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the quantum theory of inbreeding

❗ Important
there was a bug on main so !133 (merged) needs to be checked out

when running a given recoding strategy inside an environment with a given loss pattern, we would like to get the same measurements for a given time step t regardless of previous measurements, right?

with the following experiment

const PRNG_SEED = "0000000000000000000000000000000000000000000000000000000000000000"

const OPTS = {
    nb_bytes: (10 * 1_024),
    k: 5,
    n: 20,
    nb_measurements: 10,
    nb_scenarii: 10,
    measurement_schedule: null,    # this will be set later
    measurement_schedule_start: 0,
    max_t: 50,
    strategies: [
        "single:1",
    ],
    environment: "random-fixed:0.5:1",
}

we would like to get the same measurements for any t regardless of $.measurement_schedule!

quantum measures

however, in the current state of the bins/inbreeding crate, the same mutable rng is used for both the scenario and the measures...

use ./bins/inbreeding
use ./bins/inbreeding/consts.nu CACHE

inbreeding build

let experiment = $"($PRNG_SEED)-($OPTS.environment)-($OPTS.k)-($OPTS.n)-($OPTS.nb_bytes)"

inbreeding run --options ($OPTS | update measurement_schedule 1) --prng-seed $PRNG_SEED
inbreeding load $experiment | reject diversity.e | inbreeding plot --options { k: $OPTS.k } --save /tmp/000_1.1.png
rm -r ($CACHE | path join $PRNG_SEED)

inbreeding run --options ($OPTS | update measurement_schedule 5) --prng-seed $PRNG_SEED
inbreeding load $experiment | reject diversity.e | inbreeding plot --options { k: $OPTS.k } --save /tmp/000_1.2.png
rm -r ($CACHE | path join $PRNG_SEED)
  • with a schedule of 1 000_1.1
  • with a schedule of 5 000_1.2

we see that all measurements for any t where t is a multiple of 5 are different from one run to the other 🤔

seeing the path of the RNG

💡 Note
in the following flowcharts,

  • labels in the nodes show the state of the RNG: it starts at 0
  • labels on the link show the operation: "strta+env" will advance the state of the RNG by 1 and "measure" will advance it by 3, as if there were multiple measures

currently

the path that takes the mutable RNG is the following:

  • with a schedule of 1 
flowchart LR;
    init((start))
    init -- create rng --> 0;

    0  == measure   ==> 3
    3  -- strat+env --> 4;
    4  == measure   ==> 7
    7  -- strat+env --> 8;
    8  == measure   ==> 11
    11 -- strat+env --> 12;
    12 == measure   ==> 15
    15 -- strat+env --> 16;
    16 == measure   ==> 19;
  • with a schedule of 2 
flowchart LR;
    init((start))
    init-- create rng -->0;

    0  == measure   ==> 3
    3  -- strat+env --> 4;
    4  -- strat+env --> 5;
    5  == measure   ==> 8
    8  -- strat+env --> 9;
    9  -- strat+env --> 10;
    10 == measure   ==> 13;

💡 Note
we see that the measures influence the state of the RNG and that different measurement schedules will result in different results...

desired behaviour

what we really would like are measurements that do not influence the environment, e.g. with RNG that branches out of the main one

  • with a schedule of 1 
flowchart LR;
    init((start))
    init -- create rng --> 0;

    0 == measure   ==> 1';
    0 -- strat+env --> 1;
    1 == measure   ==> 2';
    1 -- strat+env --> 2;
    2 == measure   ==> 3';
    2 -- strat+env --> 3;
    3 == measure   ==> 4';
    3 -- strat+env --> 4;
    4 == measure   ==> 5';
  • with a schedule of 2 
flowchart LR;
    init((start))
    init-- create rng -->0;

    0 == measure   ==> 1';
    0 -- strat+env --> 1;
    1 -- strat+env --> 2;
    2 == measure   ==> 3';
    2 -- strat+env --> 3;
    3 -- strat+env --> 4;
    4 == measure   ==> 5';

💡 Note
we see that, here, the measures do NOT influence the state of the RNG and that different measurement schedules will result in the SAME results!

Edited by STEVAN Antoine