C2QA

There is promise that quantum computing can solve certain problems more efficiently than classical computing can. Problems with a proven quantum advantage involve using a black box, or oracle, whose structure encodes the solution. Interest arises in hardware studies of two fundamental black box algorithms, the Deutsch-Jozsa algorithm and the Quantum Permutation algorithm. To study the Deutsch-Jozsa (DJ) algorithm a miniaturized metastructure based on a graded-index lens is presented as a quantum emulator operate in the THz regime. In the DJ problem, an oracle block implements a binary function f. The function, f, takes n-bit binary values as input and produces either 0 or 1 as output. If the value of f is 0 or 1 on all outputs, f is called constant function. However, if the value of f is 0 and 1 for half of the output domain, f is called a balance function. The oracle subblock is made of 500 µm thick Silicon and a Fourier subblock made of 127 µm thick polyamide film. The oracle subblock modulates the phase of the transmitted THz wave with a factor k0n(y)d0 by encoding the function f(y) by assigning a phase shift of 0 or π on each spatial position along transversal direction. The Fourier subblock film acts as a gradient GRIN lens which displays the results of the output signal. We evaluated the structure using numerical simulations via the Finite-Difference Time Domain (FDTD) method and applied inverse design machine learning to validate/improve the structure and signal output. Using a ML based optimization procedure, the original design of the GRIN lens was improved to enhance the output signal of the wave incident to the QAE structure. Next, The Quantum Permutation Algorithm (QPA) determines the parity of a cyclic permutation in a single measurement. Previous studies have shown that one can execute the QPA on a 5-qubit real quantum computer with an average success rate of 86% for 2- and 3-qubit circuits. In this presentation, we consider the implementation of higher qubit QPA using the most recent NISQ machines and measure the impact of the quantum volume on our implementation. We construct circuits using Qiskit and implement them on IBM's simulator and a series of NISQ hardware with various qubit orderings. Using both 5- and 7-qubit machines, we implement 2, 3, 4, and 5-qubit permutation circuits and execute each circuit 5 times per 8192 counts to collect statistics. We find that the implementation on current hardware with error mitigation has shown improved performance over previous studies for 2- and 3-qubit circuits. Further, we explicitly discuss how to improve the results to realize larger 4- and 5-qubit circuits of the QPA.