Legato.jl

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A circuit isn't a sequence of gates. It's a unitary. Compile it as one.

Legato.jl is the circuit-to-pulse compilation layer of the Piccolo.jl ecosystem. Given a gate-level circuit and a hardware device profile, Legato synthesizes a single optimized control pulse that implements the whole circuit as one block unitary $U$ — skipping gate decomposition, scheduling, and gate-boundary error accumulation.

Why this is different

A conventional quantum compiler decomposes a circuit into native gates, schedules them, and lowers each gate to a precomputed pulse. That pipeline leaves pulse-level fidelity on the table — every gate boundary is a re-initialization, every idle qubit is accumulating decoherence, every decomposition hides joint optimization opportunities.

Legato treats the circuit as a unitary $U_\text{circ}$ and solves directly for a control pulse $u(t)$ on the device system $H_\text{sys}(u)$:

$$\begin{aligned} \min_{u(t),\,\varphi}\quad & 1 - \mathcal{F}\!\left(U_\text{circ},\, V_\varphi\, U(T;\,u)\right) \\\ \text{subject to}\quad & \dot{U}(t) = -i\,H_\text{sys}(u(t))\,U(t),\quad U(0) = I, \\\ & u_\text{min} \le u(t) \le u_\text{max}. \end{aligned}$$

$V_\varphi$ are per-qubit virtual-Z phases (free-phase). $\mathcal{F}$ is the Pedersen subspace fidelity on the computational levels.

	Conventional	Legato
Optimization unit	one gate	one block (or whole circuit)
Gate-boundary error	$N$ × per-gate error	one solve, no boundaries
Idle decoherence	every non-active qubit at every layer	actively driven through the block
Hardware coupling	hidden in decomposition	first-class — pulse uses the device's actual drift
Duration	$\sum$ gate durations + scheduling slack	min-time compressed against fidelity floor

Quick example

Cold-start a single-qubit X gate on a 2-level model of an IBM Heron r3 transmon:

using Random, Legato
Random.seed!(0xc0ffee)

device = HeronR3(n_levels = 2)         # qubit subspace; drop the kwarg for 3-level (with leakage)
circuit = GateCircuit([GateOp(:X, (1,))], 1)

report = compile(
    circuit, device;
    max_iter = 1500, T_ns = 60.0, N_knots = 21,
    Q = 100.0, R = 1e-4, ddu_bound = 10.0,
    free_phase = true,
)

Pulse fidelity  : 0.99283
Pulse duration  : 60.0 ns
Wall clock      : ~120 s on a workstation

The full runnable script is at scripts/x_heronr3_2level.jl.

For multi-qubit circuits or high-fidelity (≥ 5-nines) results, the substrate cold-start path isn't enough — install Strettissimo to enable parallel multistart, catalog warm-starts, and min-time compression. Public Legato lands you in the right basin; Strettissimo lands you at the bottom.

Compiling QEC blocks

The flagship use case: compile each block of a multi-block QEC circuit (e.g. surface-code syndrome extraction) once into a reusable pulse. Subsequent rounds reuse the cached pulse instead of re-decomposing.

report = compile(syndrome_circuit, device; strategy = :warm_stitch_transmon)

:warm_stitch_transmon (in Strettissimo, Harmoniqs' private competitive layer) does the full pipeline:

1. Transpile to native gates: to_native(circuit, device) — pure circuit rewriting, e.g. CNOT(c,t) → H(t)·CZ(c,t)·H(t).
2. Schedule the native gates serially (or with parallelization in v0.4+).
3. Stitch catalog pulses into a single warm-start pulse for the whole block.
4. Joint-solve the block as one optimization — eliminates gate-boundary errors, exploits the device drift.
5. Min-time compress against a fidelity floor.

What's where

Legato is a substrate that runs productively on small problems with no proprietary dependencies. Harmoniqs' competitive compilation intelligence lives in a private overlay package, Strettissimo.jl, which plugs in via Legato's strategy-registry seam:

Feature	Legato (public, MIT)	Strettissimo (private)
Circuit IR (GateCircuit, GateOp, circuit_unitary)	✅	—
Gate library (qft, toffoli, ccz, ...)	✅	—
Device profiles (HeronR3, Willow, Ankaa3, ...)	✅	—
to_native transpile pass	✅	—
compile_block substrate pipeline	✅	—
BilinearIntegrator (cold-start, 1-2Q)	✅ substrate	—
SplineIntegrator (multi-qubit scaling)	—	✅
Pulse catalog warm-starts	—	✅
Graph-based partitioning	—	✅
Parallel multistart solver	—	✅
QEC kernel compilation	thin entry point	✅ implementation
Stagnation / landscape diagnostics	—	✅

Legato users get a working substrate. Harmoniqs collaborators and NDA partners get the competitive layer.

Installation

using Pkg
Pkg.add("Legato")

For multi-qubit problems Legato's default BilinearIntegrator can exhaust memory during evaluator construction. Harmoniqs collaborators with access to Piccolissimo.jl can swap in a scalable spline-based integrator by loading Strettissimo, which auto-installs the override on __init__.

Status

Version	What ships
v0.2	Circuit IR, device profiles, compile_block, four substrate seams
v0.3	CompilationStrategy registry, select_strategy, :default strategy
v0.4	to_native(circuit, device) transpile pass
v0.5	Rename Stretto → Legato (re-registered under a new UUID)
v0.6 (planned)	QASM import
v0.7+	Framework adapters (Qiskit / Cirq via PythonCall)

Contributing

# Run substrate tests (no private deps)
julia --project=. test/runtests.jl

# Run with Piccolissimo for multi-qubit smoke tests
julia --project=. -e 'using Pkg; Pkg.develop(path="../Piccolissimo.jl")'
LEGATO_FULL_TESTS=1 julia --project=. test/runtests.jl

# Build docs
./docs/get_docs_utils.sh
julia --project=docs docs/make.jl

See also

• Piccolo.jl — the quantum optimal control engine Legato sits on top of.

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"Some people stretto. Some people wait."