Stim gate reference: all supported gates

Pauli Gates

Pauli gates apply the four fundamental single-qubit Pauli operations. They take no parenthesized arguments and accept one or more qubit targets.

Gate	Description	Stabilizer action
`I`	Identity — does nothing	X → X, Z → Z
`X`	Pauli X — bit flip	X → X, Z → −Z
`Y`	Pauli Y	X → −X, Z → −Z
`Z`	Pauli Z — phase flip	X → −X, Z → Z

# Apply X to qubit 5, then Y and Z to multiple qubits
X 5
Y 5 42
Z 0 1 2 3
I 99

Single-Qubit Clifford Gates

Single-qubit Clifford gates perform rotations within the single-qubit Clifford group. They take no parenthesized arguments and accept one or more qubit targets; when given multiple targets the gate is broadcast over each target in order.

Gate	Description
`H` / `H_XZ`	Hadamard — swaps X and Z axes
`H_XY`	Hadamard variant swapping X and Y
`H_YZ`	Hadamard variant swapping Y and Z
`H_NXZ`	Hadamard with negation on X and Z
`H_NXY`	Hadamard variant swapping −X and Y
`H_NYZ`	Hadamard variant swapping −Y and Z
`S` / `SQRT_Z`	S gate (phase gate) — 90° rotation around Z
`S_DAG` / `SQRT_Z_DAG`	S† — inverse of S
`SQRT_X`	90° rotation around X
`SQRT_X_DAG`	Inverse 90° rotation around X
`SQRT_Y`	90° rotation around Y
`SQRT_Y_DAG`	Inverse 90° rotation around Y
`C_XYZ`	Right-handed period-3 cycle X → Y → Z → X
`C_ZYX`	Left-handed period-3 cycle X → Z → Y → X
`C_NXYZ`	Period-3 cycle −X → Y → Z → −X
`C_NZYX`	Period-3 cycle X → −Z → Y → X
`C_XNYZ`	Period-3 cycle X → −Y → Z → X
`C_XYNZ`	Period-3 cycle X → Y → −Z → X
`C_ZNYX`	Period-3 cycle X → Z → −Y → X
`C_ZYNX`	Period-3 cycle X → −Z → −Y → X

# Hadamard on qubits 0, 1, 2
H 0 1 2

# S gate then its inverse (net identity up to global phase)
S 0
S_DAG 0

# Period-3 axis cycle
C_XYZ 5
C_ZYX 5

H, H_XZ, S, and SQRT_Z are aliases for the same operation. S_DAG and SQRT_Z_DAG are also aliases for each other.

Two-Qubit Clifford Gates

Two-qubit Clifford gates act on pairs of qubits. When given more than two targets they are broadcast over aligned pairs in order — CNOT 0 1 2 3 applies CNOT to (0,1) then (2,3). An odd number of targets is an error.

Gate	Description
`CNOT` / `CX` / `ZCX`	Controlled-X (controlled-NOT). Control qubit listed first.
`CY` / `ZCY`	Controlled-Y
`CZ` / `ZCZ`	Controlled-Z
`SWAP`	Swaps two qubits
`ISWAP`	SWAP with an extra iZ⊗Z phase
`ISWAP_DAG`	Inverse of ISWAP
`CXSWAP`	Applies CX then SWAP
`SWAPCX` / `CZSWAP`	Applies SWAP then CX
`SWAPCZ`	Applies SWAP then CZ
`SQRT_XX`	90° rotation in the XX plane
`SQRT_XX_DAG`	Inverse 90° rotation in the XX plane
`SQRT_YY`	90° rotation in the YY plane
`SQRT_YY_DAG`	Inverse 90° rotation in the YY plane
`SQRT_ZZ`	90° rotation in the ZZ plane
`SQRT_ZZ_DAG`	Inverse 90° rotation in the ZZ plane
`XCX`	X-controlled-X
`XCY`	X-controlled-Y
`XCZ`	X-controlled-Z
`YCX`	Y-controlled-X
`YCY`	Y-controlled-Y
`YCZ`	Y-controlled-Z
`II`	Two-qubit identity (does nothing)

# Apply CNOT to pairs (0,1) and (2,3)
CNOT 0 1 2 3

# Entangle and then swap
ISWAP 0 1
SWAP 0 1

# Controlled-Z between qubits 4 and 5
CZ 4 5

Noise Channels

Noise channels apply probabilistic errors. They take one probability argument inside parentheses, written as GATE(p) targets. They only have an effect during noisy simulation; they are no-ops in ideal stabilizer simulation unless the simulator is configured to include them.

Gate	Description
`X_ERROR(p)`	Apply X with probability `p`
`Y_ERROR(p)`	Apply Y with probability `p`
`Z_ERROR(p)`	Apply Z with probability `p`
`I_ERROR(p)`	Apply identity with probability `p` (vacuous)
`II_ERROR(p)`	Two-qubit identity error (vacuous)
`DEPOLARIZE1(p)`	Uniform single-qubit depolarizing channel: X, Y, or Z each with probability `p/3`
`DEPOLARIZE2(p)`	Uniform two-qubit depolarizing channel over all 15 non-identity Paulis
`PAULI_CHANNEL_1(px, py, pz)`	Single-qubit Pauli channel with explicit X, Y, Z probabilities
`PAULI_CHANNEL_2(pIX, pIY, pIZ, pXI, pXX, ...)`	Two-qubit Pauli channel with all 15 non-identity probabilities
`CORRELATED_ERROR(p) X0 Y1 Z2`	Apply the given Pauli product with probability `p`
`ELSE_CORRELATED_ERROR(p) ...`	Like `CORRELATED_ERROR` but conditioned on the preceding correlated error not having fired
`E(p) ...`	Alias for `CORRELATED_ERROR`
`HERALDED_ERASE(p)`	Erase qubit with probability `p`; always appends a herald measurement bit
`HERALDED_PAULI_CHANNEL_1(p_no, pX, pY, pZ)`	Heralded single-qubit Pauli channel; always appends a herald bit

# 0.1% two-qubit depolarizing noise after each CX
CX 0 1 2 3
DEPOLARIZE2(0.001) 0 1 2 3

# Custom Pauli channel: X error 1%, Z error 2%
PAULI_CHANNEL_1(0.01, 0, 0.02) 5

# Correlated error: X on qubit 0 and Z on qubit 1, with probability 0.5%
CORRELATED_ERROR(0.005) X0 Z1
ELSE_CORRELATED_ERROR(0.003) X0 Y1

PAULI_CHANNEL_2 requires exactly 15 probability arguments (one for each non-identity two-qubit Pauli). The probabilities must sum to at most 1.

Collapsing Gates (Measurements and Resets)

Collapsing gates measure and/or reset qubits. Measurement results are appended to the measurement record and can be referenced by subsequent instructions using rec[-n] targets. A ! prefix on a qubit target inverts the recorded result.Measurement gates

Gate	Basis	Resets?
`M` / `MZ`	Z	No
`MX`	X	No
`MY`	Y	No
`MR` / `MRZ`	Z	Yes
`MRX`	X	Yes
`MRY`	Y	Yes

Reset gates (no measurement result appended)

Gate	Resets to
`R` / `RZ`		0⟩ (Z basis)
`RX`		+⟩ (X basis)
`RY`		i⟩ (Y basis)

# Initialize, entangle, and measure in Z basis
R 0 1
H 0
CNOT 0 1
M 0 1

# Measure-and-reset in X basis, invert qubit 1's result
MRX 0 !1

# Feed-forward from measurement record
CZ rec[-1] 5

M and MZ are aliases. MR and MRZ are aliases. R and RZ are aliases.

Pair Measurement Gates

Pair measurement gates measure two-qubit Pauli products. Each pair of targets is measured as a joint observable.

Gate	Measured observable
`MXX`	X⊗X on each target pair
`MYY`	Y⊗Y on each target pair
`MZZ`	Z⊗Z on each target pair

# Measure XX parity of qubits 0 and 1
MXX 0 1

# Measure ZZ parities of (0,1) and (2,3)
MZZ 0 1 2 3

Generalized Pauli Product Gates

These gates apply or measure arbitrary Pauli products specified using Pauli targets (X0, Y1, Z2) joined by combiner tokens (*).

Gate	Description
`MPP`	Measure arbitrary Pauli product(s)
`SPP`	Apply the square root of a Pauli product
`SPP_DAG`	Apply the inverse square root of a Pauli product

# Measure the Pauli product X0*Y1*Z2
MPP X0*Y1*Z2

# Measure two independent products in one instruction
MPP X0*Z1 Y2*Y3

# Invert the result of the first product
MPP !X0*Z1 Y2*Y3

# Apply sqrt(X0*Z1) then its inverse
SPP X0*Z1
SPP_DAG X0*Z1

Annotations

Annotations carry metadata used for detection-event sampling, circuit drawing, and spacetime layout hinting. They have no effect on the quantum state or the measurement record.

Gate	Description
`DETECTOR(coords...)`	Declares a detection event defined by the XOR of the listed `rec[-n]` measurement results. Optional coordinate arguments hint at spacetime location.
`OBSERVABLE_INCLUDE(k)`	XORs the listed `rec[-n]` results into logical observable `k`.
`TICK`	Marks the boundary between time steps. Used for circuit drawing and timing hints.
`QUBIT_COORDS(x, y, ...)`	Annotates the spacetime coordinates of a qubit.
`SHIFT_COORDS(dx, dy, ...)`	Shifts the global coordinate offset, used inside `REPEAT` blocks.
`MPAD(bit)`	Appends a constant 0 or 1 to the measurement record without measuring a qubit.

# Label qubit positions for a surface code layout
QUBIT_COORDS(1, 1) 1
QUBIT_COORDS(2, 0) 2
QUBIT_COORDS(3, 1) 3

TICK
CX 0 1 2 3
TICK
MR 1 3

# Declare detector: fires if parity changed since last round
DETECTOR(1, 0) rec[-2] rec[-4]
DETECTOR(3, 0) rec[-1] rec[-3]

# Declare logical observable from qubit 0's measurement
OBSERVABLE_INCLUDE(0) rec[-1]

SHIFT_COORDS inside a REPEAT block accumulates the coordinate offset on each iteration, which keeps detector coordinates distinct across rounds without manually incrementing them.

Control Flow

Stim provides one control-flow construct: the REPEAT block.

Construct	Description
`REPEAT K { ... }`	Repeats the enclosed instructions exactly `K` times. `K` must be a positive integer (zero is not allowed).

# Run 1000 rounds of syndrome extraction
REPEAT 1000 {
    CX 0 1 2 3 4 5
    CX 2 1 4 3 6 5
    MR 1 3 5
    SHIFT_COORDS(0, 1)
    DETECTOR(1, 0) rec[-3] rec[-6]
    DETECTOR(3, 0) rec[-2] rec[-5]
    DETECTOR(5, 0) rec[-1] rec[-4]
}

A REPEAT 0 { ... } block is a syntax error. Vacuous repeat blocks are disallowed because they create ambiguity about whether logical observables and detectors declared inside the block exist.

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Stim gate reference: all supported gates

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