Automatic Generation of Grover Quantum Oracles for Arbitrary Data Structures

Abstract

The steadily growing research interest in quantum computing -together with the accompanying technological advances in the realization of quantum hardware -fuels the development of meaningful real-world applications, as well as implementations for well-known quantum algorithms. One of the most prominent examples till today is Grover's algorithm, which can be used for efficient search in unstructured databases. Quantum oracles that are frequently masked as black boxes play an important role in Grover's algorithm. Hence, the automatic generation of oracles is of paramount importance. Moreover, the automatic generation of the corresponding circuits for a Grover quantum oracle is deeply linked to the synthesis of reversible quantum logic, which -despite numerous advances in the field -still remains a challenge till today in terms of synthesizing efficient and scalable circuits for complex boolean functions.In this paper, we present a flexible method for automatically encoding unstructured databases into oracles, which can then be efficiently searched with Grover's algorithm. Furthermore, we develop a tailor-made method for quantum logic synthesis, which vastly improves circuit complexity over other current approaches. Finally, we present another logic synthesis method that considers the requirements of scaling onto real world backends. We compare our method with other approaches through evaluating the oracle generation for random databases and analyzing the resulting circuit complexities using various metrics.

Analyses of the viability of automating the quantum circuit construction of Grover’s Oracle for executing wildcard searches on NISQ processors

“…The latter would be fed into the API. This is to ensure that the experiments are focused on verifying the feasibility of using wildcard search in conjunction with Oracle as a database [20] and performing unstructured search using encoded search words.…”

“…The latter would be fed into the API. This is to ensure that the experiments are focused on verifying the feasibility of using wildcard search in conjunction with Oracle as a database 20 and performing unstructured search using encoded search words. PKRM synthesis is a procedure that would enable quantum circuit to be constructed programmatically based on the defined input.…”

Variational Amplitude Amplification for Solving QUBO Problems

“…In particular, we focus on amplitude amplification's ability to solve QUBO (quadratic unconstrained binary optimization) problems. The best quantum algorithm for solving this problem is an open question, with notable research efforts in variational approaches [10][11][12] and quantum annealing [13][14][15][16], as well as within amplitude amplification [17,18].…”

“…This study is a continuation of our previous work [19], in which we demonstrated an oracle design which was capable of encoding and solving a weighted directed graph problem. The motivation for this oracle was to address a common criticism of U G [18,[20][21][22][23], namely, that the circuit construction of oracles too often hardcodes the solution it aims to find, negating the use of quantum entirely. Similar to other recent studies [24][25][26][27], we showed that this problem can be solved at the circuit depth level by avoiding gates such as control-Z for constructing the oracle and instead using phase and control-phase gates (P(θ) and CP(θ)).…”

Gaussian Amplitude Amplification for Quantum Pathfinding

“…The success of Grover’s algorithm can be boiled down to two primary components: the oracle operation and diffusion operation . While is typically considered a straightforward mathematical operation—achieving a reflection about the average amplitude—critics of Grover’s algorithm often point to as problematic [ 11 , 12 , 13 , 14 ]. Neilsen and Chuang elegantly describe the dilemma of implementing as differentiating between an operation in which the desired marked state, versus a true blackbox oracle which can the answer [ 15 ].…”