Fidelity in quantum computing refers to how accurately a quantum operation (or quantum process) matches its intended behavior. Since quantum systems are inherently prone to noise, fidelity is a key metric used to evaluate the reliability and correctness of quantum gates, measurements, and full circuits.
Understanding fidelity helps researchers, engineers, and quantum developers gauge how close real-world quantum computations are to their theoretical or ideal versions.
1. What is Fidelity in Quantum Computing?
Fidelity, in general terms, is a measure of similarity between two quantum states or operations. In practice, it is used to compare:
- The expected ideal outcome of a quantum operation.
- The actual outcome achieved on a real quantum system.
A fidelity of 1 (or 100%) means perfect operation with no deviation from the ideal. A lower fidelity indicates errors or noise have altered the outcome.
2. Types of Fidelity
a. State Fidelity
Compares two quantum states:
- Used after executing a quantum circuit to check how close the final state is to what was expected.
b. Gate Fidelity
Measures how accurately a quantum gate (like X, H, CNOT) performs compared to the theoretical gate.
- Useful in hardware benchmarking and gate calibration.
c. Process Fidelity
Evaluates an entire process or sequence of gates — broader than just one gate.
- Relevant when testing quantum circuits or algorithm subroutines.
3. Why Fidelity Matters
Quantum operations must be precise, as even small errors can cascade through a quantum algorithm, especially in large circuits. Fidelity is critical for:
- Quantum algorithm success: Low fidelity operations can yield completely wrong results.
- Error correction: Understanding fidelity helps in developing and tuning quantum error correction techniques.
- Hardware benchmarking: Used to measure and compare the performance of different quantum processors or devices.
- Quantum volume: Fidelity contributes directly to the maximum circuit size and complexity a system can handle.
4. Causes of Low Fidelity
- Decoherence: Qubits lose quantum information due to environmental interactions.
- Gate errors: Imperfect calibration or timing errors when applying gates.
- Cross-talk: Operations on one qubit inadvertently affect neighboring qubits.
- Readout errors: Errors during the measurement of qubit states.
- Thermal noise and stray electromagnetic fields: Interfere with quantum operations.
5. Measuring Fidelity in Practice
a. Randomized Benchmarking
- Applies random sequences of quantum gates to qubits, then measures how close the final state is to the expected result.
- Gives average gate fidelity over many runs.
- Effective for large-scale gate testing.
b. Quantum Process Tomography
- A detailed method to reconstruct the process matrix of a quantum operation.
- More comprehensive but slower and computationally heavy.
c. Cross-Entropy Benchmarking
- Compares probability distributions from an ideal and real quantum system.
- Often used in Google’s quantum supremacy experiments.
6. Fidelity Thresholds
In practical systems:
- Gate fidelity > 99.9% is desirable for fault-tolerant quantum computing.
- State fidelity above 90–95% is considered usable in Noisy Intermediate-Scale Quantum (NISQ) devices.
- Quantum Error Correction typically requires gate fidelity above a fault-tolerant threshold, which depends on the specific error correction code used (often around 99.9%).
7. Fidelity in Real Quantum Hardware
IBM Q
- Reports individual qubit and gate fidelities in their device calibrations.
- Uses randomized benchmarking for CNOT and single-qubit gate errors.
Google Sycamore
- Used cross-entropy benchmarking to show fidelity during quantum supremacy demonstrations.
IonQ, Rigetti, Honeywell
- Also publish fidelity figures, often showing higher fidelity for trapped ion systems (IonQ) due to longer coherence times.
8. Improving Fidelity
Hardware-Level Improvements
- Better qubit isolation and cooling
- Higher quality materials
- Improved manufacturing of superconducting or ion trap qubits
Software-Level Techniques
- Gate synthesis and optimization: Reduce unnecessary operations.
- Error mitigation: Use classical post-processing to reduce error effects.
- Compiler optimization: Rearranges operations to minimize noise impact.
9. Fidelity in the Context of Quantum Volume
Quantum Volume (QV) is influenced by fidelity. A system with:
- High fidelity can run deeper and more complex circuits.
- Low fidelity will struggle to complete circuits correctly, lowering its QV score.
That’s why improving gate and state fidelity is essential for increasing QV and achieving meaningful quantum computations.