Measure instruction

A measure instruction performs a measurement to its qubit argument and assigns the outcome to a bit variable.

The measure instruction can either

  • have no parameters measure, which corresponds to a measurement in the Z-basis, or
  • accept 3 floating-point parameters measure(0,0,1), which define the axis of the basis along which the measurement is to be performed.

Note

measure(0,0,1) is equal to the non-parameterized measure as \((0,0,1)\) defines the positive \(z\)-axis.

The general form of a measure instruction is as follows:

 bit-argument = measure qubit-argument
 bit-argument = measure(parameter-list) qubit-argument

Grammar for measure instruction

measure-instruction:
  bit-argument = measure qubit-argument
  bit-argument = measure parameters qubit-argument

bit-argument:
  bit-variable
  bit-index

bit-variable:
  identifier

bit-index:
  index

parameters:
  ( parameter-list )

parameter-list:
  parameter
  parameter-list , parameter

parameter:
  floating-literal

qubit-argument:
  qubit-variable
  qubit-index

qubit-variable:
  identifier

qubit-index:
  index

Example

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qubit q
bit b
b = measure q
b = measure(1,0,0) q

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qubit[5] q
bit[2] b
b[0, 1] = measure q[2, 3]
b[1, 0] = measure(1,0,0) q[4, 3]

Note

The measure instruction accepts SGMQ notation, similar to gates. Note that when using SGMQ notation with the measure instruction, that the number of bit operands is equal to the number of qubit operands. For example, it is valid to write b[0, 2, 1] = measure q[3:5] because that unpacks to 

b[0] = measure q[3]
b[2] = measure q[4]
b[1] = measure q[5]
However, it is invalid to write b[0:1] = measure q[2] or b[2] = measure q[0:1], because in both cases the number of bit and qubit operands is unequal.

The following code snippet shows how the measure instruction might be used in context.

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version 3.0

qubit[2] q
bit[2] b

H q[0]
CNOT q[0], q[1]

b = measure q  // Measurement in the standard basis.

On the last line of this simple cQASM program, the respective states of both qubits in the qubit register are measured along the standard/computational basis.

To measure in the Hadamard basis (or X-basis) you can use the parameterized measure instruction to measure along the \(x\)-axis, defined by \((1,0,0)\).

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version 3.0

qubit q
bit b

X q
H q
b = measure(1,0,0) q // Measurement in the Hadamard basis.

On the last line of the latter cQASM program the qubit is measured along the \(x\)-axis; the measurement outcome will (always) be 1, due to measuring the \(|1\rangle\) state in the X-basis.