Backgrounds

1. IonQ Hardware (via IonQ Cloud)

Available Targets

  • Simulator (ionq.simulator)

    • GPU-accelerated, up to 29 qubits.
    • Uses the same gate set as IonQ hardware → suitable for pre-validation of encoding circuits.

  • IonQ Aria (ionq.qpu.aria-1, aria-2)

    • 25-qubit trapped-ion system.
    • Debiasing enabled by default to reduce systematic errors.
    • Provides commercial-grade performance metrics.

  • IonQ Forte (ionq.qpu.forte)

    • 32-qubit system (currently in private preview).
    • Designed for higher algorithmic qubit (#AQ) performance.

Performance Characteristics (IonQ Aria benchmark)

  • Coherence: T₁ = 10–100 s, T₂ ≈ 1 s
  • Gate times: 1Q ≈ 135 µs, 2Q ≈ 600 µs
  • Fidelity:
    • 1Q gates ≈ 99.95%
    • 2Q gates ≈ 99.6%
    • SPAM (state prep & measurement) ≈ 99.61%

Practical Implications for Encoding Optimization

  • Fully connected qubits: any pair can be entangled → eliminates SWAP overhead.
  • Workflow: design and tune circuits on ionq.simulator → deploy on Aria/Forte hardware.
  • Noise considerations:
    • Coherence and gate times impose circuit depth constraints.
    • Debiasing must be accounted for when analyzing output distributions.

Ion-Q-Thruster Project (Qiskit-based optimizer)

  • Custom transpiler tailored to IonQ’s native gate set (MS, GPi, GPi2).
  • Reduces gate count and depth compared to Qiskit defaults.
  • Research relevance: encoding circuits should integrate IonQ-native optimization passes for efficiency and noise robustness.

2. Noise-Aware & Robust Circuit Design

QuantumNAT (DAC 2022)

  • Models noise as scale + shift transformation on measurement results.
  • Combines Normalization, Noise Injection Training, and Post-measurement Quantization.
  • For IonQ:
    • Inject real hardware error rates into training.
    • Normalize measurement outputs to counteract bias.
    • Quantize readout to increase robustness.

QuantumNAS (HPCA 2022)

  • Defines a SuperCircuit and selects SubCircuits under hardware noise models.
  • Uses evolutionary search + pruning to find robust circuits.
  • For IonQ:
    • Full connectivity simplifies search space (no SWAP constraints).
    • Circuit depth and entanglement levels must be tuned against T₂ limitations.

Noise-Resilience in VQAs (2021)

  • Shows trade-off between expressivity and noise robustness.
  • For IonQ:
    • Despite high fidelities, slower gates mean fewer shots available.
    • Shallow, noise-resilient encodings outperform deeper expressive ones in practice.

3. Embedding Methods & Search

Quantum Embedding Search (2021)

  • Represents encoding circuits as graph/genotype structures.
  • Uses SMBO-TPE for efficient automated search.
  • Restricts entanglement to avoid excessive noise.
  • For IonQ:
    • Replace CNOT edges with MS gates.
    • Impose entanglement-level constraints to avoid error accumulation.
    • Integrate IonQ simulator in the search loop.

EnQode

  • Proposes fast amplitude embedding via approximation.
  • Preserves accuracy while reducing circuit depth.
  • For IonQ:
    • Mitigates long gate execution times.
    • Suitable for large datasets requiring repeated embedding.

Multiple Embeddings

  • Combines different encodings (Angle + Amplitude, etc.) to overcome single-encoding limitations.
  • For IonQ:
    • Full connectivity enables multi-layer embeddings without SWAP overhead.
    • Allows higher expressivity with manageable circuit depth.

Benchmarking Data Encoding Methods (2022)

  • Angle encoding: shallow, low expressivity.
  • Amplitude encoding: high expressivity, deep circuits.
  • Basis encoding: impractical for limited qubit counts.
  • For IonQ:
    • Basis encoding infeasible due to qubit count limits.
    • Amplitude encoding limited by execution time → requires EnQode or hybrid approaches.
    • Angle encoding lightweight but should be combined with others (e.g., Multiple Embeddings).