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Stim v1.5 Gate Reference

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Craig Gidney edited this page Jul 28, 2021 · 1 revision

Gates supported by Stim

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

    Principle 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

    Principle 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 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

    Principle 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

    Principle 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

    Principle 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

  • PAULI_CHANNEL_1

    A single qubit Pauli error channel with explicitly specified probabilities for each case.

    The gate is parameterized by 3 disjoint probabilities, one for each Pauli other than I, ordered as follows:

      X, Y, Z

    • Example:

      # Sample errors from the distribution 10% X, 15% Y, 20% Z, 55% I.
# Apply independently to qubits 1, 2, 4.
PAULI_CHANNEL_1(0.1, 0.15, 0.2) 1 2 4

    • Pauli Mixture:

      1-px-py-pz: I
px: X
py: Y
pz: Z

  • PAULI_CHANNEL_2

    A two qubit Pauli error channel with explicitly specified probabilities for each case.

    The gate is parameterized by 15 disjoint probabilities, one for each Pauli pair other than II, ordered as follows:

      IX, IY, IZ, XI, XX, XY, XZ, YI, YX, YY, XZ, ZI, ZX, ZY, ZZ

    • Example:

      # Sample errors from the distribution 10% XX, 20% YZ, 70% II.
# Apply independently to qubit pairs (1,2) (5,6) (8,3)
PAULI_CHANNEL_2(0,0,0, 0.1,0,0,0, 0,0,0,0.2, 0,0,0,0) 1 2 5 6 8 3

    • Pauli Mixture:

      1-pix-piy-piz-pxi-pxx-pxy-pxz-pyi-pyx-pyy-pyz-pzi-pzx-pzy-pzz: II
pix: IX
piy: IY
piz: IZ
pxi: XI
pxx: XX
pxy: XY
pxz: XZ
pyi: YI
pyx: YX
pyy: YY
pyz: XZ
pzi: ZI
pzx: ZX
pzy: ZY
pzz: ZZ

  • 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 (optionally noisy). Projects each target qubit into |0> or |1> and reports its value (false=|0>, true=|1>). If this gate is parameterized by a probability argument, the recorded result will be flipped with that probability. If not, the recorded result is noiseless. Note that the noise only affects the recorded result, not the target qubit's state.

    Prefixing a target with ! inverts its recorded measurement result.

    • Example:

      M 5
M !42
M(0.001) 5 !42

    • Stabilizer Generators:

      Z -> m xor chance(p)
Z -> +Z

  • MPP

    Measure Pauli products.

    • Example:

      MPP X1*Y2           # Join products using '*'
MPP X1*Y2 Z3*Z4     # Separate products using spaces with no '*'.
MPP !Z5             # Negate products (invert results) using '!'.
MPP !Z5*X4
MPP(0.001) Z1*Z2*Z3 # Add result noise using a probability argument.

    If this gate is parameterized by a probability argument, the recorded result will be flipped with that probability. If not, the recorded result is noiseless. Note that the noise only affects the recorded result, not the target qubit's state.

    Prefixing a target with ! inverts its recorded measurement result.

    • Stabilizer Generators:

      P -> m xor chance(p)
P -> P

  • MR

    Alternate name: MRZ

    Z-basis demolition measurement (optionally noisy). Projects each target qubit into |0> or |1>, reports its value (false=|0>, true=|1>), then resets to |0>. If this gate is parameterized by a probability argument, the recorded result will be flipped with that probability. If not, the recorded result is noiseless. Note that the noise only affects the recorded result, not the target qubit's state.

    Prefixing a target with ! inverts its recorded measurement result.

    • Example:

      MR 5
MR !42
MR(0.001) 5 !42

    • Stabilizer Generators:

      Z -> m xor chance(p)
1 -> +Z

  • MRX

    X-basis demolition measurement (optionally noisy). Projects each target qubit into |+> or |->, reports its value (false=|+>, true=|->), then resets to |+>. If this gate is parameterized by a probability argument, the recorded result will be flipped with that probability. If not, the recorded result is noiseless. Note that the noise only affects the recorded result, not the target qubit's state.

    Prefixing a target with ! inverts its recorded measurement result.

    • Example:

      MRX 5
MRX !42
MRX(0.001) 5 !42

    • Stabilizer Generators:

      X -> m xor chance(p)
1 -> +X

  • MRY

    Y-basis demolition measurement (optionally noisy). Projects each target qubit into |i> or |-i>, reports its value (false=|i>, true=|-i>), then resets to |i>. If this gate is parameterized by a probability argument, the recorded result will be flipped with that probability. If not, the recorded result is noiseless. Note that the noise only affects the recorded result, not the target qubit's state.

    Prefixing a target with ! inverts its recorded measurement result.

    • Example:

      MRY 5
MRY !42
MRY(0.001) 5 !42

    • Stabilizer Generators:

      Y -> m xor chance(p)
1 -> +Y

  • MX

    X-basis measurement (optionally noisy). Projects each target qubit into |+> or |-> and reports its value (false=|+>, true=|->). If this gate is parameterized by a probability argument, the recorded result will be flipped with that probability. If not, the recorded result is noiseless. Note that the noise only affects the recorded result, not the target qubit's state.

    Prefixing a target with ! inverts its recorded measurement result.

    • Example:

      MX 5
MX !42
MX(0.001) 5 !42

    • Stabilizer Generators:

      X -> +m xor chance(p)
X -> +X

  • MY

    Y-basis measurement (optionally noisy). Projects each target qubit into |i> or |-i> and reports its value (false=|i>, true=|-i>). If this gate is parameterized by a probability argument, the recorded result will be flipped with that probability. If not, the recorded result is noiseless. Note that the noise only affects the recorded result, not the target qubit's state.

    Prefixing a target with ! inverts its recorded measurement result.

    • Example:

      MY 5
MY !42
MY(0.001) 5 !42

    • Stabilizer Generators:

      Y -> m xor chance(p)
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. N can be any positive integer from 1 to a quintillion (10^18).

    Currently, repetition counts of 0 are not allowed because they create corner cases with ambiguous resolutions. For example, if a logical observable is only given measurements inside a repeat block with a repetition count of 0, it's ambiguous whether the output of sampling the logical observables includes a bit for that logical observable.

    • 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).

    Detectors can optionally be parameterized by coordinates (e.g. DETECTOR(1,2) has coordinates 1,2). These coordinates aren't really used for anything in stim, but can act as drawing hints for other tools. Note that the coordinates are relative to accumulated coordinate shifts from SHIFT_COORDS instructions. Also note that putting two detectors at the same coordinate does not fuse them into one detector (beware that OBSERVABLE_INCLUDE does fuse observables at the same index, which looks very similar). See SHIFT_COORDS for more details on using coordinates.

    Note that detectors are always defined with respect to noiseless behavior. For example, placing an X gate before a measurement cannot create detection events on detectors that include that measurement, but placing an X_ERROR(1) does create detection events.

    • 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.

    Note that observables are always defined with respect to noiseless behavior. For example, placing an X gate before a measurement cannot flip a logical observable that includes that measurement, but placing an X_ERROR(1) does flip the observable. This is because observables are used for detecting errors, not for verifying noiseless functionality.

    Note that observable indices are NOT shifted by SHIFT_COORDS.

    • Example:

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

  • QUBIT_COORDS

    An annotation used to indicate the intended location of a qubit. The coordinates are double precision floating point numbers, relative to accumulated offsets from SHIFT_COORDS. The coordinates are not in any particular order or number of dimensions. As far as stim is concerned the coordinates are a list of opaque and mysterious numbers. They have no effect on simulations of the circuit, but are potentially useful for tasks such as drawing the circuit.

    See also: SHIFT_COORDS.

    Note that a qubit's coordinates can be specified multiple times. The intended interpretation is that the qubit is at the location of the most recent assignment. For example, this could be used to indicate a simulated qubit is iteratively playing the role of many physical qubits.

    • Example:

      QUBIT_COORDS(100, 101) 0
QUBIT_COORDS(100, 101) 1
SQRT_XX 0 1
MR 0 1
QUBIT_COORDS(2.5, 3.5) 2  # Floating point coordinates are allowed.
QUBIT_COORDS(2.5, 4.5) 1  # Hint that qubit 1 is now referring to a different physical location.
SQRT_XX 1 2
M 1 2

  • SHIFT_COORDS

    Accumulates offsets to apply to qubit coordinates and detector coordinates.

    See also: QUBIT_COORDS, DETECTOR.

    Note: when qubit/detector coordinates use fewer dimensions than SHIFT_COORDS, the offsets from the additional dimensions are ignored (i.e. not specifying a dimension is different from specifying it to be 0).

    • Example:

      SHIFT_COORDS(500.5)
QUBIT_COORDS(1510) 0  # Actually at 2010.5
SHIFT_COORDS(1500)
QUBIT_COORDS(11) 1    # Actually at 2011.5
QUBIT_COORDS(10.5) 2  # Actually at 2011.0
REPEAT 1000 {
    CNOT 0 2
    CNOT 1 2
    MR 2
    DETECTOR(10.5, 0) rec[-1] rec[-2]  # Actually at (2011.0, iteration_count).
    SHIFT_COORDS(0, 1)  # Advance 2nd coordinate to track loop iterations.
}

  • 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
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