ApproximatelyPreparePureStateCP operation

Fully qualified name: Microsoft.Quantum.Unstable.StatePreparation.ApproximatelyPreparePureStateCP

operation ApproximatelyPreparePureStateCP(tolerance : Double, coefficients : ComplexPolar[], qubits : Qubit[]) : Unit is Adj + Ctl

Summary

Given a set of coefficients and a big-endian quantum register, prepares a state on that register described by the given coefficients, up to a given approximation tolerance.

Description

This operation prepares an arbitrary quantum state |𝜓⟩ with complex coefficients rⱼ·𝒆^(𝒊·tⱼ) from the n-qubit computational basis state |0...0⟩. In particular, the action of this operation can be simulated by the a unitary transformation U which acts on the all-zeros state as

$$ \begin{align} U\ket{0...0} & = \ket{\psi} \\ & = \frac{ \sum_{j=0}^{2^n-1} r_j e^{i t_j} \ket{j} }{ \sqrt{\sum_{j=0}^{2^n-1} |r_j|^2} }. \end{align} $$

Input

tolerance

The approximation tolerance to be used when preparing the given state.

coefficients

Array of up to 2ⁿ complex coefficients represented by their absolute value and phase (rⱼ, tⱼ). The j-th coefficient indexes the number state |j⟩ encoded in a big-endian format.

qubits

Qubit register encoding number states in a big-endian format. This is expected to be initialized in the computational basis state |0...0⟩.

Remarks

coefficients will be padded with elements (rⱼ, tⱼ) = (0.0, 0.0) if fewer than 2ⁿ are specified.

References

• arXiv:quant-ph/0406176 "Synthesis of Quantum Logic Circuits", Vivek V. Shende, Stephen S. Bullock, Igor L. Markov