Holonomic implementation of CNOT gate on topological Majorana qubits

Abstract

The CNOT gate is a two-qubit gate which is essential for universal quantum computation. A well-established approach to implement it within Majorana-based qubits relies on subsequent measurement of (joint) Majorana parities. We propose an alternative scheme which operates a protected CNOT gate via the holonomic control of a handful of system parameters, without requiring any measurement. We show how the adiabatic tuning of pair-wise couplings between Majoranas can robustly lead to the full entanglement of two qubits, insensitive with respect to small variations in the control of the parameters.

Multi-mode architectures for noise-resilient superconducting qubits

“…Interestingly, the corresponding unitary operation on the qubit's state does not originate from dynamical phases (since the computational states are always degenerate) but rather from different (geometric) Berry phases accumulated during the adiabatic evolution of the system along loops in the parameter space. Such an approach has been proposed as a convenient way to implement (possibly non-Clifford) gates in several topologically protected platforms, which guarantees the existence of a robust degenerate computational space [150][151][152][153][154][155][156]. In the specific case under examination [148], the tunable parameters that allow for the implementation of holonomic gates are the external flux ϕ ext and the offset charge n g , controlled by the external gate shown in gray in figure 5(c), which modifies the capacitive term in…”

Novel architectures for noise-resilient superconducting qubits

“…Interestingly, the corresponding unitary operation on the qubit's state does not originate from dynamical phases (since the computational states are always degenerate) but rather from different (geometric) Berry phases accumulated during the adiabatic evolution of the system along loops in the parameter space. Such an approach has been proposed as a convenient way to implement (possibly non-Clifford) gates in several topologically protected platforms, which guarantees the existence of a robust degenerate computational space [141,142,143,144,145,146,147]. In the specific case under examination [139], the tunable parameters that allow for the implementation of holonomic gates are the external flux φ ext and the offset charge n g , controlled by the external gate shown in gray in Figure 5(c), which modifies the capacitive term in…”

Multiplicative Majorana zero-modes

“…In order to construct a topological qubit from unpaired Majorana zero-modes, two pairs of unpaired Majorana zeromodes are required at minimum by proposals based on braiding 7,8 , and some gate operations required for topological quantum computation utilize controlled entanglement 9 . The recently introduced multiplicative topological phases (MTPs) 10 -topological phases of matter corresponding to a symmetry-protected tensor product structure in which multiple parent topological phases may be combined in a multiplicative fashion to realize novel topology-present an opportunity to elegantly meet these requirements.…”