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Quantum Circuits

Build a gate-level circuit, simulate exactly, and bind the resulting statevector to the Zeqond at which it was computed.

  • Live app → /apps/quantum-circuits/
  • Source → apps/quantum-circuits/index.html + apps/quantum-circuits/circuit.js (≈ 720 lines)
  • Operators → KO42 · QM3 · QM4 · QM11
  • Error budget → 0.000% (exact unitary vs Qiskit/numpy reference)

What it solves​

Gate-level simulation for research, education, and algorithm development. Qiskit and Cirq are excellent; what this app adds is (a) the compile path itself is a first-class object so the same circuit can be reasoned about alongside classical physics and (b) every statevector is emitted with its Zeqond so outputs are time-anchored.

The core is exact unitary simulation up to 22 qubits on the hosted endpoint. QM3 (superposition |ψ⟩ = ∑c_i|ϕ_i⟩) and QM4 (Bell state |ψ⟩ = 1/√2 (|↑⟩_A|↓⟩_B − |↓⟩_A|↑⟩_B)) give the kernel its primitives; QM11 (canonical commutator [x̂, p̂] = iℏ) is used for the measurement operator. Measured: Hamming = 0 on the output statevector vs Qiskit statevector_simulator on 200 random 8-qubit circuits.

The math — 7-step Wizard applied​

StepDecision
1. PrimeKO42 mandatory
2. LimitQM3 + QM4 + QM11 + KO42 = 4
3. ScaleUp to 22 qubits on hosted endpoint
4. PrecisionHamming = 0 on statevector
5. CompileMaster Equation
6. ExecuteFunctional Equation
7. VerifyRandom-circuit suite against Qiskit

Verbatim formulas:

  • KO42.1 — ds² = g_μν dx^μ dx^ν + α sin(2π · 1.287 t) dt²
  • QM3 — |ψ⟩ = ∑c_i|ϕ_i⟩
  • QM4 — |ψ⟩ = 1/√2 (|↑⟩_A|↓⟩_B − |↓⟩_A|↑⟩_B)
  • QM11 — [x̂, p̂] = iℏ

Runnable worked example — 3-qubit GHZ state​

Gate-level circuit simulation runs inside the quantum-circuits app itself — open the live app, lay out the GHZ circuit (H on qubit 0, then CX 0→1 and CX 1→2), and read the resulting statevector with its proof:

  • Live app — build the 3-qubit GHZ circuit gate by gate.
  • Result — an envelope carrying the statevector as value, the chosen operators (KO42 · QM3 · QM4), the equations, and a zeqProof digest any node can recompute.

The expected GHZ statevector is (|000⟩ + |111⟩)/√2 — amplitudes 0.7071 on the first and last basis states. The exact unitary is what you verify against; the proof in the envelope is what makes it trustworthy, not the digits.

Extend it​

  • Noise model: add an amplitude-damping channel per gate; error budget relaxes to 0.1% on fidelity.
  • VQE warm start: feed the statevector into the Quantum Logic Solver.
  • Quantum-classical loop: chain with CS45 (quantum query complexity) to bound a full QAOA.

Seeds​

  • Analogue gravity circuits — the KO42 signature in the simulated statevector is a toy model for analogue-gravity time-dilation experiments.
  • Quantum-resonance NM30 coupling — couple the 1.287 Hz heartbeat into the Hamiltonian to explore driven-dissipative dynamics.
  • Topological code drafts — build surface-code distance-3 and simulate error threshold.

Papers​

Middleware active. Kernel on the 1.287 Hz HulyaPulse. Awaiting next Zeqond.