State & evolution

Qubits

Evolution time

Time steps

Total shot budget

Random seed

Product formula order

Initial state

Simulation backend

1–14 qubits; 1–256 steps; 2–4096 total shots, at least 2 per group. Time and coefficient magnitudes ≤ 1,000,000; seed 0–4,294,967,295. Evolution plus preparation: at most 4096 gates. Source: at most 32 KiB. Measurement timeout: 5 s, checked cooperatively; Cancel terminates the Worker.

Hamiltonian terms · source order

Enter a real coefficient and a Pauli word such as X0 Y1 or Z0. Use I for identity. Indices start at 0 and must be distinct within a term. Keep the term order: noncommuting evolution depends on it. Up to 64 terms; repeated words merge and cancelling terms disappear.

Term 1 coefficient
Term 1 Pauli word
Term 2 coefficient
Term 2 Pauli word
Term 3 coefficient
Term 3 Pauli word

Enable Hamiltonian evolution and grouped measurement for this experimentBoth prototype permissions start off. Selecting this enables this run and its explicit Playground handoff; it does not change global defaults.

Ready. Changing any setting clears previous results.

Planned measurement groups

Requested: 256 shots · allocated: 256 · unallocated: 0. Identity offset: 0.25.

Bases are labelled q0 first. I means no basis rotation is needed on that qubit. Groups use a deterministic greedy plan and L1-weighted allocation, not a guaranteed minimum group count or precision gain.

Qubit-wise commuting groups · planned allocation
Group	Weighted Pauli terms	Local basis · q0 first	L1 weight	Shots
g1	0.75 × Z0	q0:Z · q1:I	0.75	153
g2	0.5 × X0 X1	q0:X · q1:X	0.5	103

Generated N/M source

Evolution: 65 generated gates · preparation: 2 gates. This exact source is sent to the Worker.

module hamiltonian_lab;
@seed(2026);
@shots_budget(256);
fn main() {
  let q = qreg[2];
  H(q[0]);
  H(q[1]);
  observable Hamiltonian = 0.75 * Z(q[0]) + 0.5 * X(q[0]) X(q[1]) + 0.25 * I;
  evolve Hamiltonian for 0.7 steps 4 order 2 on q;
  let energy = expect Hamiltonian;
  return q;
}

Guide: from Hamiltonian to energy

Choose zero, plus or a Bell pair as the initial state. Only noiseless state vector and MPS simulation are supported here.
Evolution approximates exp(−itH) with a first-order or symmetric second-order product formula. More steps can improve noncommuting evolution, but increase the gate budget. Identity terms preserve their global phase.
Compatible local Pauli bases share a joint histogram. Globally commuting operators can still need different groups, such as X0 X1 and Y0 Y1. Each measured group receives at least two shots; the total budget is shared by this experiment’s single expectation.
Compare sampled energy with the analytic value for the simulated state. Read the standard error and concentration interval with their stated assumptions. Reusing a seed repeats this local sampling procedure; it is not a cross-engine bitwise or hardware guarantee.
Enable both prototype permissions, review the generated source, then run. Editing or disabling clears results and cancels active work; Cancel returns control immediately. Open the same source and explicit flags in Playground to inspect it further.