What Is the Quantum Circuit Depth & Fidelity Estimator?
Quantum circuit depth and fidelity quantify the complexity and survivability of a quantum program against physical errors.
How Does the Quantum Circuit Depth & Fidelity Estimator Work?
Multiplies individual gate success probabilities assuming uncorrelated stochastic Pauli errors.
Quantum Circuit Depth & Fidelity Estimator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
F_{ ext{total}} = (1 - epsilon_1)^{N_1} cdot (1 - epsilon_2)^{N_2}, quad t_{ ext{run}} = ext{Depth} imes t_{ ext{cycle}}
Multiplicative independent gate fidelity and total parallel execution latency.
How to Use the Quantum Circuit Depth & Fidelity Estimator
- Enter 1-qubit and 2-qubit gate counts, hardware error rates per gate, circuit depth, and hardware gate cycle time.
Step-by-Step Example Calculation
NISQ Algorithm Execution
Input Values:
singleQubitGates:150
twoQubitGates:40
singleGateErrorRate:0.0005
twoGateErrorRate:0.005
circuitDepth:50
cycleTimeNs:25
Worked Steps: Yields estimated circuit fidelity of 75.8% with execution runtime of 1.25 µs.
Understanding Your Result
Indicates whether the circuit is likely to yield valid measurement signals or devolve into uniform noise.
Factors That Affect the Result
- Two-qubit gates are typically an order of magnitude more error-prone than single-qubit gates.
When Should You Use This Calculator?
- VQE and QAOA algorithm compilation, circuit transpilation optimization, and quantum benchmarking.
Assumptions & Limitations
- Assumes uncorrelated errors; ignores cross-talk, leakage, and idle qubit dephasing during execution.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Stochastic Pauli error model baseline.