schemd
schemd · simulation laboratory v0.1.2 · 13 environments

Enter the circuit frontier.

13 live experiments span foundational circuits and frontier systems: switched-mode power, deterministic chaos, phase-lock acquisition, quantum protocols, and classical logic. Every test bed is compiled from the same @schemd/core source and instrumented with fault injection, probes, and live numerical models.

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domains
11
environments
13
frontier labs
5
experiment catalogue

13 of 13 laboratories online

  • 01 · Digital

    8-Bit Digital Adder

    Cascading ripple-carry gate matrix with a live combinational pass.

    Core event-driven Boolean solver
    Si=Ai⊕Bi⊕Ci  ⋅  Ci+1=AiBi+Ci(Ai⊕Bi)S_i = A_i \oplus B_i \oplus C_i \;\cdot\; C_{i+1} = A_iB_i + C_i(A_i \oplus B_i)
    • 8× full-adder cell
    • 16× XOR + 16× AND
    • 8× OR carry merge
    • A/B/Cᵢₙ + Sum ports

    8-bit operands · 0–255 · sum 0–511 with carry-out · per-gate propagation delay

    ⚠ carry chain stuck-at-0 Initialize module →
  • 02 · Analog

    Dynamic RC Low-Pass Filter

    Sweep R, C, and frequency; watch the pole attenuate the output trace.

    Core frequency-domain transfer function
    fc=12πRC  ⋅  ∣H(jω)∣=11+(f/fc)2f_c = \dfrac{1}{2\pi RC} \;\cdot\; |H(j\omega)| = \dfrac{1}{\sqrt{1 + (f/f_c)^2}}
    • input source node
    • series resistor R
    • shunt capacitor C
    • reference ground

    R 100 Ω – 1 MΩ · C 1 nF – 10 µF · sweep 10 Hz – 100 kHz

    ⚠ capacitor branch open Initialize module →
  • 03 · Quantum

    Bell-State Entanglement Visualizer

    Prepare the four Bell states; sample the ⟨Z⊗Z⟩ correlation.

    Advanced state-vector + Born sampler
    ∣Φ+⟩=∣00⟩+∣11⟩2  ⋅  ⟨Z⊗Z⟩∈[−1,+1]|\Phi^+\rangle = \dfrac{|00\rangle + |11\rangle}{\sqrt{2}} \;\cdot\; \langle Z \otimes Z \rangle \in [-1, +1]
    • 2× qubit register line
    • Hadamard gate
    • CNOT control/target
    • measurement ports

    4 Bell states · amplitudes ±1/√2 · CHSH witness S ∈ [0, 2√2]

    ⚠ CNOT entangler offline Initialize module →
  • 04 · Mixed-signal

    555 Astable Multivibrator

    A real charge/discharge loop clocking an output LED.

    Core hybrid charge/discharge integrator
    f=1.44(RA+2RB) C  ⋅  D=RA+RBRA+2RBf = \dfrac{1.44}{(R_A + 2R_B)\,C} \;\cdot\; D = \dfrac{R_A + R_B}{R_A + 2R_B}
    • 8-pin 555 IC block
    • R_A + R_B timing pair
    • timing capacitor C_T
    • output LED + limiter

    V_cc = 5 V · threshold ⅔ · trigger ⅓ · astable + monostable modes

    ⚠ THRES shorted to ground Initialize module →
  • 05 · Advanced quantum

    Quantum Teleportation Protocol

    Step a three-qubit register through the full teleportation script.

    Advanced stepped three-qubit protocol
    ∣ψ⟩=α∣0⟩+β∣1⟩  ⋅  α=cos⁡θ2, β=eiϕsin⁡θ2|\psi\rangle = \alpha|0\rangle + \beta|1\rangle \;\cdot\; \alpha = \cos\tfrac{\theta}{2},\ \beta = e^{i\phi}\sin\tfrac{\theta}{2}
    • 3× qubit trace (ψ, A, B)
    • H + CNOT preparation
    • Bell-basis measurement
    • X/Z correction gates

    Bloch θ ∈ [0, π], φ ∈ [0, 2π] · 6-step protocol · fidelity F = |⟨ψ|ψ_out⟩|²

    ⚠ classical correction link cut Initialize module →
  • 06 · Power electronics

    Closed-Loop Buck Converter

    Drive a PWM power stage across CCM, boundary, and discontinuous conduction.

    Frontier continuous-time averaged state space
    i˙L=DVin−voL,v˙o=iL−vo/RC\dot i_L = \dfrac{D V_{in}-v_o}{L},\quad \dot v_o = \dfrac{i_L-v_o/R}{C}
    • PWM feedback controller
    • PMOS high-side switch
    • Schottky freewheel diode
    • L–C output network

    V_in 5–36 V · f_sw 20–500 kHz · CCM / BCM / DCM classification

    ⚠ high-side MOSFET gate drive lost Initialize module →
  • 07 · Nonlinear dynamics

    Chua Double-Scroll Oscillator

    Tune a physical circuit through fixed points, limit cycles, and deterministic chaos.

    Frontier RK4 nonlinear ODE integration
    x˙=α(y−x−h(x)),y˙=x−y+z,z˙=−βy\dot x = \alpha(y-x-h(x)),\quad \dot y=x-y+z,\quad \dot z=-\beta y
    • piecewise-linear Chua diode
    • C₁ / C₂ energy stores
    • coupling resistor R
    • inductor current state

    α 7–18 · β 18–35 · bifurcation sweep on α

    ⚠ nonlinear negative-resistance branch bypassed Initialize module →
  • 08 · Control + RF

    Adaptive Clock-Recovery PLL

    Watch an integer-N synthesizer acquire, track, and lose phase lock.

    Frontier second-order phase-domain loop
    fout=Nfref,e¨+2ζωne˙+ωn2e=0f_{out}=Nf_{ref},\quad \ddot e + 2\zeta\omega_n\dot e + \omega_n^2e=0
    • phase/frequency detector
    • charge pump + loop filter
    • voltage-controlled oscillator
    • programmable ÷N feedback

    N 2–64 · loop bandwidth 0.2–8 kHz · lock threshold ±50 ppm

    ⚠ reference clock disconnected Initialize module →
  • 09 · UML statechart

    Live State Machine

    Fire events and watch a token walk the transitions of a running UML machine.

    Advanced event-driven finite-state executor
    δ:S×Σ→S  ⋅  (s,e)↦snext if guard(e)\delta : S \times \Sigma \rightarrow S \;\cdot\; (s, e) \mapsto s_{\text{next}} \text{ if guard}(e)
    • initial pseudostate
    • Red / Green / Yellow states
    • 4 guarded transitions
    • event queue + trace log

    deterministic δ · one active state · guarded, timed transitions

    ⚠ transition guard inverted (deadlock) Initialize module →
  • 10 · Quantum

    Quantum Error Correction

    Protect a qubit you are forbidden to read by measuring only disagreement.

    Frontier stabilizer parity + syndrome decoder
    ∣0⟩L=∣000⟩, ∣1⟩L=∣111⟩  ⋅  s=(q0⊕q1, q1⊕q2)|0\rangle_L = |000\rangle,\ |1\rangle_L = |111\rangle \;\cdot\; s = (q_0{\oplus}q_1,\ q_1{\oplus}q_2)
    • logical qubit → 3 physical
    • injectable X error
    • 2 ancilla syndrome bits
    • majority-vote decoder

    corrects any single bit-flip · syndrome ∈ {00,01,10,11} · logical fidelity 0/1

    ⚠ syndrome decoder miswired Initialize module →
  • 11 · Active analog

    Wien-Bridge Oscillator

    An amplifier with just enough positive feedback sings a pure tone out of noise.

    Advanced second-order loop with amplitude limiting
    f0=12πRC  ⋅  Aβ=1 (Barkhausen), gain =3f_0 = \dfrac{1}{2\pi RC} \;\cdot\; A\beta = 1 \text{ (Barkhausen), gain } = 3
    • op-amp gain stage
    • series + shunt RC bridge
    • R_f / R_g gain setting
    • amplitude-limiting element

    gain 2.8 – 3.2 · f₀ from RC · Hopf onset at gain = 3

    ⚠ gain-set resistor open (latch-up) Initialize module →
  • 12 · Sequential digital

    Maximal-Length LFSR

    Four flip-flops and one XOR make a stream that looks random but repeats after exactly 15.

    Advanced clocked shift register over GF(2)
    x4+x3+1  ⋅  period=2n−1=15x^4 + x^3 + 1 \;\cdot\; \text{period} = 2^n - 1 = 15
    • shared clock
    • 4× D flip-flop chain
    • XOR feedback taps 3,4
    • serial m-sequence output

    period 2⁴ − 1 = 15 · all-zero state forbidden · primitive polynomial taps

    ⚠ feedback tap moved (short cycle) Initialize module →
  • 13 · Quantum

    Grover 3-Qubit Search

    Rotate the whole haystack toward the needle — √N queries, not N.

    Frontier amplitude amplification over 8 states
    ∣s⟩→(D Uf)k∣s⟩,k≈π4N  ⋅  N=8|s\rangle \to (D\,U_f)^k|s\rangle,\quad k \approx \dfrac{\pi}{4}\sqrt{N} \;\cdot\; N = 8
    • 3-qubit uniform superposition
    • oracle U_f (phase flip)
    • diffusion 2|s⟩⟨s| − I
    • 8-state amplitude readout

    N = 8 search space · optimal k = 2 rounds · peak P(target) ≈ 0.945

    ⚠ oracle marks the wrong state Initialize module →