Simulate 1,000-qubit quantum circuits on classical hardware. Exact results. No GPU. No quantum hardware required.
What is this?
Qumulator is a cloud API — and this is its Python client — for simulating quantum circuits, spin systems, photonic amplitudes, and molecular properties on standard classical hardware. It does not require a quantum computer, a GPU, or any special hardware. It runs in the cloud (Google Cloud Run, 4 vCPU, 16 GB RAM) and returns results over HTTP.
The key numbers: a 1,000-qubit circuit at depth 3 runs in under 1 second using 1 MB of memory
— where the equivalent statevector would require
The simulation engine is built on the KLT Engine, a proprietary classical simulation framework that routes each problem to the most efficient representation — tensor network, cluster-exact, Gaussian covariance matrix, nexus graph, or full statevector — based on the entanglement structure of the specific circuit. Callers select a mode with a single parameter; the engine handles routing automatically.
Benchmarks
Measured on a standard cloud CPU (4 vCPU, no GPU). "Exact" means output agrees with full statevector simulation to double-precision floating point (< 10⁻¹⁴ L² error on the amplitude vector).
| Problem | Size | Result | Reference | Error | Time |
|---|---|---|---|---|---|
| CHSH Bell violation | N=2 | S = 2.828427 | 2√2 = 2.828427 | < 0.0001% | < 1 ms |
| H₁₂ Heisenberg chain | 12 sites | −11.000 | −11.000 (exact diag.) | 0.00% | ~0.27 s |
| Photonic hafnian (GBS) | 8×8 matrix | 0.2598−0.0078i | exact DP | < 2×10⁻¹⁵ | 39 ms |
| Photonic hafnian (GBS) | 12×12 matrix | 0.0239+0.9947i | exact DP | < 5×10⁻¹⁵ | 43 ms |
| RCS circuit (exact) | 12 q, depth 20 | XEB = 1.014 | exact statevector | 0.00% | 15–23 ms |
| RCS circuit (exact) | 20 q, depth 20 | XEB = 1.024 | exact statevector | 0.00% | 8.5–9.6 s |
| MBL discrete time crystal | 8 q, 24 Floquet | autocorr = 0.827 | Google Sycamore 2021 | Consistent | ~1 s |
| Holographic wormhole | 2×6 SYK sites | fidelity 94.89% | Google Sycamore 2022 | — | ~5 s |
| Non-Abelian anyon braiding | Fibonacci anyons | ‖[σ₁,σ₂]‖ = 1.272 | SU(2)₃ exact | < 0.001% | < 1 ms |
| Kitaev chain BdG | L=1000 sites | W=−1, gap=2.000 | analytic (exact) | < 10⁻¹² | 0.84 s |
| QUBO dense optimisation | N=100 | matches SA optimum | simulated annealing | 0% | ~3 s |
| Kuramoto BEC (large-scale) | N=500 oscillators, 2 MB | r=0.114 (Mott-like) | statevector: 2⁵⁰⁰ bytes (impossible) | — | 3.22 s |
Circuit depth limits (approximation modes)
Bond dimension
| Tier | Qubit range | Max depth | Peak memory | Notes |
|---|---|---|---|---|
| 1 | 1 – 20 | 20 | 335 MB | Exact for structured circuits |
| 2 | 21 – 54 | 6 | 3.5 MB | χ = 64 (exact) |
| 3 | 55 – 105 | 5 | 1.7 MB | χ = 32 (exact) |
| 4 | 106 – 1,000 | 3 | 1 MB | χ = 8 (exact) |
Statevector mode: max 20 qubits at any depth.
Install
pip install qumulator-sdk
Optional extras:
pip install "qumulator-sdk[qiskit]" # Qiskit drop-in backend pip install "qumulator-sdk[cirq]" # Cirq drop-in simulator pip install "qumulator-sdk[all]" # everything
Get a free API key
curl -s -X POST https://api.qumulator.com/keys \
-H "Content-Type: application/json" \
-d '{"name": "my-key"}' | python -m json.toolOr via the CLI (after install):
qumulator key
Quick start — 1,000-qubit circuit in 30 seconds
import os from qumulator import QumulatorClient client = QumulatorClient( api_url="https://api.qumulator.com", api_key=os.environ["QUMULATOR_API_KEY"], ) # 1000-qubit GHZ state via the fluent builder API eng = client.circuit.engine(n_qubits=1000) eng.apply("h", 0) for i in range(999): eng.apply("cx", [i, i + 1]) result = eng.sample(shots=1024) print(result) # {'0000...0000': 512, '1111...1111': 512} # Exact result. No quantum hardware. No GPU. Standard cloud CPU.
Run the built-in demo against the live API:
qumulator demo # 1000-qubit GHZ qumulator demo --willow # 105-qubit Willow-layout RCS
OpenQASM 2/3
result = client.circuit.run_qasm(""" OPENQASM 2.0; include "qelib1.inc"; qreg q[2]; creg c[2]; h q[0]; cx q[0], q[1]; measure q -> c; """, shots=1024) print(result.counts) # {'00': ~512, '11': ~512} print(result.entropy_map) # [0.999, 0.999] — entanglement per qubit
Drop into Qiskit — two lines of code
from qumulator.backends.qiskit_backend import QumulatorBackend from qiskit import transpile backend = QumulatorBackend(client) # replaces AerSimulator() job = backend.run(transpile(qc, backend), shots=1024) counts = job.result().get_counts()
Everything else in your Qiskit workflow is unchanged.
Drop into Cirq — two lines of code
from qumulator.backends.cirq_simulator import QumulatorSimulator sim = QumulatorSimulator(client) # replaces cirq.Simulator() result = sim.run(circuit, repetitions=1024)
Simulation modes
Pass mode= to any run() call. The server selects auto by default.
| User-facing mode | Internal mode | Max qubits | Best for |
|---|---|---|---|
auto |
(server-routed) | 1,000 | General circuits; server auto-routes |
exact |
(statevector) | 20 | Unconditionally correct; small N |
compressed |
(tensor network) | 1,000 | VQE, QAOA, chemistry ansätze |
tensor |
(MPS) | 1,000 | 1D-structured, low-entanglement circuits |
hamiltonian |
(operator algebra) | 1,000 | Hamiltonian simulation without gate decomposition |
gaussian |
(covariance matrix) | unlimited | Clifford circuits; returns Wigner negativity certificate |
Other computation types
# Molecular HOMO/LUMO frontier orbital energies (SMILES input) homo = client.homo.run("Oc1ccc(/C=C/c2cc(O)cc(O)c2)cc1") print(homo.homo_E_eV, homo.lumo_E_eV, homo.gap_eV) # Ground-state energy of a spin Hamiltonian (Ising / Heisenberg / general) import numpy as np J = np.random.randn(8, 8); J = (J + J.T) / 2 result = client.klt.run(J.tolist()) print(result.energy) # Hafnian / GBS photonic amplitude A = np.random.randn(8, 8); A = (A + A.T) / 2 h = client.hafnian.run(A.tolist()) print(h.value)
Free tier limits
| Limit | Value |
|---|---|
| Compute Units / month | 500 CU (1 CU = 1 CPU-second of engine time) |
| Max qubits (statevector mode) | 20 |
| Max qubits (MPS mode) | 54 |
| Max depth (MPS, ≤ 54 q) | 9 |
| Rate limit | 1 request / minute |
| Daily limit | 100 requests / day |
| Free tier availability | Beta only — may be discontinued at any time |
Paid plans start at $99/month (10,000 CU). See qumulator.com/#pricing.
Demo notebooks
Click to open in Google Colab — no install required, just add your API key:
| Notebook | Description |
|---|---|
 |
Willow RCS — 105-qubit exact simulation, Willow-layout |
|
Holographic wormhole — traversable wormhole, matches Google 2022 |
|
Anyon braiding — Fibonacci anyons, matches Microsoft topological target |
|
Discrete time crystal — MBL Floquet, matches Google Sycamore 2021 |
|
QUBO optimisation — 100-variable dense combinatorial optimisation |
CLI
The qumulator command ships with the SDK:
qumulator demo # 1000-qubit GHZ demo vs. the public API
qumulator demo --willow # 105-qubit Willow-layout benchmark
qumulator demo --wormhole # holographic wormhole
qumulator demo --anyon # anyon braiding
qumulator key # instructions to get a free API key
qumulator run circuit.qasm # submit a QASM file and print the result
Set QUMULATOR_API_KEY in your environment, or pass --key YOUR_KEY.
Documentation
Full API reference and examples: qumulator.com
License
MIT — see LICENSE.