A new method for multi-bit and qudit transfer based on commensurate waveguide arrays

Abstract

The faithful state transfer is an important requirement in the construction of classical and quantum computers. While the high-speed transfer is realized by optical-fibre interconnects, its implementation in integrated optical circuits is affected by cross-talk. The cross-talk between densely packed optical waveguides limits the transfer fidelity and distorts the signal in each channel, thus severely impeding the parallel transfer of states such as classical registers, multiple qubits and qudits. Here, we leverage on the suitably engineered cross-talk between waveguides to achieve the parallel transfer on optical chip. Waveguide coupling coefficients are designed to yield commensurate eigenvalues of the array and hence, periodic revivals of the input state. While, in general, polynomially complex, the inverse eigenvalue problem permits analytic solutions for small number of waveguides. We present exact solutions for arrays of up to nine waveguides and use them to design realistic buses for multi-(qu)bit and qudit transfer. Advantages and limitations of the proposed solution are discussed in the context of available fabrication techniques.

Bend-free multiarm interferometers on optical chips

“…, where T k,j (z) = (e −iHz ) k,j constitute the unitary transfer matrix T. The nearest-neighbour approximation is justified by the exponential decay of the coupling coefficients with the distance between waveguides [16,17]. This has been corroborated by numerical simulations [18].…”

“…Their coupling coefficients are expressed as functions of the arbitrary unequal integers n 1 and n 2 . A detailed derivation is given in [18] and results in…”

A new concept for design of photonic integrated circuits with the ultimate density and low loss

“…Inverse solutions. The CWGA Hamiltonian composed of the waveguide coupling coefficients has been derived following the inverse procedure described in [24]. While the Hamiltonians of symmetric CWGAs are fully defined by the chosen eigenfrequencies, the Hamiltonians of asymmetric CW-GAs can be tuned by analogue real parameters.…”

“…The essential feature of a CWGA is that the ratio of any two of its eigenfrequencies is a rational number. It restricts the generally quasi-periodic light dynamics in WGAs to the highly-ordered periodic propagation [22,23,24]. In the tight-binding and the next-neighbour-coupling approximations, the fundamental mode in the i th waveguide can be modelled by a scalar complex wavefunction ψ i (z) and the CWGA by a tridiagonal model Hamiltonian H. The Hamiltonian features the waveguide coupling coefficients on the side diagonals and the relative detunings between waveguide modes on the main diagonal.…”

“…ψ M (z)) T , is evolved by the operator T = e −iHz . The evolution operator describes the functionality of the array and can be related to its eigenspectrum by analytic expressions [24]. This enables construction of the Hamiltonians of the basic building blocks of PICs with freely chosen commensurate eigenfrequencies.…”