Quantum Simulation
EXACT TO 20 QUBITS · CERTIFIED ACCURACY TO 1,000 QUBITS
Whether you are developing a new quantum algorithm, testing a VQE or QAOA ansätz, or benchmarking your circuit against published quantum hardware results — Qumulator delivers exact simulation results for random circuits up to 20 qubits and structured circuits up to 1,000 qubits through its cloud simulation platform. Submit a circuit in any supported format; the engine routes it to the appropriate solver automatically.
Gate-Based Circuit Simulation
Submit circuits in OpenQASM 3, Qiskit, or Cirq. Simulate up to 1,000 qubits for structured circuits at shallow depth, or up to 20 qubits at full depth — exact in both cases. All three formats are accepted as-is, with full fidelity to the original circuit structure.
Algorithm Development & Testing
Test VQE, QAOA, and variational ansätze in the qubit range where near-term quantum hardware actually runs. Understand your circuit’s entanglement structure and verify your ansatz is achieving what you designed it for — without waiting for hardware access.
Quantum Advantage Benchmarking
Generate cross-entropy benchmarking (XEB) fidelity scores for random circuit sampling — the standard metric used by Google and IBM to claim quantum advantage. Compare classical simulation performance against hardware at any circuit size.
Multiple Simulation Modes
The engine analyses each circuit’s entanglement structure and selects the optimal solver automatically. Statevector for exact full-depth simulation up to 20 qubits. MPS for structured circuits up to 1,000 qubits. Cluster for sparse-connectivity circuits of any size. Every result includes a TVD accuracy bound so you always know whether your result is exact or approximate, and by how much.
SIMULATION ACCURACY — EXACT VS APPROXIMATE
How the engine classifies your circuit
As simulation runs, the engine measures per-bond von Neumann entropy across the quantum state
and assigns a phase label — Z1 (near-product)
through Z5 (volume-law). This determines which solver
is used and whether the result is exact. Circuits in Z1–Z3 are solved exactly within
their entanglement depth limits. Z4–Z5 circuits are solved approximately — every
result then includes a predicted_tvd, a guaranteed
theoretical upper bound on Total Variation Distance from the ideal result. For Z1–Z3
this bound is typically below 1 %.
| Mode | Scale | Entanglement Depth | Accuracy | TVD |
|---|---|---|---|---|
| Statevector | Up to 20 qubits | Any | EXACT | 0 |
| MPS — Structured Circuits | Up to 1,000 qubits | ≤ 6 layers (random) · ≤ 20 layers (structured) | EXACT | 0 at full bond dimension |
| MPS — Deep Circuits | Up to 1,000 qubits | > 6 layers (random) · > 20 layers (structured) | APPROXIMATE | Guaranteed bound returned with every result |
| Cluster Statevector — Sparse Circuits | Any N · largest entangled group ≤ 24 qubits | Any depth (within cluster size limit) | EXACT | 0 |
| Cluster MPS — Dense Circuits | Any N · cluster merges beyond 24 qubits | Depth causing full-width entanglement | APPROXIMATE | Gaussian propagator handoff — bound returned |
BENCHMARK NOTEBOOKS
Click any notebook to open the documentation and run it in Google Colab.
Molecular Chemistry
GROUND-STATE ENERGIES AND ORBITAL PROPERTIES — CHEMICAL ACCURACY
Quantum simulation offers a path to accurate molecular energy calculations that go beyond what classical Hartree-Fock can achieve. Pass active-space integrals for ground-state energies, or a SMILES string for frontier orbital properties — and receive a chemically accurate result, returned via API.
Molecular Ground-State Energy
Provide the one- and two-electron integrals for your molecule’s active space and get the exact ground-state energy using DMRG. Accepts integrals from PySCF, PSI4, or ORCA. Verified at chemical accuracy on H ₂, LiH, and N ₂. Active spaces up to 30 orbitals supported.
Frontier Orbital Energies from SMILES
Pass a SMILES string — the standard shorthand for any molecule — and receive HOMO and LUMO energies in electronvolts. HOMO/LUMO gaps predict reactivity, charge-transfer tendency, and drug-likeness. B3LYP/6-31G*, with per-atom density contributions returned.
Correlation Energy Recovery
Hartree-Fock systematically misses the electron correlation energy — the contribution that makes bond energies, reaction barriers, and excitation energies accurate. The DMRG solver recovers 100% of the active-space correlation energy, verified on N ₂ at equilibrium geometry.
VERIFIED BENCHMARKS — THREE METHODS, THREE ACCURACY LEVELS
DMRG Ground-State Energies
— /dmrg/energy
Two-site DMRG recovers 100% of the active-space correlation energy. Results are exact within the chosen active space — verified against PySCF FCI to machine precision. Accepts active-space integrals (h1e, h2e) from PySCF, PSI4, or ORCA.
| Molecule | Active Space | DMRG Energy | FCI Reference | Error |
|---|---|---|---|---|
| H ₂ / STO-3G | CAS(2,2) · 4 q | −1.1510 Ha | −1.1510 Ha | 0.00 mHa |
| LiH / STO-3G | CAS(2,2) · 4 q | −7.8823 Ha | −7.8823 Ha | 0.00 mHa |
| N ₂ / STO-3G | CASCI(6,6) · 12 q | −107.6218 Ha | −107.6218 Ha | 0.00 mHa |
| Aspirin / STO-3G | CASCI(8,8) · 16 q | −636.6968 Ha | −636.6968 Ha | 0.00 mHa |
MPS / MPO Ground-State Energies
— /molecular/energy
The MPS engine assigns intra-fragment bond dimensions to the full particle-conserving FCI dimension, and inter-fragment bonds to χ = 1 (exact product-state factorisation). For molecules whose active-space orbital graph decomposes into separated fragments, this is exact with no approximation.
| Molecule | Active Space | Fragments | MPS Energy | Status |
|---|---|---|---|---|
| N ₂ / STO-6G | CAS(10,8) | 1 bonding + 1 antibonding | −107.6218 Ha | EXACT |
| Aspirin / STO-3G | CAS(8,8) | 2 orbital fragments | −636.6488 Ha | EXACT HF ref per fragment |
For aspirin’s strongly correlated π system, full correlation recovery requires DMRG
(see table above). MPS gives the exact Hartree-Fock reference per fragment. Use
client.dmrg when < 0.1 mHa accuracy is required
within a single fragment.
DFT Frontier Orbital Energies
— /homo/energy
B3LYP/6-31G* delivers the frontier orbital energies that predict reactivity, charge-transfer tendency, and drug-likeness. This is the standard method in computational drug discovery. The B3LYP functional is an approximation — expect ± 0.3–0.5 eV vs. direct experiment. The basis set (6-31G*) is not the limiting factor; the exchange-correlation functional is.
| Molecule | Method | HOMO | LUMO | Gap | Accuracy |
|---|---|---|---|---|---|
| Aspirin (C ₉H ₈O ₄) | B3LYP / 6-31G* | −7.034 eV | −1.459 eV | 5.575 eV | ± 0.3–0.5 eV vs. experiment |
| Resveratrol (C ₁₄H ₁₂O ₃) | B3LYP / 6-31G* | −5.515 eV | −0.821 eV | 4.694 eV | ± 0.3–0.5 eV vs. experiment |
CHEMISTRY NOTEBOOKS
Click any notebook to open the documentation and run it in Google Colab.
Condensed Matter
SPIN MODELS · PHASE TRANSITIONS · TOPOLOGICAL QUANTUM MATTER
Condensed matter physics asks how large collections of quantum particles organise themselves — into magnets, superconductors, and exotic topological phases. Submit a Hamiltonian preset or custom coupling terms and receive ground-state energies, real-time trajectories, correlation functions, and topological invariants — all computed through Qumulator’s cloud simulation platform.
Spin Model Ground States
Compute ground-state energies and spin configurations for Ising, Heisenberg, XY, and custom exchange Hamiltonians on 1D and 2D lattices. Use imaginary-time evolution to prepare the ground state directly — no variational ansatz required. Returns energy per site, magnetisation profile, and per-bond entanglement entropy.
Real-Time and Imaginary-Time Evolution
Evolve a quantum state forward in real time using TEBD — the standard method for simulating Hamiltonian dynamics in 1D. Watch spin correlations propagate, observe light-cone spreading, and track entanglement growth step by step. Imaginary-time evolution prepares ground states of arbitrary local Hamiltonians with no variational parameters to tune.
Kibble-Zurek Quench Protocols
Drive a quantum system through a phase transition at finite speed and measure how defect density scales with quench rate — the Kibble-Zurek mechanism. Sweep the transverse field of an Ising chain across the critical point and recover the predicted power-law scaling. Returns defect density, domain-wall density, and the full post-quench correlation function at each quench rate.
Topological Phases & Majorana Modes
Characterise topological phases of matter using the Kitaev chain model. Compute the winding number and bulk energy gap as a function of chemical potential and hopping, identify the topological phase boundary, and extract the spatial profiles of Majorana zero modes pinned to the chain ends. The same methods used in leading research on fault-tolerant quantum computing.
VERIFIED BENCHMARKS — CONDENSED MATTER
MPS Ground States & Real-Time
Evolution — /evolve
MPS ground states are converged to machine precision at the minimal bond dimension required by the phase. Real-time TEBD evolution conserves energy and particle number exactly at each timestep. Benchmarks verified against exact diagonalisation and published analytical results.
| System | Method | Observable | Result | Verification |
|---|---|---|---|---|
| AKLT / Heisenberg chain | MPS ground state · χ = 2 · 50 sites | Topological string order | −0.2500 (all L) | 0.00 error vs. analytical |
| Transverse-field Ising quench | TEBD real-time · 20 sites · dt = 0.05 | Entanglement entropy · ZZ correlator · QFI | Linear S(t) growth | Light-cone spreading confirmed |
CONDENSED MATTER NOTEBOOKS
Click any notebook to open the documentation and run it in Google Colab.
Photonics
GAUSSIAN BOSON SAMPLING · HAFNIAN · PHOTONIC AMPLITUDES
Photonic quantum computing uses particles of light instead of superconducting qubits. Verifying whether a photonic device is actually performing quantum computations — or designing new photonic circuits — requires computing the hafnian: a quantity that determines photon-counting probabilities and grows exponentially hard with photon number. Qumulator computes hafnians and photonic transition amplitudes exactly on classical cloud hardware, enabling fast verification, experimental design, and quantum advantage analysis for photonic systems.
Hafnian & Permanent Computation
Compute the hafnian or permanent of complex matrices — the quantities that determine photon-counting probabilities in Gaussian boson sampling experiments. High-precision arithmetic handles ill-conditioned and large matrices. Returns the exact complex value to machine precision.
Boson Sampling Verification
Given output samples from a photonic quantum device, compute the expected boson sampling distribution and compare against experimental results. Used to verify quantum advantage claims and to cross-check photonic hardware outputs against theory — the standard validation step in GBS experiments.
Photonic Network Amplitudes
Compute transition amplitudes for structured photonic networks combining beamsplitters, phase shifters, and squeezed states. Supports numerical testing of photonic circuit designs — verify output distributions before fabrication, without access to physical photonic hardware.
Quantum Advantage Analysis
Determine the classical spoofability threshold for a given photonic device — compute hafnians across matrix sizes, fit the $O(2^n \cdot n^2)$ Ryser scaling curve, and identify the crossover point where no classical computer can match the device in real time. Used to certify and contextualise quantum advantage claims in the style of Jiuzhang.
VERIFIED BENCHMARKS — PHOTONICS
Hafnian & Permanent —
/hafnian
Computed using Ryser’s algorithm with Gray code enumeration. Results are exact to machine precision and verified against published reference values from the Strawberry Fields and The Walrus libraries.
| Instance | Matrix Size | Re(haf) | Im(haf) | Verification |
|---|---|---|---|---|
| 8-mode GBS instance | 16×16 complex symmetric | −1.884×10−6 | +3.905×10−6 | Matches reference to 15 s.f. |
PHOTONICS NOTEBOOKS
Click any notebook to open the documentation and run it in Google Colab.
Pricing
FREE FOR RESEARCH. CUSTOM FOR BUSINESS.
Free for non-commercial use and academic research. Commercial teams start with a conversation.
1,000 compute units / month
Statevector up to 20 q
All MPS tiers (up to 1,000 q)
No account. No credit card.
Unlimited compute (fair-use)
Dedicated cloud instances available
SLA + custom engine parameters
What is a Compute Unit (CU)?
1 Compute Unit = 1 second of engine CPU time. Each simulation job consumes CU equal to its actual wall-clock execution time on Qumulator’s cloud engine. A simple statevector circuit may use 1–3 CU; a large MPS run at 1,000 qubits (depth 3–7) may use 60–300 CU. Your monthly CU budget resets on the first of each month. Unused CU do not roll over.
Non-commercial tier limits
The following limits apply to the NON-COMMERCIAL tier only. Commercial plans have no fixed qubit cap, rate limit, or daily ceiling — contact us for details.
Get in Touch
QUESTIONS, PARTNERSHIPS, OR EARLY ACCESS — WE’D LOVE TO HEAR FROM YOU.
LOCATION
Virginia, United States