> ## Documentation Index > Fetch the complete documentation index at: https://docs.haiqu.ai/llms.txt > Use this file to discover all available pages before exploring further. # Benchmarks data sheet > Specifications and benchmarks of core functions ## Error suppression & mitigation stack ### Benchmark: 2D transverse-field Ising model We reproduce the experiment from [IBM's Nature publication](https://www.nature.com/articles/s41586-023-06096-3) using Haiqu's lightweight error mitigation techniques. Ising Model simulation, 127 qubits, IBM Kingston In [the paper](https://www.nature.com/articles/s41586-023-06096-3) (see Figure 3 a)), the authors used Sparse Pauli-Lindblad Noise Learning to perform zero-noise extrapolation (ZNE) with Probabilistic Error Amplification (PEA) which comes at significant overhead in terms of total number of shots (more than 100x) and number of extra circuits. Haiqu delivers similar error suppression using essentially the same quantum resources you'd use for the raw, uncorrected experiment. Check for more details in **`IsingModelSimulation.ipynb`** notebook. ### Benchmark: GHZ state preparation We prepare GHZ states on IBM Heron r2 processor by hardware-efficient circuits (found by breadth-first search (BFS) algorithm) with Haiqu's bitstring distribution error mitigation. Ghz State Benchmark Pn You can reproduce the results using the `GHZStatePreparation.ipynb` notebook. ### Mitigation Loading Specifications | | Observable-based mitigation | Bitstring distribution mitigation | | ------------------------------- | ------------------------------------------------------------------------------------------------------- | --------------------------------------------- | | Supported backends | IBM QPUs, AWS Braket (TBD) | IBM QPUs, AWS Braket (TBD) | | Max number of qubits | up to 156 qubits (largest QPU) | up to 156 qubits (largest QPU) | | Max. circuit depth / gate count | up to 1000 2q gates for up to weight-5 observables, up to 300 2q gates for highly non-local observables | up to 300 2q gates | | Circuit execution overhead | 2x more circuit executions per unique circuit | 2x more circuit executions per unique circuit | | Shot overhead | 2x more shots per unique circuit | 2x more shots per unique circuit | | Execution speed | O(1) seconds for QEM + execution time on QPU | O(10) seconds for QEM + execution time on QPU | ## State compression ### Benchmark: Utility-scale LR-QAOA Following recent paper by [Montanez-Barrera et. al. "Evaluating the performance of quantum processing units at large width and depth"](https://arxiv.org/abs/2502.06471), we use linear ramp quantum approximate optimization algorithm (LR-QAOA), a fixed-parameter, deterministic variant of QAOA, as a benchmarking protocol. Haiqu's compression enables execution of nearly **20x** more layers of LR-QAOA with the increasing approximation ratio. LR-QAOA benchmark, 100 qubits, IBM Kingston ## State Compression Specifications | **Parameter** | **Details** | | :-------------------------- | :------------------------------------------------------------------------------------------------------------------------------------------------------------------ | | **Number of qubits** | Up to 500 | | **Runtime (at 100 qubits)** | From few seconds and
up to 2 minutes with no fine-tuning;
up to 15 minutes with heavy fine-tuning | | **Runtime scaling** | Linear scaling with circuit size, problem-dependent | | **Supported circuits** | - Circuits decomposable into CNOT, RX, RY, RZ basis gates
- Circuits with mid-circuit measurements are supported, but compression applies only prior to MCM | | **Supported connectivity** | Any.
Not transpiled input with Linear connectivity is preferred. | | **Compression rate** | Up to 100× for various application circuits | | **Returned metrics** | - Compression rate
- Quality of the compression (fidelity-like metric) | \*runtime can vary for different circuit classes of the same size ## Data loading ## Distribution Loading Specifications | **Parameter** | **Details** | | :----------------------------- | :--------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | **Number of qubits** | Up to 500 qubits | | **Number of distributions** | 107 different classes of distributions are supported. Check SciPy docs for details. | | **Runtime** | 1–15 seconds | | **Runtime scaling** | Linear scaling with number of qubits | | **Circuit size (gates count)** | O(n), n = number of qubits | | **Circuit depth** | O(n/2), n = number of qubits | | **Circuit connectivity** | Linear | | **Other circuit properties** | - No mid-circuit measurements
- Only CNOT and single-qubit rotation gates
- No ancillary qubits
- No post-selection required in state preparation | | **Returned metrics** | Quantum state fidelity is returned for the ideal state prepared by the circuit | ### Vector Loading specifications | **Parameter** | **Details** | | :----------------------------- | :------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | **Number of qubits** | Up to 20 qubits | | **Input data** | 1D vector | | **Data type** | Real and complex values | | **Data size** | Up to \~1M features in the vector | | **Runtime** | 0.5–2 minutes | | **Runtime scaling** | Linear scaling with number of qubits | | **Circuit size (gates count)** | O(n), n = number of qubits | | **Circuit depth** | O(n/2), n = number of qubits | | **Circuit connectivity** | Linear | | **Other circuit properties** | - No mid-circuit measurements
- Only CNOT and single-qubit rotation gates
- No ancilla qubits
- No post-selection required in state preparation | | **Returned metrics** | Quantum state fidelity is returned for the ideal state prepared by the circuit | ### Block Vector Loading specifications | **Parameter** | **Details** | | :----------------------------- | :------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | **Number of qubits** | 1000+ qubits; no more than 20 qubits for a single block | | **Input data** | 1D vector
2D matrix | | **Data type** | Real and complex values | | **Data size** | Any, with no more than \~1M features for a single block | | **Runtime** | 0.5–2 minutes per block | | **Runtime scaling** | Linear scaling with number of qubits | | **Circuit size (gates count)** | O(n), n = number of qubits | | **Circuit depth** | O(m/2), m = number of qubits in each block | | **Circuit connectivity** | Linear within each block | | **Other circuit properties** | - No mid-circuit measurements
- Only CNOT and single-qubit rotation gates
- No ancilla qubits
- No post-selection required in state preparation | | **Returned metrics** | Quantum state fidelity is returned for the ideal state prepared by the circuit |