A sister instrument to Ephemera

CIRCUIT

A Quantum State Vector You Can Play.

|ψ⟩ = Σ cₖ|k⟩ → loudnessₖ = |cₖ|²

N qubits give 2^N partials. Reversible gates rearrange the spectrum; Grover steps amplify the partial you mark until a chord rings clean.

Open the state vector →Hear a Grover chord

Free in browser · play with QWERTY · hold Space to amplify

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 2^Namplitudes 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.

Grover

Grover · major triad

Press a key and root + third + fifth voice together, in tune - the marked chord auto-focuses to its cleanest Grover peak.

Test-drive →Grover

Grover amplification

6 qubits, one marked partial (#42). Each trigger applies one Grover iteration; peak audibility at k* = 6.

Test-drive →Entanglement

Bell-pair chord lock

Two qubits in |Φ+⟩. Partials 0 and 3 voice equally with zero phase difference - the simplest entanglement you can hear.

Test-drive →Entanglement

GHZ-3 triplet lock

Three qubits in (|000⟩+|111⟩)/√2. Partials 0 and 7 lock together - the three-qubit cousin of the Bell-pair chord.

Test-drive →Algorithm

Teleportation

Alice teleports a |+⟩ payload to Bob via the canonical Bennett 1993 circuit - fidelity = 1 EXACT, whatever the measurements draw.

Test-drive →Topological

Braid weave (Fibonacci)

One logical qubit woven by a cited 3-anyon Fibonacci braid. The two partials' balance morphs as the universal weave plays out.

Test-drive →

Not a quantum theme - quantum math

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.

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.

row per Break it

Perturb one gate entry and exactly one row turns red - tamper-isolated falsifiability, asserted surgically in CI.

Open the proof page →Browse the compendium

Try it first, own it later

One instrument, three doors.

Free Web

The full state-vector instrument in your browser. Play, shape the gates, and share a preset by link. No install, no account.

Launch in browser →

Desktop

$19.99

Native app. Offline. Real MIDI in, .mid export, CC-routable observables, lifetime updates.

Get the desktop app →

Ephemera Bundle

Included

Circuit ships free with Ephemera Premium, alongside its sibling instruments Poles and Wavefunction.

See Ephemera →

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.

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.

Open the state vector →See the proof