Fidelity-restorable photonic linear operator
The present disclosure relates to implementations of a photonic circuit, and particularly to a photonic circuit that includes one or more matrix circuits. For example, the present disclosure relates to photonic circuit implementations of unitary matrices, and of arbitrary real and/or complex matrices factorized using unitary matrices, that utilize special generalized Mach-Zehnder interferometers (SGMZIs) as building blocks of various matrix circuit architectures.
1. An arbitrary matrix circuit, comprising:
a first matrix block including a first plurality of special generalized Mach-Zehnder Interferometers (SGMZIs) coupled in series in order of dimensionality from a lowest dimensionality of the plurality of SGMZIs to a highest dimensionality of the plurality of SGMZIs;
a second matrix block including a second plurality of SGMZIs coupled in series in reverse order of dimensionality relative to the order of dimensionality that the first plurality of SGMZIs are ordered within the first matrix block, wherein a first orientation of the first plurality of SGMZIs is horizontally mirrored to a second orientation of the second plurality of SGMZIs; and
a plurality of waveguide paths passing through the first matrix block and the second matrix block.
2. The arbitrary matrix circuit of claim 1 , further comprising a plurality of attenuators positioned between the first matrix block and the second matrix block, each attenuator of the plurality of attenuators corresponding to a waveguide path from the plurality of waveguide paths.
3. The arbitrary matrix circuit of claim 1 , wherein each waveguide path of the plurality of waveguide paths passes through an equal number of SGMZIs from the first plurality of SGMZIs and the second plurality of SGMZIs.
4. The arbitrary matrix circuit of claim 3 , wherein losses are balanced between the plurality of waveguide paths based on signals passing through the plurality of waveguide paths passing through the equal number of SGMZIs.
5. The arbitrary matrix circuit of claim 1 , wherein each waveguide path of the plurality of waveguide paths passes through a first number of SGMZIs equal to one greater than the highest dimensionality of the plurality of SGMZIs.
6. The arbitrary matrix circuit of claim 5 , wherein each waveguide path of the plurality of waveguide paths passes through the first number of SGMZIs without passing through a second number of SGMZIs equal to one less than the highest dimensionality of the plurality of SGMZIs.
7. The arbitrary matrix circuit of claim 5 , wherein each waveguide path of the plurality of waveguide paths passes through a different combination of SGMZIs from other waveguide paths of the plurality of waveguide paths.
8. The arbitrary matrix circuit of claim 1 , wherein the second matrix block includes a same number of SGMZIs as the first matrix block.
9. The arbitrary matrix circuit of claim 1 ,
wherein the first plurality of SGMZIs has a first cascaded orientation associated with the order of dimensionality in which the first plurality of SGMZIs are positioned within the first matrix block,
wherein the second plurality of SGMZIs has a second cascaded orientation associated with the order of dimensionality in which the second plurality of SGMZIs are positioned within the second matrix block, and
wherein the first cascaded orientation is horizontally mirrored to the second cascaded orientation.
10. The arbitrary matrix of claim 9 , wherein the first cascaded orientation is both horizontally and vertically mirrored to the second cascaded orientation.
11. A photonic circuit comprising at least one arbitrary matrix circuit, the at least one arbitrary matrix circuit including:
a first matrix block including a first plurality of special generalized Mach-Zehnder Interferometers (SGMZIs) coupled in series in order of dimensionality from a lowest dimensionality of the plurality of SGMZIs to a highest dimensionality of the plurality of SGMZIs;
a second matrix block including a second plurality of SGMZIs coupled in series in reverse order of dimensionality relative to the order of dimensionality that the first plurality of SGMZIs are ordered within the first matrix block, wherein a first orientation of the first plurality of SGMZIs is horizontally mirrored to a second orientation of the second plurality of SGMZIs; and
a plurality of waveguide paths passing through the first matrix block and the second matrix block.
12. The photonic circuit of claim 11 , further comprising a plurality of attenuators positioned between the first matrix block and the second matrix block, each attenuator of the plurality of attenuators corresponding to a waveguide path from the plurality of waveguide paths.
13. The photonic circuit of claim 11 , wherein each waveguide path of the plurality of waveguide paths passes through an equal number of SGMZIs from the first plurality of SGMZIs and the second plurality of SGMZIs, and wherein losses are balanced between the plurality of waveguide paths based on signals passing through the plurality of waveguide paths passing through the equal number of SGMZIs.
14. The photonic circuit of claim 11 ,
wherein the first plurality of SGMZIs has a first cascaded orientation associated with the order of dimensionality in which the first plurality of SGMZIs are positioned within the first matrix block,
wherein the second plurality of SGMZIs has a second cascaded orientation associated with the order of dimensionality in which the second plurality of SGMZIs are positioned within the second matrix block, and
wherein the first cascaded orientation is horizontally mirrored to the second cascaded orientation.
15. The photonic circuit of claim 14 , wherein the first cascaded orientation is both horizontally and vertically mirrored to the second cascaded orientation.