R0 = r0 R_k = R_k-1 + r_k * [simm(R_k-1,r_k)]^pwhere r_k are superpositions, simm is our similarity metric, and if we set p = 0 this reduces to a simple sum:

R_k = r1 + r2 + ... + r_kThe intended effect is that you add new superpositions weighted somewhat on how close they are to those already in the sum. Noting of course, that simm gives results in [0,1]. Like I said, I don't know if this will turn out useful, but figured why not add it.

Here is the python:

def simm_add(one,context,parameters): try: op,p = parameters.split(',') p = int(p) # maybe try float(p) later except: return ket("",0) head, *tail = one Rk = head.apply_op(context,op) for x in tail: rk = x.apply_op(context,op) similarity = silent_simm(Rk,rk)**p Rk = Rk + rk.multiply(similarity) return RkAnd a use case from earlier:

sadd |result 1> => simm-add[noise,1] select[1,1] rel-kets[noise] |> sadd |result 2> => simm-add[noise,1] select[1,2] rel-kets[noise] |> ... sadd |result 40> => simm-add[noise,1] select[1,40] rel-kets[noise] |>Though in that case the difference from just a plain sum was essentially zero.

In general, usage is simply: simm-add[op,p] with some similarity to common[op] and union[op].

May as well note, since simm is in [0,1], and assuming all superpositions have positive coeffs, then we have the property:

0 <= R_k <= r1 + r2 + ... + r_kwhere it reaches the upper bound only if p = 0, or all r_k are identical. The more "diverse" the superpositions (ie, smaller simm values), the smaller R_k will be.

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