Cross-platform protected qubits from entanglement

A crucial ingredient for scalable, fault-tolerant quantum computing is the construction of logical qubits with low error rates and intrinsic noise protection. We propose a construction for such hardware-level noise protection, in which the qubits are protected from depolarizing (relaxation) dephasing errors induced by local noise. These logical qubits arise from the entanglement between two internal degrees of freedom, hence we term them . Our construction is based on the emergence of collective degrees of freedom from a generalized coherent state construction, similar in spirit to spin coherent states, of a set of such internally entangled units. These degrees of freedom, for a finite number of units, parametrize the quantized version of complex projective space <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi mathvariant="double-struck">C</a:mi><a:mi mathvariant="normal">P</a:mi></a:mrow></a:math>(3). The noise protection of the entanglemon qubit is then a consequence of a weakly coupled emergent degree of freedom arising due to the nonlinear geometry of complex projective space. We present two simple models for entanglemons, which are platform agnostic, provide varying levels of protection, and in which the qubit-basis states are the two lowest-energy states with a higher-energy gap to other states. We end by commenting on how entanglemons could be realized in platforms ranging from superconducting circuits, and trapped ion platforms, to possibly also quantum Hall skyrmions in graphene and quantum dots in semiconductors. The inherent noise protection in our models combined with the platform agnosticism highlights the potential of encoding information in additional weakly coupled emergent degrees of freedom arising in nonlinear geometrical spaces and curved phase spaces, thereby proposing a different route to achieve scalable fault tolerance.