise).

  1. Temperature Factor:

    \[ F_T = \frac{T_{\text{ref}}}{T} \]

    Where:

    • \( F_T \): Temperature factor
    • \( T \): Temperature (mK)
    • \( T_{\text{ref}} \): Reference temperature (50 mK)

  2. Magnetic Noise Factor:

    \[ F_M = \frac{M_{\text{ref}}}{M} \]

    Where:

    • \( F_M \): Magnetic noise factor
    • \( M \): Magnetic field noise (nT)
    • \( M_{\text{ref}} \): Reference magnetic noise (10 nT)

  3. Coherence Time:

    \[ T_2 = T_{2,\text{base}} \cdot \min\left(1, F_T \cdot F_M\right) \]

    Where:

    • \( T_2 \): Coherence time (µs)
    • \( T_{2,\text{base}} \): Baseline coherence time (µs, based on qubit type)
    • \( \min(1, F_T \cdot F_M) \): Caps environmental impact at 1 to avoid amplification

  4. Stability Level:

    Based on \( T_2 \):

    • Low: \( T_2 \leq 10 \, \mu\text{s} \)
    • Moderate: \( 10 < T_2 \leq 50 \, \mu\text{s} \)
    • High: \( 50 < T_2 \leq 100 \, \mu\text{s} \)
    • Very High: \( T_2 > 100 \, \mu\text{s} \)

Example Calculations

Example 1: Superconducting Qubit in Ideal Conditions

Inputs: Temperature = 20 mK, Magnetic Noise = 5 nT, Qubit Type = Superconducting (100 µs)

Calculations:

  • Temperature Factor: \[ \frac{50}{20} = 2.5 \]
  • Magnetic Noise Factor: \[ \frac{10}{5} = 2 \]
  • Coherence Time: \[ 100 \cdot \min(1, 2.5 \cdot 2) = 100 \cdot 1 = 100 \, \mu\text{s} \]
  • Stability Level: High (50–100 µs)

Result: Coherence Time: 100.0 µs (High)

Example 2: Trapped Ion Qubit in Moderate Conditions

Inputs: Temperature = 100 mK, Magnetic Noise = 20 nT, Qubit Type = Trapped Ion (50 µs)

Calculations:

  • Temperature Factor: \[ \frac{50}{100} = 0.5 \]
  • Magnetic Noise Factor: \[ \frac{10}{20} = 0.5 \]
  • Coherence Time: \[ 50 \cdot \min(1, 0.5 \cdot 0.5) = 50 \cdot 0.25 = 12.5 \, \mu\text{s} \]
  • Stability Level: Moderate (10–50 µs)

Result: Coherence Time: 12.5 µs (Moderate)

Example 3: Neutral Atom Qubit in Harsh Conditions

Inputs: Temperature = 500 mK, Magnetic Noise = 50 nT, Qubit Type = Neutral Atom (10 µs)

Calculations:

  • Temperature Factor: \[ \frac{50}{500} = 0.1 \]
  • Magnetic Noise Factor: \[ \frac{10}{50} = 0.2 \]
  • Coherence Time: \[ 10 \cdot \min(1, 0.1 \cdot 0.2) = 10 \cdot 0.02 = 0.2 \, \mu\text{s} \]
  • Stability Level: Low (≤10 µs)

Result: Coherence Time: 0.2 µs (Low)

How to Use the Calculator

Follow these steps to estimate qubit coherence time:

  1. Enter Temperature: Input the cryogenic temperature in mK (10–1000, e.g., 50). Use the decimal button (.) for precision.
  2. Enter Magnetic Field Noise: Input the magnetic noise in nT (0.1–100, e.g., 10). Use the decimal button for precision.
  3. Select Qubit Type: Choose superconducting (100 µs), trapped ion (50 µs), neutral atom (10 µs), or topological (200 µs) from the dropdown.
  4. Calculate: Click “Calculate Coherence Time” to see the result.
  5. Interpret Result: The result shows the coherence time in µs with a stability level (Low: ≤10, Moderate: 10–50, High: 50–100, Very High: >100). If you see “Please fill in all fields,” ensure all inputs are valid.
  6. Share or Embed: Use the share buttons to post results on social media, copy the result, or get an embed code.

Note: This is a simplified model. Actual coherence time may depend on additional factors like gate operations, material defects, and error correction.