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).

Research Plan

1. Background on Encoding Methods

Angle Encoding (AE)

  • Concept: Encodes each feature of the classical data into the rotation angle of a single-qubit gate (e.g., RY, RZ).
  • Pros: Shallow circuits, low gate count, hardware-efficient.
  • Cons: Limited expressive power, often requires entangling layers or repetition.
  • Use Case: Lightweight baseline for low-dimensional (PCA-16/32) tasks.

Data Re-Uploading (DRU)

  • Concept: Re-injects classical data multiple times across different layers of parameterized quantum circuits.
  • Pros: Significantly boosts expressive capacity; proven universal with enough repetitions.
  • Cons: Parameter-heavy, more sensitive to noise as depth grows.
  • Use Case: Mid-scale datasets (PCA-32/64), where richer decision boundaries are needed.

Amplitude Encoding (AMP)

  • Concept: Maps a normalized vector directly to the amplitude of a quantum state.
  • Pros: Compresses high-dimensional data efficiently, expressive.
  • Cons: Exact preparation is circuit-depth heavy; approximate methods (e.g., EnQode) reduce overhead but introduce approximation error.
  • Use Case: PCA-32 (exact encoding), PCA-64 (approximate EnQode-style).

Hybrid / Multiple Embeddings

  • Concept: Combines multiple encoding schemes, e.g., Angle + Amplitude.
  • Pros: Balances resource efficiency and expressivity.
  • Cons: More complex circuit design, risk of increasing depth.
  • Use Case: Multi-class classification (4-class, 10-class) with balanced requirements.

Kernel Feature Maps (ZZFeatureMap / IQP)

  • Concept: Uses fixed quantum feature maps to transform classical inputs, followed by classical kernel methods like SVM.
  • Pros: No trainable quantum parameters, robust to barren plateaus.
  • Cons: Requires computation of kernel matrices; shot-intensive.
  • Use Case: Baseline comparison, binary or 4-class tasks.

Quantum Kitchen Sinks (QKS)

  • Concept: Random quantum circuits generate nonlinear embeddings, which are then classified classically.
  • Pros: Simple, hardware-friendly, requires no optimization.
  • Cons: Needs many random circuits to be effective.
  • Use Case: Binary classification as a quick baseline.

## 2. Training Environment Setup
  • Dataset: Fashion-MNIST (10 classes).
  • Preprocessing:
    • Downsampled 8×8 (64D).
    • PCA-32 and PCA-64 variants.
  • Tasks:
    • T2: Binary classification (e.g., T-shirt vs Pullover).
    • T4: 4-class classification (T-shirt, Pullover, Coat, Shirt).
    • T10: Reduced 10-class task (balanced subset).
  • Splits: Train 80%, Validation 10%, Test 10%.
  • Frameworks: PennyLane (preferred), Qiskit/Cirq for IonQ submission.
  • Optimization:
    • Loss: Cross-Entropy.
    • Simulations: Adam optimizer, learning rate 5e-3 with decay.
    • Hardware runs: SPSA or finite-difference for noise-friendly updates.
  • Training Schedule:
    • Simulation: 20–40 epochs, batch size 32.
    • Hardware: 3–8 epochs, batch size 32.
  • Evaluation Metrics: Accuracy, F1, gate count, circuit depth, shots, runtime, hardware queue/wait logs.
  • Error Mitigation: Measurement calibration, Zero-Noise Extrapolation (ZNE), readout error mitigation where possible.

3. Step-by-Step Experimental Plan

Week 3 — Baseline Encoding Verification

  • Implement AE, DRU, AMP (exact/approximate), Hybrid, and Kernel circuits.
  • Train on noiseless simulators with PCA-16/32/64 datasets.
  • Record baseline performance and resource consumption (accuracy, depth, gates).

Week 4 — Noise Modeling and Structure Search

  • Incorporate realistic noise models (IonQ gate fidelities, depolarizing/readout error).
  • Run noisy simulations with shots sweep (256, 512, 1000).
  • Evaluate robustness of AE, DRU, AMP, Hybrid under noise.
  • Conduct circuit structure search using Evolutionary algorithms (Robust Ansatz) and ML-based methods (NACL).

Week 5 — IonQ Hardware First Run

  • Select representative circuits (AE, DRU, AMP-Approx, Hybrid, Kernel).
  • Submit binary classification (T2, PCA-16D) jobs with shots = 500, 1000.
  • Apply error mitigation strategies (ZNE, calibration).
  • Compare results with simulator outputs.

Week 6 — Hardware-Guided Optimization

  • Analyze first-run results, select top 2–3 encodings based on accuracy vs. resource efficiency.
  • Re-run on IonQ with shots = 2000.
  • Expand to 4-class classification (T4, PCA-32).
  • Generate plots of accuracy vs. depth/gates and noise sensitivity.
  • Perform comprehensive comparison across AE, DRU, AMP, Hybrid, Kernel.
  • Run final experiments with shots 2000–4000 on selected encodings.
  • Produce final figures:
    • Accuracy vs. shots.
    • Gate count vs. accuracy Pareto fronts.
    • Simulator vs. hardware scatter plots.
  • Write final survey: encoding definitions, experimental setup, results, IonQ-specific guidelines (optimal encoding per dataset size, recommended depth/shots).

4. Expected Deliverables

  1. Survey Paper: Detailed methodology, results, trade-offs, and IonQ-specific encoding recommendations.
  2. Figures & Tables: Performance vs. resource trade-off, noise robustness comparison, error mitigation impact.
  3. Supplementary: Code repository with all encodings, IonQ submission logs, preprocessing scripts.