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Error suppression & mitigation stack

Benchmark: 2D transverse-field Ising model

We reproduce the experiment from IBM’s Nature publication using Haiqu’s lightweight error mitigation techniques. Ising Model simulation, 127 qubits, IBM Kingston In the paper (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 mitigationBitstring distribution mitigation
Supported backendsIBM QPUs, AWS Braket (TBD)IBM QPUs, AWS Braket (TBD)
Max number of qubitsup to 156 qubits (largest QPU)up to 156 qubits (largest QPU)
Max. circuit depth / gate countup to 1000 2q gates for up to weight-5 observables, up to 300 2q gates for highly non-local observablesup to 300 2q gates
Circuit execution overhead2x more circuit executions per unique circuit2x more circuit executions per unique circuit
Shot overhead2x more shots per unique circuit2x more shots per unique circuit
Execution speedO(1) seconds for QEM + execution time on QPUO(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”, 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

ParameterDetails
Number of qubitsUp 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 scalingLinear 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 connectivityAny.
Not transpiled input with Linear connectivity is preferred.
Compression rateUp 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

ParameterDetails
Number of qubitsUp to 500 qubits
Number of distributions107 different classes of distributions are supported. Check SciPy docs for details.
Runtime1–15 seconds
Runtime scalingLinear scaling with number of qubits
Circuit size (gates count)O(n), n = number of qubits
Circuit depthO(n/2), n = number of qubits
Circuit connectivityLinear
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 metricsQuantum state fidelity is returned for the ideal state prepared by the circuit

Vector Loading specifications

ParameterDetails
Number of qubitsUp to 20 qubits
Input data1D vector
Data typeReal and complex values
Data sizeUp to ~1M features in the vector
Runtime0.5–2 minutes
Runtime scalingLinear scaling with number of qubits
Circuit size (gates count)O(n), n = number of qubits
Circuit depthO(n/2), n = number of qubits
Circuit connectivityLinear
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 metricsQuantum state fidelity is returned for the ideal state prepared by the circuit

Block Vector Loading specifications

ParameterDetails
Number of qubits1000+ qubits; no more than 20 qubits for a single block
Input data1D vector
2D matrix
Data typeReal and complex values
Data sizeAny, with no more than ~1M features for a single block
Runtime0.5–2 minutes per block
Runtime scalingLinear scaling with number of qubits
Circuit size (gates count)O(n), n = number of qubits
Circuit depthO(m/2), m = number of qubits in each block
Circuit connectivityLinear 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 metricsQuantum state fidelity is returned for the ideal state prepared by the circuit