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Gates in Stim

General Facts

  • Qubit Targets: Qubits are referred to by non-negative integers. There is a qubit 0, a qubit 1, and so forth (up to an implemented-defined maximum of 16777215). For example, the line X 2 says to apply an X gate to qubit 2. Beware that touching qubit 999999 implicitly tells simulators to resize their internal state to accommodate a million qubits.

  • Measurement Record Targets: Measurement results are referred to by rec[-#] arguments, where the index within the square brackets uses python-style negative indices to refer to the end of the growing measurement record. For example, CNOT rec[-1] 3 says "toggle qubit 3 if the most recent measurement returned True and CZ 1 rec[-2] means "phase flip qubit 1 if the second most recent measurement returned True. There is implementation-defined maximum lookback of -16777215 when accessing the measurement record. Non-negative indices are not permitted.

    (The reason the measurement record indexing is relative to the present is so that it can be used in loops.)

  • Broadcasting: Most gates support broadcasting over multiple targets. For example, H 0 1 2 will broadcast a Hadamard gate over qubits 0, 1, and 2. Two qubit gates can also broadcast, and do so over aligned pair of targets. For example, CNOT 0 1 2 3 will apply CNOT 0 1 and then CNOT 2 3. Broadcasting is always evaluated in left-to-right order.

Supported Gates

Pauli Gates

  • I

    Identity gate. Does nothing to the target qubits.

    • Example:

      I 5
I 42
I 5 42

    • Stabilizer Generators:

      X -> +X
Z -> +Z

    • Bloch Rotation:

      Axis: 
Angle: 0 degrees

    • Unitary Matrix:

      [+1  ,     ]
[    , +1  ]

  • X

    Pauli X gate. The bit flip gate.

    • Example:

      X 5
X 42
X 5 42

    • Stabilizer Generators:

      X -> +X
Z -> -Z

    • Bloch Rotation:

      Axis: +X
Angle: 180 degrees

    • Unitary Matrix:

      [    , +1  ]
[+1  ,     ]

  • Y

    Pauli Y gate.

    • Example:

      Y 5
Y 42
Y 5 42

    • Stabilizer Generators:

      X -> -X
Z -> -Z

    • Bloch Rotation:

      Axis: +Y
Angle: 180 degrees

    • Unitary Matrix:

      [    ,   -i]
[  +i,     ]

  • Z

    Pauli Z gate. The phase flip gate.

    • Example:

      Z 5
Z 42
Z 5 42

    • Stabilizer Generators:

      X -> -X
Z -> +Z

    • Bloch Rotation:

      Axis: +Z
Angle: 180 degrees

    • Unitary Matrix:

      [+1  ,     ]
[    , -1  ]

Single Qubit Clifford Gates

  • C_XYZ

    Right handed period 3 axis cycling gate, sending X -> Y -> Z -> X.

    • Example:

      C_XYZ 5
C_XYZ 42
C_XYZ 5 42

    • Stabilizer Generators:

      X -> +Y
Z -> +X

    • Bloch Rotation:

      Axis: +X+Y+Z
Angle: 120 degrees

    • Unitary Matrix:

      [+1-i, -1-i]
[+1-i, +1+i] / 2

  • C_ZYX

    Left handed period 3 axis cycling gate, sending Z -> Y -> X -> Z.

    • Example:

      C_ZYX 5
C_ZYX 42
C_ZYX 5 42

    • Stabilizer Generators:

      X -> +Z
Z -> +Y

    • Bloch Rotation:

      Axis: +X+Y+Z
Angle: -120 degrees

    • Unitary Matrix:

      [+1+i, +1+i]
[-1+i, +1-i] / 2

  • H

    Alternate name: H_XZ

    The Hadamard gate. Swaps the X and Z axes.

    • Example:

      H 5
H 42
H 5 42

    • Stabilizer Generators:

      X -> +Z
Z -> +X

    • Bloch Rotation:

      Axis: +X+Z
Angle: 180 degrees

    • Unitary Matrix:

      [+1  , +1  ]
[+1  , -1  ] / sqrt(2)

  • H_XY

    A variant of the Hadamard gate that swaps the X and Y axes (instead of X and Z).

    • Example:

      H_XY 5
H_XY 42
H_XY 5 42

    • Stabilizer Generators:

      X -> +Y
Z -> -Z

    • Bloch Rotation:

      Axis: +X+Y
Angle: 180 degrees

    • Unitary Matrix:

      [    , +1-i]
[+1+i,     ] / sqrt(2)

  • H_YZ

    A variant of the Hadamard gate that swaps the Y and Z axes (instead of X and Z).

    • Example:

      H_YZ 5
H_YZ 42
H_YZ 5 42

    • Stabilizer Generators:

      X -> -X
Z -> +Y

    • Bloch Rotation:

      Axis: +Y+Z
Angle: 180 degrees

    • Unitary Matrix:

      [+1  ,   -i]
[  +i, -1  ] / sqrt(2)

  • S

    Alternate name: SQRT_Z

    Principal square root of Z gate. Phases the amplitude of |1> by i.

    • Example:

      S 5
S 42
S 5 42

    • Stabilizer Generators:

      X -> +Y
Z -> +Z

    • Bloch Rotation:

      Axis: +Z
Angle: 90 degrees

    • Unitary Matrix:

      [+1  ,     ]
[    ,   +i]

  • SQRT_X

    Principal square root of X gate. Phases the amplitude of |-> by i. Equivalent to H then S then H.

    • Example:

      SQRT_X 5
SQRT_X 42
SQRT_X 5 42

    • Stabilizer Generators:

      X -> +X
Z -> -Y

    • Bloch Rotation:

      Axis: +X
Angle: 90 degrees

    • Unitary Matrix:

      [+1+i, +1-i]
[+1-i, +1+i] / 2

  • SQRT_X_DAG

    Adjoint of the principal square root of X gate. Phases the amplitude of |-> by -i. Equivalent to H then S_DAG then H.

    • Example:

      SQRT_X_DAG 5
SQRT_X_DAG 42
SQRT_X_DAG 5 42

    • Stabilizer Generators:

      X -> +X
Z -> +Y

    • Bloch Rotation:

      Axis: +X
Angle: -90 degrees

    • Unitary Matrix:

      [+1-i, +1+i]
[+1+i, +1-i] / 2

  • SQRT_Y

    Principal square root of Y gate. Phases the amplitude of |-i> by i. Equivalent to S then H then S then H then S_DAG.

    • Example:

      SQRT_Y 5
SQRT_Y 42
SQRT_Y 5 42

    • Stabilizer Generators:

      X -> -Z
Z -> +X

    • Bloch Rotation:

      Axis: +Y
Angle: 90 degrees

    • Unitary Matrix:

      [+1+i, -1-i]
[+1+i, +1+i] / 2

  • SQRT_Y_DAG

    Adjoint of the principal square root of Y gate. Phases the amplitude of |-i> by -i. Equivalent to S then H then S_DAG then H then S_DAG.

    • Example:

      SQRT_Y_DAG 5
SQRT_Y_DAG 42
SQRT_Y_DAG 5 42

    • Stabilizer Generators:

      X -> +Z
Z -> -X

    • Bloch Rotation:

      Axis: +Y
Angle: -90 degrees

    • Unitary Matrix:

      [+1-i, +1-i]
[-1+i, +1-i] / 2

  • S_DAG

    Alternate name: SQRT_Z_DAG

    Adjoint of the principal square root of Z gate. Phases the amplitude of |1> by -i.

    • Example:

      S_DAG 5
S_DAG 42
S_DAG 5 42

    • Stabilizer Generators:

      X -> -Y
Z -> +Z

    • Bloch Rotation:

      Axis: +Z
Angle: -90 degrees

    • Unitary Matrix:

      [+1  ,     ]
[    ,   -i]

Two Qubit Clifford Gates

  • CX

    Alternate name: ZCX

    Alternate name: CNOT

    The Z-controlled X gate. First qubit is the control, second qubit is the target. The first qubit can be replaced by a measurement record.

    Applies an X gate to the target if the control is in the |1> state.

    Negates the amplitude of the |1>|-> state.

    • Example:

      CX 5 6
CX 42 43
CX 5 6 42 43
CX rec[-1] 111

    • Stabilizer Generators:

      X_ -> +XX
Z_ -> +Z_
_X -> +_X
_Z -> +ZZ

    • Unitary Matrix:

      [+1  ,     ,     ,     ]
[    ,     ,     , +1  ]
[    ,     , +1  ,     ]
[    , +1  ,     ,     ]

  • CY

    Alternate name: ZCY

    The Z-controlled Y gate. First qubit is the control, second qubit is the target. The first qubit can be replaced by a measurement record.

    Applies a Y gate to the target if the control is in the |1> state.

    Negates the amplitude of the |1>|-i> state.

    • Example:

      CY 5 6
CY 42 43
CY 5 6 42 43
CY rec[-1] 111

    • Stabilizer Generators:

      X_ -> +XY
Z_ -> +Z_
_X -> +ZX
_Z -> +ZZ

    • Unitary Matrix:

      [+1  ,     ,     ,     ]
[    ,     ,     ,   -i]
[    ,     , +1  ,     ]
[    ,   +i,     ,     ]

  • CZ

    Alternate name: ZCZ

    The Z-controlled Z gate. First qubit is the control, second qubit is the target. Either qubit can be replaced by a measurement record.

    Applies a Z gate to the target if the control is in the |1> state.

    Negates the amplitude of the |1>|1> state.

    • Example:

      CZ 5 6
CZ 42 43
CZ 5 6 42 43
CZ rec[-1] 111
CZ 111 rec[-1]

    • Stabilizer Generators:

      X_ -> +XZ
Z_ -> +Z_
_X -> +ZX
_Z -> +_Z

    • Unitary Matrix:

      [+1  ,     ,     ,     ]
[    , +1  ,     ,     ]
[    ,     , +1  ,     ]
[    ,     ,     , -1  ]

  • ISWAP

    Swaps two qubits and phases the -1 eigenspace of the ZZ observable by i. Equivalent to SWAP then CZ then S on both targets.

    • Example:

      ISWAP 5 6
ISWAP 42 43
ISWAP 5 6 42 43

    • Stabilizer Generators:

      X_ -> +ZY
Z_ -> +_Z
_X -> +YZ
_Z -> +Z_

    • Unitary Matrix:

      [+1  ,     ,     ,     ]
[    ,     ,   +i,     ]
[    ,   +i,     ,     ]
[    ,     ,     , +1  ]

  • ISWAP_DAG

    Swaps two qubits and phases the -1 eigenspace of the ZZ observable by -i. Equivalent to SWAP then CZ then S_DAG on both targets.

    • Example:

      ISWAP_DAG 5 6
ISWAP_DAG 42 43
ISWAP_DAG 5 6 42 43

    • Stabilizer Generators:

      X_ -> -ZY
Z_ -> +_Z
_X -> -YZ
_Z -> +Z_

    • Unitary Matrix:

      [+1  ,     ,     ,     ]
[    ,     ,   -i,     ]
[    ,   -i,     ,     ]
[    ,     ,     , +1  ]

  • SQRT_XX

    Phases the -1 eigenspace of the XX observable by i.

    • Example:

      SQRT_XX 5 6
SQRT_XX 42 43
SQRT_XX 5 6 42 43

    • Stabilizer Generators:

      X_ -> +X_
Z_ -> -YX
_X -> +_X
_Z -> -XY

    • Unitary Matrix:

      [+1+i,     ,     , +1-i]
[    , +1+i, +1-i,     ]
[    , +1-i, +1+i,     ]
[+1-i,     ,     , +1+i] / 2

  • SQRT_XX_DAG

    Phases the -1 eigenspace of the XX observable by -i.

    • Example:

      SQRT_XX_DAG 5 6
SQRT_XX_DAG 42 43
SQRT_XX_DAG 5 6 42 43

    • Stabilizer Generators:

      X_ -> +X_
Z_ -> +YX
_X -> +_X
_Z -> +XY

    • Unitary Matrix:

      [+1-i,     ,     , +1+i]
[    , +1-i, +1+i,     ]
[    , +1+i, +1-i,     ]
[+1+i,     ,     , +1-i] / 2

  • SQRT_YY

    Phases the -1 eigenspace of the YY observable by i.

    • Example:

      SQRT_YY 5 6
SQRT_YY 42 43
SQRT_YY 5 6 42 43

    • Stabilizer Generators:

      X_ -> -ZY
Z_ -> +XY
_X -> -YZ
_Z -> +YX

    • Unitary Matrix:

      [+1+i,     ,     , -1+i]
[    , +1+i, +1-i,     ]
[    , +1-i, +1+i,     ]
[-1+i,     ,     , +1+i] / 2

  • SQRT_YY_DAG

    Phases the -1 eigenspace of the YY observable by -i.

    • Example:

      SQRT_YY_DAG 5 6
SQRT_YY_DAG 42 43
SQRT_YY_DAG 5 6 42 43

    • Stabilizer Generators:

      X_ -> +ZY
Z_ -> -XY
_X -> +YZ
_Z -> -YX

    • Unitary Matrix:

      [+1-i,     ,     , -1-i]
[    , +1-i, +1+i,     ]
[    , +1+i, +1-i,     ]
[-1-i,     ,     , +1-i] / 2

  • SQRT_ZZ

    Phases the -1 eigenspace of the ZZ observable by i.

    • Example:

      SQRT_ZZ 5 6
SQRT_ZZ 42 43
SQRT_ZZ 5 6 42 43

    • Stabilizer Generators:

      X_ -> +YZ
Z_ -> +Z_
_X -> +ZY
_Z -> +_Z

    • Unitary Matrix:

      [+1  ,     ,     ,     ]
[    ,   +i,     ,     ]
[    ,     ,   +i,     ]
[    ,     ,     , +1  ]

  • SQRT_ZZ_DAG

    Phases the -1 eigenspace of the ZZ observable by -i.

    • Example:

      SQRT_ZZ_DAG 5 6
SQRT_ZZ_DAG 42 43
SQRT_ZZ_DAG 5 6 42 43

    • Stabilizer Generators:

      X_ -> -YZ
Z_ -> +Z_
_X -> -ZY
_Z -> +_Z

    • Unitary Matrix:

      [+1  ,     ,     ,     ]
[    ,   -i,     ,     ]
[    ,     ,   -i,     ]
[    ,     ,     , +1  ]

  • SWAP

    Swaps two qubits.

    • Example:

      SWAP 5 6
SWAP 42 43
SWAP 5 6 42 43

    • Stabilizer Generators:

      X_ -> +_X
Z_ -> +_Z
_X -> +X_
_Z -> +Z_

    • Unitary Matrix:

      [+1  ,     ,     ,     ]
[    ,     , +1  ,     ]
[    , +1  ,     ,     ]
[    ,     ,     , +1  ]

  • XCX

    The X-controlled X gate. First qubit is the control, second qubit is the target.

    Applies an X gate to the target if the control is in the |-> state.

    Negates the amplitude of the |->|-> state.

    • Example:

      XCX 5 6
XCX 42 43
XCX 5 6 42 43

    • Stabilizer Generators:

      X_ -> +X_
Z_ -> +ZX
_X -> +_X
_Z -> +XZ

    • Unitary Matrix:

      [+1  , +1  , +1  , -1  ]
[+1  , +1  , -1  , +1  ]
[+1  , -1  , +1  , +1  ]
[-1  , +1  , +1  , +1  ] / 2

  • XCY

    The X-controlled Y gate. First qubit is the control, second qubit is the target.

    Applies a Y gate to the target if the control is in the |-> state.

    Negates the amplitude of the |->|-i> state.

    • Example:

      XCY 5 6
XCY 42 43
XCY 5 6 42 43

    • Stabilizer Generators:

      X_ -> +X_
Z_ -> +ZY
_X -> +XX
_Z -> +XZ

    • Unitary Matrix:

      [+1  , +1  ,   -i,   +i]
[+1  , +1  ,   +i,   -i]
[  +i,   -i, +1  , +1  ]
[  -i,   +i, +1  , +1  ] / 2

  • XCZ

    The X-controlled Z gate. First qubit is the control, second qubit is the target. The second qubit can be replaced by a measurement record.

    Applies a Z gate to the target if the control is in the |-> state.

    Negates the amplitude of the |->|1> state.

    • Example:

      XCZ 5 6
XCZ 42 43
XCZ 5 6 42 43
XCZ 111 rec[-1]

    • Stabilizer Generators:

      X_ -> +X_
Z_ -> +ZZ
_X -> +XX
_Z -> +_Z

    • Unitary Matrix:

      [+1  ,     ,     ,     ]
[    , +1  ,     ,     ]
[    ,     ,     , +1  ]
[    ,     , +1  ,     ]

  • YCX

    The Y-controlled X gate. First qubit is the control, second qubit is the target.

    Applies an X gate to the target if the control is in the |-i> state.

    Negates the amplitude of the |-i>|-> state.

    • Example:

      YCX 5 6
YCX 42 43
YCX 5 6 42 43

    • Stabilizer Generators:

      X_ -> +XX
Z_ -> +ZX
_X -> +_X
_Z -> +YZ

    • Unitary Matrix:

      [+1  ,   -i, +1  ,   +i]
[  +i, +1  ,   -i, +1  ]
[+1  ,   +i, +1  ,   -i]
[  -i, +1  ,   +i, +1  ] / 2

  • YCY

    The Y-controlled Y gate. First qubit is the control, second qubit is the target.

    Applies a Y gate to the target if the control is in the |-i> state.

    Negates the amplitude of the |-i>|-i> state.

    • Example:

      YCY 5 6
YCY 42 43
YCY 5 6 42 43

    • Stabilizer Generators:

      X_ -> +XY
Z_ -> +ZY
_X -> +YX
_Z -> +YZ

    • Unitary Matrix:

      [+1  ,   -i,   -i, +1  ]
[  +i, +1  , -1  ,   -i]
[  +i, -1  , +1  ,   -i]
[+1  ,   +i,   +i, +1  ] / 2

  • YCZ

    The Y-controlled Z gate. First qubit is the control, second qubit is the target. The second qubit can be replaced by a measurement record.

    Applies a Z gate to the target if the control is in the |-i> state.

    Negates the amplitude of the |-i>|1> state.

    • Example:

      YCZ 5 6
YCZ 42 43
YCZ 5 6 42 43
YCZ 111 rec[-1]

    • Stabilizer Generators:

      X_ -> +XZ
Z_ -> +ZZ
_X -> +YX
_Z -> +_Z

    • Unitary Matrix:

      [+1  ,     ,     ,     ]
[    , +1  ,     ,     ]
[    ,     ,     ,   -i]
[    ,     ,   +i,     ]

Noise Channels

  • DEPOLARIZE1

    The single qubit depolarizing channel.

    Applies a randomly chosen Pauli with a given probability.

    Pauli Mixture:

      ```
  1-p: I
  p/3: X
  p/3: Y
  p/3: Z
  ```

    • Example:

      DEPOLARIZE1(0.001) 5
DEPOLARIZE1(0.001) 42
DEPOLARIZE1(0.001) 5 42

  • DEPOLARIZE2

    The two qubit depolarizing channel.

    Applies a randomly chosen two-qubit Pauli product with a given probability.

    Pauli Mixture:

      ```
   1-p: II
  p/15: IX
  p/15: IY
  p/15: IZ
  p/15: XI
  p/15: XX
  p/15: XY
  p/15: XZ
  p/15: YI
  p/15: YX
  p/15: YY
  p/15: YZ
  p/15: ZI
  p/15: ZX
  p/15: ZY
  p/15: ZZ
  ```

    • Example:

      DEPOLARIZE2(0.001) 5 6
DEPOLARIZE2(0.001) 42 43
DEPOLARIZE2(0.001) 5 6 42 43

  • E

    Alternate name: CORRELATED_ERROR

    Probabilistically applies a Pauli product error with a given probability. Sets the "correlated error occurred flag" to true if the error occurred. Otherwise sets the flag to false.

    See also: ELSE_CORRELATED_ERROR.

    • Example:

      # With 40% probability, uniformly pick X1*Y2 or Z2*Z3 or X1*Y2*Z3.
CORRELATED_ERROR(0.2) X1 Y2
ELSE_CORRELATED_ERROR(0.25) Z2 Z3
ELSE_CORRELATED_ERROR(0.33333333333) X1 Y2 Z3

  • ELSE_CORRELATED_ERROR

    Probabilistically applies a Pauli product error with a given probability, unless the "correlated error occurred flag" is set. If the error occurs, sets the "correlated error occurred flag" to true. Otherwise leaves the flag alone.

    See also: CORRELATED_ERROR.

    • Example:

      # With 40% probability, uniformly pick X1*Y2 or Z2*Z3 or X1*Y2*Z3.
CORRELATED_ERROR(0.2) X1 Y2
ELSE_CORRELATED_ERROR(0.25) Z2 Z3
ELSE_CORRELATED_ERROR(0.33333333333) X1 Y2 Z3

  • X_ERROR

    Applies a Pauli X with a given probability.

    Pauli Mixture:

      ```
  1-p: I
   p : X
  ```

    • Example:

      X_ERROR(0.001) 5
X_ERROR(0.001) 42
X_ERROR(0.001) 5 42

  • Y_ERROR

    Applies a Pauli Y with a given probability.

    Pauli Mixture:

      ```
  1-p: I
   p : Y
  ```

    • Example:

      Y_ERROR(0.001) 5
Y_ERROR(0.001) 42
Y_ERROR(0.001) 5 42

  • Z_ERROR

    Applies a Pauli Z with a given probability.

    Pauli Mixture:

      ```
  1-p: I
   p : Z
  ```

    • Example:

      Z_ERROR(0.001) 5
Z_ERROR(0.001) 42
Z_ERROR(0.001) 5 42

Collapsing Gates

  • M

    Alternate name: MZ

    Z-basis measurement. Projects each target qubit into |0> or |1> and reports its value (false=|0>, true=|1>). Prefixing a target with ! inverts its recorded measurement result.

    • Example:

      M 5
M !42
M 5 !42

    • Stabilizer Generators:

      Z -> m
Z -> +Z

  • MR

    Alternate name: MRZ

    Z-basis demolition measurement. Projects each target qubit into |0> or |1>, reports its value (false=|0>, true=|1>), then resets to |0>. Prefixing a target with ! inverts its recorded measurement result.

    • Example:

      MR 5
MR !42
MR 5 !42

    • Stabilizer Generators:

      Z -> m
1 -> +Z

  • MRX

    X-basis demolition measurement. Projects each target qubit into |+> or |->, reports its value (false=|+>, true=|->), then resets to |+>. Prefixing a target with ! inverts its recorded measurement result.

    • Example:

      MRX 5
MRX !42
MRX 5 !42

    • Stabilizer Generators:

      X -> m
1 -> +X

  • MRY

    Y-basis demolition measurement. Projects each target qubit into |i> or |-i>, reports its value (false=|i>, true=|-i>), then resets to |i>. Prefixing a target with ! inverts its recorded measurement result.

    • Example:

      MRY 5
MRY !42
MRY 5 !42

    • Stabilizer Generators:

      Y -> m
1 -> +Y

  • MX

    X-basis measurement. Projects each target qubit into |+> or |-> and reports its value (false=|+>, true=|->). Prefixing a target with ! inverts its recorded measurement result.

    • Example:

      MX 5
MX !42
MX 5 !42

    • Stabilizer Generators:

      X -> m
X -> +X

  • MY

    Y-basis measurement. Projects each target qubit into |i> or |-i> and reports its value (false=|i>, true=|-i>). Prefixing a target with ! inverts its recorded measurement result.

    • Example:

      MY 5
MY !42
MY 5 !42

    • Stabilizer Generators:

      Y -> m
Y -> +Y

  • R

    Alternate name: RZ

    Z-basis reset. Forces each target qubit into the |0> state by silently measuring it in the Z basis and applying an X gate if it ended up in the |1> state.

    • Example:

      R 5
R 42
R 5 42

    • Stabilizer Generators:

      1 -> +Z

  • RX

    X-basis reset. Forces each target qubit into the |+> state by silently measuring it in the X basis and applying a Z gate if it ended up in the |-> state.

    • Example:

      RX 5
RX 42
RX 5 42

    • Stabilizer Generators:

      1 -> +X

  • RY

    Y-basis reset. Forces each target qubit into the |i> state by silently measuring it in the Y basis and applying an X gate if it ended up in the |-i> state.

    • Example:

      RY 5
RY 42
RY 5 42

    • Stabilizer Generators:

      1 -> +Y

Control Flow

  • REPEAT

    Repeats the instructions in its body N times. The implementation-defined maximum value of N is 9223372036854775807.

    • Example:

      REPEAT 2 {
    CNOT 0 1
    CNOT 2 1
    M 1
}
REPEAT 10000000 {
    CNOT 0 1
    CNOT 2 1
    M 1
    DETECTOR rec[-1] rec[-3]
}

Annotations

  • DETECTOR

    Annotates that a set of measurements have a deterministic result, which can be used to detect errors.

    Detectors are ignored in measurement sampling mode. In detector sampling mode, detectors produce results (false=expected parity, true=incorrect parity detected).

    • Example:

      H 0
CNOT 0 1
M 0 1
DETECTOR rec[-1] rec[-2]

  • OBSERVABLE_INCLUDE

    Adds measurement results to a given logical observable index.

    A logical observable's measurement result is the parity of all physical measurement results added to it.

    A logical observable is similar to a Detector, except the measurements making up an observable can be built up incrementally over the entire circuit.

    Logical observables are ignored in measurement sampling mode. In detector sampling mode, observables produce results (false=expected parity, true=incorrect parity detected). These results are optionally appended to the detector results, depending on simulator arguments / command line flags.

    • Example:

      H 0
CNOT 0 1
M 0 1
OBSERVABLE_INCLUDE(5) rec[-1] rec[-2]

  • TICK

    Indicates the end of a layer of gates, or that time is advancing. For example, used by stimcirq to preserve the moment structure of cirq circuits converted to/from stim circuits.

    • Example:

      TICK
TICK
# Oh, and of course:
TICK