# cirq.sim.SparseSimulatorStep

A StepResult that includes StateVectorMixin methods.

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.

qubit_map

## Methods

### bloch_vector_of

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Returns the bloch vector of a qubit in the state.

Calculates the bloch vector of the given qubit in the state given by self.state_vector(), given that self.state_vector() follows the standard Kronecker convention of numpy.kron.

Args
qubit qubit who's bloch vector we want to find.

Returns
A length 3 numpy array representing the qubit's bloch vector.

Raises
ValueError if the size of the state represents more than 25 qubits.
IndexError if index is out of range for the number of qubits corresponding to the state.

### density_matrix_of

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Returns the density matrix of the state.

Calculate the density matrix for the system on the list, qubits. Any qubits not in the list that are present in self.state_vector() will be traced out. If qubits is None the full density matrix for self.state_vector() is returned, given self.state_vector() follows standard Kronecker convention of numpy.kron.

#### For example:

self.state_vector() = np.array([1/np.sqrt(2), 1/np.sqrt(2)], dtype=np.complex64) qubits = None gives us

$$\rho = \begin{bmatrix} 0.5 & 0.5 \\ 0.5 & 0.5 \end{bmatrix}$$

Args
qubits list containing qubit IDs that you would like to include in the density matrix (i.e.) qubits that WON'T be traced out.

Returns
A numpy array representing the density matrix.

Raises
ValueError if the size of the state represents more than 25 qubits.
IndexError if the indices are out of range for the number of qubits corresponding to the state.

### dirac_notation

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Returns the state vector as a string in Dirac notation.

Args
decimals How many decimals to include in the pretty print.

Returns
A pretty string consisting of a sum of computational basis kets and non-zero floats of the specified accuracy.

### sample

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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

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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_state_vector

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Set the state vector.

One can pass a valid full state to this method by passing a numpy array. Or, alternatively, one can pass an integer, and then the state will be set to lie entirely in the computation basis state for the binary expansion of the passed integer.

Args
state If an int, the state vector set is the state vector corresponding to a computational basis state. If a numpy array this is the full state vector.

### state_vector

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Return the state vector at this point in the computation.

The state 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).

#### Example:

• qubit_map: {QubitA: 0, QubitB: 1, QubitC: 2} Then the returned vector will have 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 state vector. If False, then the state vector is not copied, potentially saving memory. If one only needs to read derived parameters from the state vector and store then using False can speed up simulation by eliminating a memory copy.

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