Deterministic and Entanglement-Efficient Preparation of Amplitude-Encoded Quantum Registers

Abstract: Quantum computing promises to provide exponential speed-ups to certain classes of problems. In many such algorithms, a classical vector $\mathbf{b}$ is encoded in the amplitudes of a quantum state $\left |b \right >$. However, efficiently preparing $\left |b \right >$ is known to be a difficult problem because an arbitrary state of $Q$ qubits generally requires approximately $2^Q$ entangling gates, which results in significant decoherence on today's Noisy Intermediate Scale Quantum (NISQ) computers. We present a deterministic (nonvariational) algorithm that allows one to flexibly reduce the quantum resources required for state preparation in an entanglement efficient manner. Although this comes at the expense of reduced theoretical fidelity, actual fidelities on current NISQ computers might actually be higher due to reduced decoherence. We show this to be true for various cases of interest such as the normal and log-normal distributions. For low entanglement states, our algorithm can prepare states with more than an order of magnitude fewer entangling gates as compared to isometric decomposition.