Variational Quantum Eigensolver (Pillar 6 main entry point)

Runs the Peruzzo et al. 2014 VQE on the supplied Hamiltonian with a hardware-efficient EfficientSU2 ansatz (Kandala et al. 2017) and a classical optimiser (default COBYLA). The optimisation trajectory is captured by a callback so the energy curve can be plotted or audited after the fact.

Usage

quantum_vqe_fit(
  hamiltonian,
  ansatz_reps = 2L,
  optimizer = c("COBYLA", "SPSA", "SLSQP", "L-BFGS-B"),
  max_iter = 200L,
  backend = c("aer_statevector", "aer_shots", "ibmq"),
  shots = NULL,
  mitigation = c("none", "m3", "zne"),
  ibmq_backend = NULL,
  seed = NULL,
  initial_point = NULL
)

Arguments

hamiltonian

An edaphos_quantum_hamiltonian.

ansatz_reps

Integer — number of EfficientSU2 repetition blocks. More blocks increase expressivity at the cost of more variational parameters.

optimizer

Character — one of "COBYLA" (default), "SPSA", "SLSQP", "L-BFGS-B". Shot-based and hardware runs strongly prefer "SPSA" because it is robust to stochastic cost-function evaluations (Spall 1998).

max_iter

Integer — maximum classical-optimiser iterations.

backend

Character — one of "aer_statevector" (default, exact), "aer_shots" (shot-based simulation), "ibmq" (real IBM Quantum hardware). See Details.

shots

Integer — number of circuit shots per energy evaluation. Ignored when backend = "aer_statevector". Defaults to 4096 for "aer_shots" and "ibmq" when left NULL.

mitigation

Character — one of "none" (default), "m3", "zne". Controls hardware error mitigation; see Details.

ibmq_backend

Character — name of the target IBM Quantum backend (e.g. "ibm_brisbane", "ibm_sherbrooke") when backend = "ibmq". If NULL, the least-busy operational backend available to the account is selected automatically.

seed

Optional integer — seeds NumPy / Qiskit RNGs for reproducible runs.

initial_point

Optional numeric vector — custom starting ansatz parameters. Defaults to Qiskit's random initial point.

Value

An edaphos_quantum_vqe object with:

energy

Ground-state energy estimate.

exact

Numerically exact ground-state energy, for reference.

gap

Absolute difference |energy - exact|.

parameters

Numeric vector of optimal ansatz parameters.

history

Numeric vector of energy values, one per optimiser iteration (via callback).

n_iter

Integer iteration count.

shots, mitigation

Echo of the execution configuration.

hamiltonian,ansatz,optimizer,backend

Configuration echo.

Details

Three execution back ends are supported as of v0.9.0:

"aer_statevector" (default)

Exact noiseless statevector simulation via qiskit.primitives.StatevectorEstimator. The ansatz is not transpiled. Deterministic; limited by memory to roughly 24 qubits.

"aer_shots"

Shot-based simulation via qiskit_aer.primitives.EstimatorV2. Each energy evaluation is estimated from shots circuit executions and therefore carries a finite-sample noise of order 1/sqrt(shots). The ansatz is transpiled to the standard \{id, rz, sx, x, cx, u\} basis gate set so that the Aer primitive can dispatch it.

"ibmq"

Real hardware via qiskit_ibm_runtime.EstimatorV2 inside a Runtime Session. Requires the qiskit-ibm-runtime Python package and an IBMQ_TOKEN environment variable. Supports two mitigation strategies (Kim et al. 2023, see References):

• mitigation = "m3" — Matrix-free Measurement Mitigation (TREX + M3 readout correction), mapped to IBM runtime resilience_level = 1;

• mitigation = "zne" — Zero-Noise Extrapolation over gate-folding noise scales, mapped to IBM runtime resilience_level = 2.

References

Peruzzo, A. et al. (2014). A variational eigenvalue solver on a photonic quantum processor. Nature Communications 5, 4213.

Kandala, A. et al. (2017). Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549, 242–246.

Kim, Y. et al. (2023). Evidence for the utility of quantum computing before fault tolerance. Nature 618, 500–505.

Spall, J. C. (1998). Implementation of the simultaneous perturbation algorithm for stochastic optimisation. IEEE Transactions on Aerospace and Electronic Systems 34, 817–823.

Examples

if (FALSE) { # \dontrun{
  ham <- quantum_hamiltonian_h2()

  # 1) Exact noiseless reference (fast).
  fit <- quantum_vqe_fit(ham, backend = "aer_statevector", seed = 1L)

  # 2) Shot-based simulation with SPSA (honest to finite sampling).
  fit_s <- quantum_vqe_fit(ham, backend = "aer_shots",
                            shots = 4096L, optimizer = "SPSA",
                            max_iter = 100L, seed = 1L)

  # 3) Real IBM Quantum hardware with M3 readout mitigation.
  if (quantum_ibmq_available()) {
    fit_q <- quantum_vqe_fit(ham, backend = "ibmq",
                              shots = 4096L,
                              mitigation = "m3",
                              ibmq_backend = "ibm_brisbane",
                              optimizer = "SPSA",
                              max_iter = 50L)
  }
} # }