Quantum Simulators deep dive

In this post , I am coving the types of simulators and advanced simulation strategies for quantum computing and testing the algorithms before moving to actual hardware.

1. Simulator Types

Four types of simulators used in validation of quantum algorithms:

Statevector Simulators:

• Memory requirement: 2^n complex numbers (16 bytes each) = exponential

• Concrete numbers:

  • 30 qubits = 16 GB RAM

  • 35 qubits = 512 GB RAM

  • 40 qubits = 16 TB RAM (impossible on single machine)

• Optimization tricks: Sparse matrix representation, GPU acceleration gains

• When it fails: Entangled states with all qubits force full vector storage

Tensor Network Simulators:

• How they work: Decompose quantum state into tensor contractions

• Trade-off: Approximate for highly entangled states, exact for low-entanglement

• Sweet spot: 50-100 qubits with limited entanglement structure

• Use case: Chemistry simulations (molecules have local interactions)

Density Matrix Simulators:

• Why they exist: Model mixed states and decoherence

• Memory cost: 2^(2n) - even more expensive than statevector

• Practical limit: ~15-20 qubits with noise modeling

• When to use: Testing error mitigation strategies

Clifford Simulators:

• The hack: Clifford circuits classically simulable in polynomial time

• Scale: Can simulate 1000+ qubits if circuit is Clifford-only

• Application: Benchmarking, error correction testing

• Limitation: No T gates allowed (not universal)

2. Advanced Simulator Techniques

Some of the advanced techniques used to save states, memory in quantum computing are

Hybrid Simulation:

• Simulate classical parts classically, quantum parts quantumly

• Save enormous memory for hybrid algorithms

• Example: VQE classical optimizer doesn't need quantum simulation

Checkpoint/Resume:

• Save quantum state mid-circuit

• Resume from checkpoint with different parameters

• Useful for variational algorithms

Distributed Simulation:

• Split state vector across multiple machines

• Can reach 45-50 qubits with cluster

• IBM's Qiskit Aer supports MPI for this

Noise Model Customization:

• Extract real device noise data from provider

• Build custom noise model matching specific hardware

• Test error mitigation before expensive hardware runs

How to simulate with real noise and compare to noiseless and quantify noise impact in python:

# Get real device noise

device = provider.get_backend('ibm_quebec')

noise_model = NoiseModel.from_backend(device)

# Simulate with real noise

simulator = AerSimulator(noise_model=noise_model)

result_noisy = simulator.run(circuit).result()

# Compare to noiseless

result_ideal = simulator.run(circuit).result()

# Quantify noise impact

fidelity_loss = compare(result_ideal, result_noisy)

References and further reading:

• IBM Quantum Documentation. "Calibration jobs." https://docs.quantum.ibm.com/guides/calibration-jobs

• The Rise of Logical Qubits: How Quantum Computers Fight Errors." (2025). Post Quantum. https://postquantum.com/quantum-computing/logical-qubits/

• McEwen, M., et al. (2021). "Removing leakage-induced correlated errors in superconducting quantum error correction." Nature Communications, 12, 1761. https://www.nature.com/articles/s41467-021-21982-y

• Acharya, R., et al. (2023). "Overcoming leakage in quantum error correction." Nature Physics, 19, 1619–1624. https://www.nature.com/articles/s41567-023-02226-w

• Google Quantum AI. "Overcoming leakage on error-corrected quantum processors." https://research.google/blog/overcoming-leakage-on-error-corrected-quantum-processors/

• McDermott, R., et al. (2021). "Quantum-classical tradeoffs and multi-controlled quantum gate decompositions in variational algorithms." Quantum, 5, 446.

• Sarovar, M., et al. (2020). "Detecting crosstalk errors in quantum information processors." Quantum, 4, 321. https://quantum-journal.org/views/qv-2020-10-29-46/