Visual play · Drag to choose and amplify a partial
Ephemera · Harmonic state-vector synth
CIRCUIT
Shape the chord. Move the harmonics.
|ψ⟩ = Σ cₖ|k⟩ → loudnessₖ = |cₖ|²
Build a chord from a harmonic state. Reversible gates rearrange its partials; Grover steps amplify the one you mark until a new color rings through. The state vector is the score, and you choose the moves.
The hero is a visual prelude. Open the instrument to play its sound.
The idea
Most synths add up sine waves. This one adds up a quantum state.
An additive synth is a bank of partials, each with its own loudness. Circuit takes that bank and makes it a state vector: the 2Namplitudes of N qubits, where each partial’s loudness is the Born-rule probability |amplitude|². Nothing about the sound is metaphor - the spectrum you hear is the state.
Because the state evolves under reversible gates, you don’t turn knobs - you apply operations. A Hadamard spreads a partial into a superposition; a Grover step amplifies the one you marked; a CNOT entangles two so their partials lock in phase. The grammar of quantum computing, played as a chord.
How it works
Four gestures, one quantum loop.
01noteOn → |ψ⟩
Press a key
QWERTY maps to the qubit register (or plug in a MIDI controller on desktop). A key prepares a state and voices its 2^N partials - the chord is the amplitudes.
02U·|ψ⟩
Apply a gate
Pick a preset or a mode and the gates rearrange the spectrum: Hadamard spreads, CNOT entangles, a phase gate tilts. Every gate is reversible, so no information - and no partial - is ever lost.
03(reflect·oracle)ᵏ
Hold Space to amplify
Each beat applies one Grover iteration, rotating amplitude toward the partial you marked. The chosen partial swells to its cleanest peak at k*, then recedes if you keep going.
04|amp|² → sound
Read the state
The visualization shows the live amplitude spectrum, the stabilizer generators, and the phrase ring. Shift-release does a projective measurement; the Born rule picks the outcome.
What's inside
A real quantum engine, tuned to be an instrument.
Amplitudes are the spectrum
Up to 256 partials voiced straight from a 2^N state vector - loudness is |amplitude|², the Born rule, with no mapping layer in between.
Reversible gate grammar
H, X, Y, Z, S, T, CNOT, CZ, SWAP, Toffoli - the universal Clifford+T set. Gates rearrange the spectrum without ever losing a partial.
Grover amplification, audible
Mark a chord and step Grover's algorithm; the marked partials rotate to a clean peak at k*, then recede. Amplitude amplification you can hear.
Entanglement you can play
Bell pairs and GHZ states lock partials into fixed phase relationships no independent gesture can reach - the simplest entanglement, voiced.
Live state readout
A three-layer canvas shows the amplitude spectrum, the stabilizer generators, and the phrase-progress ring - the state vector, drawn while it sounds.
MIDI in and out
Play the register from any controller and export what you played as a .mid (desktop). Route classical observables (⟨σz⟩, marked probability, Grover step) to other engines as CV or CC.
Start somewhere
Open a preset and play.
Each one drops you into the live instrument with its gates already loaded - from a single amplified partial to an entangled chord to a topological braid.
The sound is the proof, and the proof is checkable.
The same engine that voices the partials recomputes a battery of cited claims live. Open the proof page and there’s a Break it control that perturbs a single gate and turns exactly one row red - so you can watch the falsifiability work, in your browser.
32
cited proof rows
Each anchored to a paper and DOI - Grover, QFT, teleportation, Solovay-Kitaev, surface codes, Fibonacci braids.
≤1e-12
pinned tolerance
Every audible state has a closed-form anchor in the literature, checked against the live runtime path to substrate-ULP.
1
row per Break it
Perturb one gate entry and exactly one row turns red - tamper-isolated falsifiability, asserted surgically in CI.
One-time purchase · no subscriptions, ever · free forever in the browser
“A quantum computer rearranges amplitudes you can’t see. Here, the amplitudes arewhat you hear - so the algorithm isn’t simulated, it’s performed.”
The Circuit design note
FAQ
Questions, answered.
No. Press a key and a chord rings; hold Space and it brightens, then recedes. That's the whole loop. The gate names and the |amp|² labels are there if you're curious, but you never have to read them to play.
A quantum state vector, voiced as additive synthesis. N qubits give 2^N basis states; each one is a partial, and its loudness is exactly |amplitude|², the Born-rule probability. Reversible gates rearrange the amplitudes, so the spectrum is the state, live.
That's Grover's algorithm. Each press applies one Grover iteration, which rotates amplitude toward the partial you marked. The chosen partial swells toward a clean peak at the optimal step k*, then (because it's a rotation, not a ramp) overshoots and recedes if you keep going. You're hearing amplitude amplification.
Real. The same math that makes the sound is pinned against the literature on the /circuit/proof page: 32 cited proof rows, each anchored to a paper and a closed-form quantity to ≤1e-12. There's a Break it control that perturbs one gate and turns exactly one row red, so you can watch the falsifiability work.
Two keys held together can prepare an entangled pair (a Bell state) so their partials lock into a fixed phase relationship you can't get by playing them independently. The Bell-pair and GHZ presets start you there: partials voice equally with zero phase difference, the simplest entanglement you can hear.
The full Circuit instrument runs free in your browser. No account, no install. The native desktop build is a one-time $19.99 (and it's included if you own Ephemera Premium).
Offline use, real MIDI in (play the register from any controller) and .mid export of what you played, CC-routable observables you can patch to other engines, and lifetime updates. The web version covers everything else: play, shape the gates, and share a preset by link.
Yes, in modern mobile browsers. The state vector stays small (≤256 partials), so it's light; audio needs one tap to start (browsers require a gesture before they'll make sound). A keyboard makes the QWERTY → qubit mapping easier, but the on-screen keys work on touch.
Same team, same family of physics-first instruments. Poles plays the decay of a sound on the s-plane; Wavefunction plays a continuous quantum field collapsing under observation; Circuit plays the discrete, gate-driven state vector, the algorithms quadrant. All three began around Ephemera and ship free with Ephemera Premium.
Mark a partial. Hold Space. Hear it bloom.
The full quantum state-vector instrument runs free in your browser with no account, no install. Press a key and the amplitudes start to sound.
