An ansatz is a parameterized quantum circuit used as a trial wavefunction in variational algorithms like VQE and QAOA. Different ansatz designs trade off expressibility, circuit depth, and hardware compatibility. This page compares four architectures from our paper replications and maps them onto three quantum processors.
Nodes are qubits. Edges are entangling gates (CNOT / ZZ). Select one to see its hardware mapping below.
How Subspace-Preserving VQE maps onto physical qubit connectivity. Bright edges are used by the ansatz; dim edges are available but unused.
QuTech · 9 qubits total
Ry(α) + CNOT + X preserves particle number in the {|01⟩, |10⟩} subspace. Minimal circuit for H₂ ground state.
q0: ─[Ry(α)]─●─[X]─ q1: ──────────⊕─────
E(θ) for the 2-qubit H₂ VQE at R=0.735 Å, from Sagastizabal 2019. The single parameter θ controls the superposition cos(θ/2)|10⟩ + sin(θ/2)|01⟩. Green band shows chemical accuracy (1 kcal/mol). Hover to explore.
| Ansatz | Type | Qubits | Params | CNOTs | Depth | Tuna-9 | Garnet | Torino |
|---|---|---|---|---|---|---|---|---|
| Subspace-Preserving VQE | Chemistry | 2 | 1 | 1 | 3 | Native | Native | Native |
| UCCSD (DoubleExcitation) | Chemistry | 4 | 1 | 16 | 20 | Native | Native | Native |
| Hardware-Efficient | Generic | 4 | 12/layer | 3 | 6 | Native | Native | Native |
| QAOA MaxCut p=1 | Optimization | 4 | 2 (γ, β) | 3 | 4 | Native | Native | Native |
See the full glossary for more definitions.
A parameterized quantum circuit used as a trial wavefunction in variational algorithms. The name comes from German, meaning "approach" or "initial guess."
Variational Quantum Eigensolver — a hybrid quantum-classical algorithm that finds the ground state energy of a molecule by minimizing ⟨ψ(θ)|H|ψ(θ)⟩ over parameters θ.
Quantum Approximate Optimization Algorithm — alternates cost and mixer layers to find approximate solutions to combinatorial problems like MaxCut.
Controlled-NOT gate — a two-qubit entangling gate that flips the target qubit when the control is |1⟩. The primary source of noise in most circuits.
Unitary Coupled Cluster Singles and Doubles — a chemistry-motivated ansatz derived from classical coupled cluster theory. Preserves particle number and spin symmetry.
The number of sequential gate layers in a circuit. Deeper circuits accumulate more noise from decoherence. Keeping depth low is critical on NISQ hardware.
1 kcal/mol (1.6 mHa) — the precision threshold needed for quantum chemistry to be practically useful. Achieving this on real hardware is a key benchmark.
How closely a measured quantum state matches the ideal target state. A Bell state fidelity of 93.5% means 93.5% of measurements agree with the expected entangled outcome.
The physical gate set a quantum processor can execute directly. Non-native gates must be decomposed, adding depth and noise. SWAP routing adds ~3 CNOTs per non-native connection.
A region of parameter space where the cost function gradient vanishes exponentially with qubit count, making optimization intractable. Hardware-efficient ansatze are especially prone to this.
The three quantum processors shown above are real, publicly accessible superconducting transmon chips. All topology and fidelity data on this page comes from our own measurements — verify the hardware specs below.
Tuna-9 — QuTech / TU Delft. 9-qubit transmon, diamond topology, 12 flux-tunable couplers. Fabricated by DiCarlo Lab at QuTech. Available since December 2025.
IQM Garnet — IQM Quantum Computers. 20-qubit transmon, square-lattice topology, 30 tunable couplers. CZ native gate with 99.51% median two-qubit fidelity. Quantum Volume 32.
IBM Torino — IBM Quantum. 133-qubit Heron r1 processor, heavy-hex topology. CZ + SX + RZ native gate set. Echoed cross-resonance entangling gates.
The ansatz circuits above come from these published experiments, which we replicated on all three backends.
R. Sagastizabal et al., “Experimental error mitigation via symmetry verification in a variational quantum eigensolver,” Phys. Rev. A 100, 010302(R) (2019).
A. Peruzzo et al., “A variational eigenvalue solver on a photonic quantum processor,” Nature Communications 5, 4213 (2014).
A. Kandala et al., “Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets,” Nature 549, 242-246 (2017).
M.P. Harrigan et al., “Quantum approximate optimization of non-planar graph problems on a planar superconducting processor,” Nature Physics 17, 332-336 (2021).
A.W. Cross et al., “Validating quantum computers using randomized model circuits,” Phys. Rev. A 100, 032328 (2019).
An ansatz is a parameterized quantum circuit used as a trial wavefunction in variational algorithms like VQE. The choice of ansatz determines what states the algorithm can explore and how efficiently it converges. Different architectures make different trade-offs between expressibility (which states can be reached) and trainability (how easy it is to optimize).
Hardware-efficient ansätze use only the native gates of a specific processor, minimizing circuit depth. Chemistry-inspired ansätze like UCCSD respect the physical symmetries of molecules but require more gates. The Hamiltonian variational ansatz structures its layers to match the problem Hamiltonian.
This explorer compares 4 architectures from landmark papers, showing real transpilation data for Tuna-9 (CZ + Ry/Rz native gates), IQM Garnet, and IBM processors. Gate counts, circuit depth, and expected fidelity help determine which ansatz works best on which hardware.