# cirq.sim.DensityMatrixStepResult

A single step in the simulation of the DensityMatrixSimulator.

Inherits From: `StepResultBase`, `StepResult`

`sim_state` The qubit:ActOnArgs lookup for this step.
`simulator` The simulator used to create this.
`dtype` The `numpy.dtype` used by the simulation. One of `numpy.complex64` or `numpy.complex128`.

`measurements` A dictionary from measurement gate key to measurement results, ordered by the qubits that the measurement operates on.

## Methods

### `density_matrix`

View source

Returns the density matrix at this step in the simulation.

The density matrix that is stored in this result is returned in the computational basis with these basis states defined by the qubit_map. In particular the value in the qubit_map is the index of the qubit, and these are translated into binary vectors where the last qubit is the 1s bit of the index, the second-to-last is the 2s bit of the index, and so forth (i.e. big endian ordering). The density matrix is a `2 ** num_qubits` square matrix, with rows and columns ordered by the computational basis as just described.

#### Example:

• `qubit_map`: {QubitA: 0, QubitB: 1, QubitC: 2} Then the returned density matrix will have (row and column) indices mapped to qubit basis states like the following table

QubitA QubitB QubitC
0 0 0 0
1 0 0 1
2 0 1 0
3 0 1 1
4 1 0 0
5 1 0 1
6 1 1 0
7 1 1 1

Args
`copy` If True, then the returned state is a copy of the density matrix. If False, then the density matrix is not copied, potentially saving memory. If one only needs to read derived parameters from the density matrix and store then using False can speed up simulation by eliminating a memory copy.

### `sample`

View source

Samples from the system at this point in the computation.

Note that this does not collapse the state vector.

Args
`qubits` The qubits to be sampled in an order that influence the returned measurement results.
`repetitions` The number of samples to take.
`seed` A seed for the pseudorandom number generator.

Returns
Measurement results with True corresponding to the `|1⟩` state. The outer list is for repetitions, and the inner corresponds to measurements ordered by the supplied qubits. These lists are wrapped as a numpy ndarray.

### `sample_measurement_ops`

View source

Samples from the system at this point in the computation.

Note that this does not collapse the state vector.

In contrast to `sample` which samples qubits, this takes a list of `cirq.GateOperation` instances whose gates are `cirq.MeasurementGate` instances and then returns a mapping from the key in the measurement gate to the resulting bit strings. Different measurement operations must not act on the same qubits.

Args
`measurement_ops` `GateOperation` instances whose gates are `MeasurementGate` instances to be sampled form.
`repetitions` The number of samples to take.
`seed` A seed for the pseudorandom number generator.

Returns: A dictionary from measurement gate key to measurement results. Measurement results are stored in a 2-dimensional numpy array, the first dimension corresponding to the repetition and the second to the actual boolean measurement results (ordered by the qubits being measured.)

Raises
`ValueError` If the operation's gates are not `MeasurementGate` instances or a qubit is acted upon multiple times by different operations from `measurement_ops`.

### `set_density_matrix`

View source

Set the density matrix to a new density matrix.

Args
`density_matrix_repr` If this is an int, the density matrix is set to the computational basis state corresponding to this state. Otherwise if this is a np.ndarray it is the full state, either a pure state or the full density matrix. If it is the pure state it must be the correct size, be normalized (an L2 norm of 1), and be safely castable to an appropriate dtype for the simulator. If it is a mixed state it must be correctly sized and positive semidefinite with trace one.

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