Coding Classical Logic Gates on the D-Wave Quantum Annealer

Abstract

The D-Wave Quantum Annealer is a machine that uses qubits in place of bits since they have special behaviors desirable for solving optimization problems. These machines are not able to natively replicate logical gates (AND gate). Logical gates process binary information in order to output processed information in binary too. Without the basic function of these gates, larger circuits, such as a multiplication circuit, are impossible to replicate. This project was conducted in order to build and write a program that would allow the quantum annealer to replicate the behavior of classical logic gates. Given a certain input, the quantum computer should be able to realize the correct outputs based on the behavior of the gate that is being encoded. The technical report “Boosting Integer Factoring Performance via Quantum Annealing Offsets” was used in order to formulate a binary quadratic model which replicates the behavior of the AND gate, and the half-and full-adder circuits. These models use the Ising penalty model, where constraints are set in order to achieve the wanted behavior; these models are encoded using binary, or in this case, the Ising model. This project took place over the course of 5 months, under the mentorship of Professor Terrill Frantz and Alex Khan from Harrisburg University. In the report, the binary formulation is used to encode the constraints. In practice, it is more practical to use the Ising formulation, which encodes 0 as -1, and 1 as 1. In this binary quadratic model, two dictionaries are required as inputs: the linear dictionary (for the values of qubits) and the quadratic dictionary (for the connections between these qubits). These values were taken from the charts and graphics from the “Boosting” report and then implemented in a Python program. The results showed inputs and outputs that correspond with the expected values from an AND gate, and the half and full-adders. The results of the project were posted in full detail in an article on Medium.com (https://tinyurl.com/yj55fc7m). The program successfully replicates the AND gate and other small circuits (the half and full-adders). Continuing on the success in encoding logical gates (such as the AND gate), more complex and useful circuits can be created to solve problems never done before on a quantum annealer.