Information and gravity may seem like completely different things, but one thing they have in common is that they can both be described in the framework of geometry. Building on this connection, a new paper suggests that the rules for optimal quantum computation are set by gravity.

Physicists Paweł Caputa at Kyoto University and Javier Magan at the Instituto Balseiro, Centro Atómico de Bariloche in Argentina have published their paper on the link between quantum computing and gravity in a recent issue of Physical Review Letters.

In the field of computational complexity, one of the main ideas is minimizing the cost (in terms of computational resources) to solve a problem. In 2006, Michael Nielsen demonstrated that, when viewed in the context of differential geometry, computational costs can be estimated by distances. This means that minimizing computational costs is equivalent to finding minimal “geodesics,” which are the shortest possible distances between two points on a curved surface.

The discovery could help overcome a major quantum computing hurdle.

Mechanical systems facilitate the development of a hybrid quantum technology comprising electrical, optical, atomic and acoustic degrees of freedom, and entanglement is essential to realize quantum-enabled devices. Continuous-variable entangled fields—known as Einstein–Podolsky–Rosen (EPR) states—are spatially separated two-mode squeezed states that can be used for quantum teleportation and quantum communication. In the optical domain, EPR states are typically generated using nondegenerate optical amplifiers, and at microwave frequencies Josephson circuits can serve as a nonlinear medium^4,5,6. An outstanding goal is to deterministically generate and distribute entangled states with a mechanical oscillator, which requires a carefully arranged balance between excitation, cooling and dissipation in an ultralow noise environment. Here we observe stationary emission of path-entangled microwave radiation from a parametrically driven 30-micrometre-long silicon nanostring oscillator, squeezing the joint field operators of two thermal modes by 3.40 decibels below the vacuum level. The motion of this micromechanical system correlates up to 50 photons per second per hertz, giving rise to a quantum discord that is robust with respect to microwave noise. Such generalized quantum correlations of separable states are important for quantum-enhanced detection and provide direct evidence of the non-classical nature of the mechanical oscillator without directly measuring its state. This noninvasive measurement scheme allows to infer information about otherwise inaccessible objects, with potential implications for sensing, open-system dynamics and fundamental tests of quantum gravity. In the future, similar on-chip devices could be used to entangle subsystems on very different energy scales, such as microwave and optical photons.