How do I carry electrical power across a pond?
What we know won't work

First off -- a cable or conduit submerged in a pond is in something beyond a wet location from the standpoint of the Code, so our wiring method needs to be suitable for the conditions.  Second, laying sticks of rigid conduit is probably not practical either -- you either have to pull or push the conduit across the pond or lay it from a boat, while making joints in the conduit every 10', and ensuring it bends properly under the forces involved, as any kinking or damage will make pulling the wire through it far more difficult.

Furthermore, any wiring method that uses anything other than an insulated copper wire for its grounding conductor is no good as well, as it violates NEC 682.31(A):


  (A) Type. Equipment grounding conductors shall be insulated copper conductors sized in accordance with 250.122 but
  not smaller than 12 AWG.


As a practical matter, this rules out UF and USE cables, as well as armor-grounded or bare-wire-only grounded direct burial (jacketed) MC cables.  Furthermore, neither cordage nor typical submersible pump cable is directly suitable for this application as they are unlikely to be robust enough to handle a long run across a pond.  This leaves us with two general groups of options:


Liquidtight flexible conduit (LFNC as LFMC to LFMC couplings do not seem to be a thing) with listed watertight fittings and appropriately rated cable (likely an unjacketed/multiplex submersible pump cable) inside as THWN or XHHW-2 singles aren't rated to sit in water 24/7/365
Direct burial rated cables suitable for the application (some TC and MC constructions)


Going the conduit route

We will be using LFNC by the spool for a long run, or at least the longest coils you can get, here, to minimize the number of couplings to act as potential leak points.  Furthermore, LFNC-B is the construction of choice for this application as all the LFNC to LFNC couplings I can find are for LFNC-B.

You can lay the conduit from shore, or from a small workboat if you prefer (remember your PFD!).  Once the conduit's in from starting point to ending point, using listed LFNC fittings to transition into the boxes or handholes at each end, then pull an unjacketed (twisted multiplex) submersible pump cable through it -- individual type THWN wires are not rated for continuous submersion.  Note that it may be necessary to use a wet-dry vac to "suck" the conduit dry before pulling, depending on if water was allowed to freely enter the conduit during the conduit-laying process, and it also may be a difficult pull due to the inability to install usable pull points underwater to conform with bending limits.

If you wish to go the cable route

If the above idea seems too difficult, then it is possible to do this using cable wiring methods, using either type TC-ER-JP (Tray Cable, Exposed wiring Rated, Joist Pull rated) cable or some type MC cables.   TC-ER-JP has the advantage that it's cheaper and easier to run/handle; however, it will need conduit protection at the stub-ups as it's not suitable for exposed work outside of supervised industrial installations, which increases the difficulty of installation here.  Jacketed MC is somewhat stiffer/harder to run and terminate, but can be obtained in a construction called MC-HL (Metal Clad, Hazardous Location rated), which offers some advantages for a submerged application -- the welded armor on MC-HL is basically watertight, and it's tested to survive a greater degree of abuse than ordinary type MC cable as well.

Either way, you'll need a cable construction that fits the following criteria:


Copper conductors, minimum 12AWG, with THWN (acceptable) or XHHW-2 (preferred) insulation 
PVC outer jacket, direct bury/wet location rated
3 conductors (hot, hot, neutral) + an insulated ground (for MC-HL, insulated ground wires can be obtained in control cable constructions only)
For type MC cable, MC-HL (continuous welded corrugated armor) construction is preferred, with AIA (aluminum interlocked armor) construction acceptable depending on availability and cable sizing.
Type TC cable needs to be TC-ER-JP (Tray Cable, Exposed usage Rated, Joist Pull rated) in order to be adequate for this application -- this ensures that it has a fighting chance at surviving abrasion and other such physical abuse


I would terminate the cable and trench it in to 24" topcover at one end, then use a workboat to lay the rest of the cable (remember your PFD!) to the opposite shore of the pond, where you can then trench in the rest of the cable and terminate it at the other enclosure. Termination is fairly simple here -- the insulated ground wire lands on a ground bar or lug within each enclosure, while the armor of type MC cable is terminated at the fitting.  With TC cable, a suitably sized Schedule 80 PVC or rigid metal conduit can be used to provide stub-up protection; this is terminated normally at the enclosure, with the jacket cut off and the insulated ground wire landed on the enclosure ground bar/lug.