Semiconductor Quantum Dot Qubit Exchange Interaction Calculator
Named weak-tunneling two-site Hubbard exchange J≈4t²/U at zero detuning; not general biased-dot exchange Hamiltonian or spin gate timing.
Description
Weak-tunneling two-site Hubbard exchange has an approximate zero-detuning energy of four times tunnel energy squared divided by on-site energy.
Weak-tunneling two-site Hubbard exchange has an approximate zero-detuning energy of four times tunnel energy squared divided by on-site energy.1
Its limited branch should be read with the supplied energy conventions.
When to use Semiconductor Quantum Dot Qubit Exchange Interaction Calculator
Use this tool when you need to reproduce the stated calculation from measured records or independently selected model inputs. Prepare measured device or specimen records under independently matched branch, temperature, frame, and unit conventions.
How to use Semiconductor Quantum Dot Qubit Exchange Interaction Calculator and understand its results
- Prepare measured device or specimen records under independently matched branch, temperature, frame, and unit conventions.
- Enter callerHubbardTunnelEnergy, callerHubbardOnsiteEnergy, following the field table and rules below, then run the tool.
- Read approximateAntiferromagneticExchangeEnergy. Use the output meanings below to interpret units, signs, flags, and any nested result fields.
- Correct reported input issues and run again. For a successful result, check the stated evidence coverage and assumptions before using it in your review.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| callerHubbardTunnelEnergy | Caller hubbard tunnel energy | list of number | Required |
| callerHubbardOnsiteEnergy | Caller hubbard onsite energy | list of number | Required |
Use aligned nonempty positive tunnel and on-site energies in the same unit. Require tunnel/on-site ≤ 0.1 for every pair. Return one positive approximate exchange energy per pair; detuning and general spin dynamics are not modeled.
J_i≈4t_i²/U_i Symbols follow the input and output meanings and the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| approximateAntiferromagneticExchangeEnergy | Approximate antiferromagnetic exchange energy | list of number |
{
"input": {
"callerHubbardTunnelEnergy": [
1,
2
],
"callerHubbardOnsiteEnergy": [
10,
20
]
},
"output": {
"approximateAntiferromagneticExchangeEnergy": [
0.4,
0.8
]
}
}Limitations and assumptions
Matched measurement branch, material state, calibration, and conventions must be independently established. Results do not certify device performance or operating conditions.
Missing required fields, unknown fields, wrong types, and violated calculation rules are input issues. Numeric values must be finite; nonfinite results are rejected. Evidence arrays must be dense, with no missing cells. Numeric observation lists allow at most 10,000 entries, subject to any smaller bounds stated above.
Alternative or Complementary methods
For a related review, use Semiconductor Transmon Qubit Frequency Calculator: A transmon frequency approximation uses Josephson and charging energies in a regime where their ratio is large. The asymptotic expression estimates the 0-to-1 transition instead of diagonalizing the full Hamiltonian. For a complementary step, use Semiconductor Transmon Anharmonicity Calculator: Anharmonicity compares adjacent transition frequencies. Subtracting measured f01 from f12 retains the sign and expresses the mismatch relative to f01.
References
Similar or alternative tools
- Semiconductor Transmon Qubit Frequency Calculator
A transmon frequency approximation uses Josephson and charging energies in a regime where their ratio is large. The asymptotic expression estimates the 0-to-1 transition instead of diagonalizing the full Hamiltonian.
- Semiconductor Transmon Anharmonicity Calculator
Anharmonicity compares adjacent transition frequencies. Subtracting measured f01 from f12 retains the sign and expresses the mismatch relative to f01.