# quantum.gate.QuantumMeasurement class

**Package: **quantum.gate

**Installation Required:** This functionality requires MATLAB Support Package for Quantum Computing.

## Description

A `QuantumMeasurement`

object represents the measurement result of a
quantum circuit, either by running the circuit remotely on a quantum device or by simulating
the circuit locally with random sampling. This object contains information about the counts of
all measured states of the *n* qubits of the circuit.

## Creation

Use

`run`

to run a circuit remotely on a quantum device and fetch the finished task using`fetchOutput`

to return a`QuantumMeasurement`

object.Use

`randsample`

on a`QuantumState`

object that represents the quantum state of the qubits of a circuit.`randsample`

randomly samples this state locally (with a specified number of shots) and returns the measurement result as a`QuantumMeasurement`

object.

## Properties

`MeasuredStates`

— Measured states in Z basis

string array

Measured states in the Z basis, returned as a string array.

#### Attributes:

`GetAccess` | `public` |

`SetAccess` | `private` |

`Counts`

— Counts of measured states

vector of positive integers or `NaN`

values

Counts of measured states, returned as a vector of positive integers or
`NaN`

values.

When you use

`randsample`

on a`QuantumState`

object, the`Counts`

property of the returned`QuantumMeasurement`

object is a vector of positive integers. Each element of this vector represents the number of counts of each measured state.When you use the

`run`

function and the remote device provider does not return the number of counts of each measured state, the`Counts`

property of the returned`QuantumMeasurement`

object is a vector of`NaN`

values. Otherwise, the`Counts`

property is a vector of positive integers.

#### Attributes:

`GetAccess` | `public` |

`SetAccess` | `private` |

`Probabilities`

— Estimated probabilities of measured states

vector of real numbers

Estimated probabilities of measured states, returned as a vector of real numbers. Each element of this vector represents how often each state was measured.

#### Attributes:

`GetAccess` | `public` |

`SetAccess` | `private` |

`NumQubits`

— Number of qubits

positive integer scalar

Number of qubits, returned as a positive integer scalar.

#### Attributes:

`GetAccess` | `public` |

`SetAccess` | `private` |

## Methods

### Public Methods

`histogram` | Histogram plot of possible states |

`probability` | Probability of measuring qubits in given state |

`querystates` | Query possible states |

## Examples

### Simulate Circuit Locally with Random Sampling

Create a quantum circuit that consists of three
*x*-axis rotation gates. The first gate acts on qubit 1 with rotation
angle `pi/4`

, the second gate acts on qubit 2 with rotation angle
`pi/2`

, and the third gate acts on qubit 3 with rotation angle
`3*pi/4`

.

g = rxGate(1:3,pi/4*(1:3)); c = quantumCircuit(g);

Simulate this circuit using the default initial state, where all qubits are in the $$|0\rangle $$ state. After running the circuit, randomly sample the quantum state with 100 shots and return the resulting simulated measurement.

s = simulate(c); m = randsample(s,100)

m = QuantumMeasurement with properties: MeasuredStates: [7×1 string] Counts: [7×1 double] Probabilities: [7×1 double] NumQubits: 3

Show the counts and estimated probabilities of the measured states.

table(m.Counts,m.Probabilities,m.MeasuredStates, ... VariableNames=["Counts","Probabilities","States"])

ans = 7×3 table Counts Probabilities States ______ _____________ ______ 6 0.06 "000" 33 0.33 "001" 5 0.05 "010" 40 0.4 "011" 5 0.05 "101" 3 0.03 "110" 8 0.08 "111"

Plot the histogram of the measurement result to show each measured state and its estimated probability.

histogram(m)

You can also specify which qubits to plot in the histogram. The histogram shows the measured states of the specified qubits (where the other qubits can be in any state) and their corresponding probability distributions (where the probabilities of the other qubits being in any state are combined).

For example, specify qubits 1 and 3 to plot in the histogram. This histogram shows
the measured states $$|00\rangle $$, $$|01\rangle $$, $$|10\rangle $$, and $$|11\rangle $$, where their corresponding probabilities are `0.11`

,
`0.73`

, `0.03`

, and `0.13`

.

histogram(m,[1 3])

Query each measured state and its estimated probability.

[states,probabilities] = querystates(m)

states = 7×1 string array "000" "001" "010" "011" "101" "110" "111" probabilities = 0.0600 0.3300 0.0500 0.4000 0.0500 0.0300 0.0800

You can also specify which qubits to query when using
`querystates`

.

[states,probabilities] = querystates(m,[1 3])

states = 4×1 string array "00" "01" "10" "11" probabilities = 0.1100 0.7300 0.0300 0.1300

### Run Circuit Remotely on AWS Quantum Device

Create a quantum circuit that consists of a Hadamard gate and a controlled X gate to entangle two qubits.

gates = [hGate(1); cxGate(1,2)]; c = quantumCircuit(gates);

Connect to a remote quantum device through AWS^{®}. Create a task that runs the circuit on the device.

```
dev = quantum.backend.QuantumDeviceAWS("Lucy");
task = run(c,dev);
```

Wait for the task to finish. Retrieve the result of running the circuit on the device.

wait(task) m = fetchOutput(task)

m = QuantumMeasurement with properties: MeasuredStates: [4×1 string] Counts: [4×1 double] Probabilities: [4×1 double] NumQubits: 2

Show the measurement result of running the circuit. Due to the noise in the physical quantum device, the $$|01\rangle $$ and $$|10\rangle $$ states can appear as measurements.

table(m.Counts,m.Probabilities,m.MeasuredStates, ... VariableNames=["Counts","Probabilities","States"])

ans = 4×3 table Counts Probabilities States ______ _____________ ______ 46 0.46 "00" 9 0.09 "10" 3 0.03 "01" 42 0.42 "11"

### Run Circuit Remotely on IBM Quantum Device Without and With Error Mitigation

Create a quantum circuit that consists of a Hadamard gate and a controlled X gate to entangle two qubits.

gates = [hGate(1); cxGate(1,2)]; c = quantumCircuit(gates);

Connect to a remote quantum device through IBM^{®} Qiskit^{®} Runtime Services. Create a task that
runs the circuit on the device without error mitigation.

```
dev = quantum.backend.QuantumDeviceIBM("ibmq_qasm_simulator");
task = run(c,dev,NumShots=500,UseErrorMitigation=false);
```

Wait for the task to finish. Retrieve the result of running the circuit on the device.

wait(task) m = fetchOutput(task)

m = QuantumMeasurement with properties: MeasuredStates: [4×1 string] Counts: [4×1 double] Probabilities: [4×1 double] NumQubits: 2

Show the measurement result of running the circuit. Due to the noise in the physical quantum device, the $$|01\rangle $$ and $$|10\rangle $$ states can appear as measurements.

table(m.Probabilities,m.MeasuredStates, ... VariableNames=["Probabilities","States"])

ans = 4×2 table Probabilities States _____________ ______ 0.536 "00" 0.018 "10" 0.024 "01" 0.422 "11"

Next, create a task that runs the circuit on the same device by applying quantum error mitigation. The error mitigation is a collection of tools and methods to process measurement results that are aimed at reducing the effects of measurement errors.

task = run(c,dev,NumShots=500,UseErrorMitigation=true);

Wait for the task to finish. Retrieve the result of running the circuit on the device.

wait(task) m = fetchOutput(task)

m = QuantumMeasurement with properties: MeasuredStates: [4×1 string] Counts: [4×1 double] Probabilities: [4×1 double] NumQubits: 2

Show the measurement result of running the circuit with error mitigation. Here, the estimated probabilities of the $$|01\rangle $$ and $$|10\rangle $$ states are closer to 0.

table(m.Probabilities,m.MeasuredStates, ... VariableNames=["Probabilities","States"])

ans = 4×2 table Probabilities States _____________ ______ 0.59254 "00" 0.001586 "10" -0.0094173 "01" 0.4153 "11"

Plot this measurement result in a bar graph.

bar(m.States,m.Probabilities) xlabel("State") ylabel("Probability")

## Version History

**Introduced in R2023a**

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