Efficient Boolean Methods for Preparing Uniform Quantum States

As each quantum algorithm requires a specific initial quantum state, quantum state preparation is an important task in quantum computing. The preparation of quantum states is performed by a quantum circuit consisting of controlled-NOT (CNOT) and single-qubit gates. Known algorithms to prepare arbitrary
$n$
-qubit quantum states create quantum circuits in
$O(2^n)$
runtime and use
$O(2^n)$
CNOTs, which are more expensive than single-qubit gates in NISQ architectures. To reduce runtime and the number of CNOTs, we simplify the problem by considering an important family of quantum states, which are
uniform quantum states
(UQSs). We map UQSs to Boolean functions and propose a
UQS preparation
(UQSP) method. Preparing UQSs using Boolean functions allows us to utilize different representations of Boolean functions. We utilize decision diagrams to reduce runtime and enable preparation for a larger number of qubits where the state-of-the-art methods are not applicable. To further reduce the number of CNOTs, we utilize variable reordering and functional dependencies among the variables. Our state preparation method requires an exponential number of CNOTs in the worst case but it reduces CNOTs significantly for practical benchmarks. Moreover, our method generates an exact representation of quantum states without using free-qubits. We compare our algorithm with QisKit. The comparison shows that our UQSP method is capable to reduce the average number of CNOTs by 75.31% for the practical benchmarks. The runtime is almost reduced by a factor of 2.