Atomic scale Quantum Hamiltonian Logic Gates

Christian Joachim

Bobby Antonio, J. Randall, W. K. Hensinger +2 more

Atomic-scale logic and the minimization of heating (dissipation) are both very high on the agenda for future computation hardware. An approach to achieve these would be to replace networks of transistors directly by classical reversible logic gates built from the coherent dynamics of a few interacting atoms. As superpositions are unnecessary before and after each such gate (inputs and outputs are bits), the dephasing time only needs to exceed a single gate operation time, while fault tolerance should be achieved with low overhead, by classical coding. Such gates could thus be a spin-off of quantum technology much before full-scale quantum computation. Thus motivated, we propose methods to realize the 3-bit Toffoli and Fredkin gates universal for classical reversible logic using a single time-independent 3-qubit Hamiltonian with realistic nearest neighbour two-body interactions. We also exemplify how these gates can be composed to make a larger circuit. We show that trapped ions may soon be scalable simulators for such architectures, and investigate the prospects with dopants in silicon.

Александр Алексеевич Горбацевич, Н. М. Шубин

Ghassen Dridi, R Julien, Mohamed Hliwa +1 more

The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor.

J. D. Pritchard

Neutral atom arrays have emerged as versatile platforms for performing both digital and analogue quantum computing and simulation, with demonstrations ranging from large-scale programmable Hamiltonians realising topological phases or weighted graph optimisation to error-corrected logical qubits with transverse gate operations. This paper provides a broad overview to the neutral atom platform, and the potential applications relevant to materials science and quantum chemistry.