ParityQC: Parity Constraints as a Quantum Computing Toolbox

A quantum computer is a device that takes advantage of the elusive phenomena of quantum mechanics to solve computational problems efficiently. This technology is just at the verge of a pivotal moment: going from experiments that fill out whole laboratories to devices that solve practical real world problems. Among the most pressing fundamental challenges on the way there is the question of scalability, robustness and universality. The aim of the present project with the title ``Parity Quantum Computing`` is to study novel schemes for quantum computing based on parity variables and constraints. In this scheme, the logical qubits are redundantly encoded in several physical qubits. For a particular application of quantum computers that aims at solving optimization problems, this allows one to program arbitrary optimization problems with local fields only. Compared to previous schemes, which are based on superconducting qubits with specific hard-wired programmable connections, this allows for a fully programmable generic device. In this novel scheme, all interactions are local between qubits on a simple geometry and can be constant, which enables implementations with qubit platforms such as cold atoms in optical lattices, ions and transmon qubits, thus opening unprecedented parameter regimes. The research addresses fundamental questions ranging from many-body physics to machine learning.

The Parity Architecture is a blueprint for quantum computers. Unlike previous quantum computers, in the Parity Architecture the qubits describe the relative information between two bits-this is the so-called parity, from which the project's name is derived. As with microprocessors, operations between bits-known as gates-must also be performed in quantum computers. Thanks to the new representation of information in the Parity Architecture, these gates are executed only on individual qubits. This leads to more scalable quantum chips and more efficient algorithms. For instance, the most efficient algorithm for the Fourier transform was presented using the Parity Architecture. The Parity Architecture is now also being commercialized in the spin-out ParityQC GmbH.