ROS: Resource-constrained Oracle Synthesis for Quantum Computers

Abstract

We present a completely automatic synthesis framework for oracle functions-a central part in many quantum algorithms. The proposed framework for resource-constrained oracle synthesis (ROS) is a LUT-based hierarchical method in which every step is specifically tailored to address hardware resource constraints. ROS embeds a LUT mapper designed to simplify the successive synthesis steps, costing each LUT according to the resources used by its corresponding quantum circuit. In addition, the framework exploits a SAT-based quantum garbage management technique. Those two characteristics give ROS the ability to beat the state-of-the-art hierarchical method both in number of qubits and in number of operations. The efficiency of the framework is demonstrated by synthesizing quantum oracles for Grover's algorithm.

Boolean satisfiability in quantum compilation

“…For SAT-based k-LUT mapping, it is interesting to investigate how associating a cost function with each LUT may improve the final result. For example, it is possible to consider the cost of each LUT after being decomposed into elementary quantum gates, as experimented in a heuristic solution in [52]. Similarly, it would be interesting to consider resource-constrained reversible pebble games, which would enable to prefer solutions where expensive computations are less often computed and uncomputed.…”

Automatic Generation of Grover Quantum Oracles for Arbitrary Data Structures

“…As Reversible Quantum Logic Synthesis is an active field of research for more than 20 years [16], more efficient methods in terms of gate counts and the usage of ancilla qubits arise frequently [17]. While many of them are available in the tweedledum [18] library, a fairly recent method of interest is denoted as resource-efficient oracle synthesis (ROS) and was initially presented in [19]. It is built on the LUT 2 -based hierarchical reversible logic synthesis framework (LHRS) [20] and improves the LUT-network approach by adding a special quantum aware k-LUT mapper, involving specially truncated XAGs 3 and a more efficient SAT-based quantum garbage management technique 4 [21], which offers control over the number of qubits used in the synthesized ciruits.…”

“…According to [19] the i-th row of the Hadamard-Matrix H N of degree N is the truth table of parity operator i. To be more precise the x-th row of the i-th column is equal to…”

“…Both of these problems can be tackled with by an approach based on calculating intermediate results and intelligently optimizing the next synthesis steps accordingly. Such an approach has already been proposed in [19]. Even though the authors could effectively demonstrate a reduction in the T-order, their technique still does not consider redundancies, since they focus on synthesizing truth tables with only a single column.…”

“…The Qiskit-synthesized circuits can be further optimized by first minimizing the input truth table via the Quine-McCluskey 19 algorithm [38], in order to find all the essential prime implicants and then by finding the exact cover via employing the DLX 20 algorithm [39]. This is exponentially heavy on classical resources and it turns out that even with those optimizations, there is a huge gap in terms of CNOT counts and U counts.…”