Representation of Qubit States using 3D Memristance Spaces: A first step towards a Memristive Quantum Simulator

Development of quantum simulators is a major step towards the universal quantum computer. Quantum simulators are quantum systems that can perform specific quantum computations, or software packages that can reproduce most of the aspects of a general universal quantum computer on a general purpose classical computer. Development of quantum simulators using digital circuits, such as FPGAs is very difficult, mainly because the unit of quantum information, the qubit, has an infinite number of states, whereas the classical bit has only two. On the other hand, analog circuits comprising R, L and C elements have no internal state variables that can be used to reproduce and store qubit states. Here we take the first step towards the development of a new quantum simulator using memristors. The qubit state is mapped to a 3D space spanned by the memristances of three identical memristors. The qubit state evolution is reproduced by the input voltages applied to the memristors. We define the correspondence between the general qubit state rotation, i.e. the one-qubit quantum gates, and memristor input voltage variations and reproduce the rotations imposed by the action of quantum gates in the 3D memristance space. Our results show that, at least in principle, qubits and one-qubit quantum gates can be simulated by memristors.