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Actions

Actions are what actually build the circuit — they apply a gate pipeline to one or more qubits or classical bits.

The general syntax is:

target -> gate_pipeline

Target types​

A named qubit​

alice : q 0
alice -> H

A direct qubit index (bare number)​

0 -> H

An explicit qubit reference (q N)​

q 0 -> H
q 0 -> CX(q 1)

An inline list​

[q 0, q 1] -> H

A named list​

pair : [q 0, q 1]
pair -> H

All qubits in the circuit (*)​

The * wildcard targets every qubit that has been added to the circuit so far:

q 0 -> H
q 1 -> X
* -> M   # measures both q0 and q1

This is the most common way to add a global measurement at the end of a circuit.

Inline gate pipelines​

Write a pipeline directly in the action without naming it first:

q 0 -> H  CX(q 1)

Using a named pipeline​

bell_prep : H  FCX(q 1)
q 0 -> bell_prep

Repeat count​

Prefix the pipeline with a number to repeat the action N times:

q 0 -> 3 X   # applies X three times (net identity for odd repeats)
q 0 -> 2 H   # applies H twice (returns to original state)

The repeat count sits between -> and the pipeline, and works with multi-gate pipelines and named instructions too:

prep : H  S
q 0 -> 4 prep   # runs H S four times

This also applies to classical bit operations:

b0 : b 0
b0 -> 3 SET(1)  # redundantly sets b0 to 1 three times

Reverse pipeline (<-)​

Append <- after a named pipeline to traverse it in the opposite direction:

diffuse_in : H  X

[q 0, q 1] -> diffuse_in          # forward:  H then X
[q 0, q 1] -> diffuse_in <-       # backward: X then H

This is the Spinach equivalent of applying the inverse (unitary adjoint) of a pipeline — essential for algorithms like Grover's diffuser.

Full example: Grover's algorithm (2 qubits)​

# Grover's Search — target state |11⟩
diffuse_in : H  X

# Uniform superposition
[q 0, q 1] -> H

# Oracle: phase flip on |11⟩
q 0 -> CZ(q 1)

# Diffuser: inversion about the mean
[q 0, q 1] -> diffuse_in
q 0 -> CZ(q 1)
[q 0, q 1] -> diffuse_in <-

* -> M