1 00:00:00,220 --> 00:00:01,649 This is Axion Kitchen. 2 00:00:01,799 --> 00:00:06,898 We first solved the factory baselines: optimal schedules of four and eight hours. 3 00:00:07,048 --> 00:00:09,480 Our extension schedules catering production. 4 00:00:09,630 --> 00:00:13,491 Cookers are machines, cleaning is setup, and departures are deadlines. 5 00:00:13,641 --> 00:00:19,956 We choose shared batches, qualified workers and timings, while respecting freshness, calendars and outages. 6 00:00:20,106 --> 00:00:21,514 First, serve complete meals. 7 00:00:21,664 --> 00:00:25,141 Then reduce waste, extra batches and changes to the plan. 8 00:00:26,220 --> 00:00:28,140 Two customers need ten meals each. 9 00:00:28,290 --> 00:00:33,794 Main A is already cooking, and one batch of twenty side portions can serve both orders. 10 00:00:33,944 --> 00:00:39,832 Here's the conflict: that side batch and one Main B option need cooker C2 at the same time. 11 00:00:39,982 --> 00:00:43,545 QAOA selects a different Main B schedule on C1. 12 00:00:43,695 --> 00:00:47,151 Both orders get a main and a side, packed before departure. 13 00:00:47,301 --> 00:00:49,583 Sharing the side batch saves making it twice. 14 00:00:50,220 --> 00:00:51,585 Remove just the side batch. 15 00:00:51,735 --> 00:00:53,527 Neither order gets a complete meal. 16 00:00:53,677 --> 00:00:55,469 Twenty main portions go to waste. 17 00:00:55,619 --> 00:00:58,265 That's why we optimize meals, rather than dishes. 18 00:01:00,220 --> 00:01:05,959 Each bit selects a batch program: how much to make, which orders it serves, who does the work, and when. 19 00:01:06,109 --> 00:01:11,549 Programs competing for the same demand sit in one block; we choose one, or leave it idle. 20 00:01:11,699 --> 00:01:13,960 Penalties rule out clashes between blocks. 21 00:01:14,110 --> 00:01:16,286 The code builds those pair terms directly. 22 00:01:16,436 --> 00:01:19,956 This small case has thirty-two programs and three idle bits. 23 00:01:20,106 --> 00:01:23,135 A restricted set of programs can miss better schedules. 24 00:01:26,220 --> 00:01:30,359 Multiply main coverage by side coverage to count complete meals. 25 00:01:30,509 --> 00:01:33,559 Their sum minus twice that product counts unpaired food. 26 00:01:33,709 --> 00:01:37,635 Coverage is linear in our bits, so both expressions stay quadratic. 27 00:01:37,785 --> 00:01:41,689 Our weights make each priority outweigh all lower costs combined. 28 00:01:41,839 --> 00:01:48,751 For constraints, we bound how much the objective can vary across all bitstrings, then set the penalty one higher. 29 00:01:48,901 --> 00:01:50,714 That proves feasible ground states. 30 00:01:50,864 --> 00:01:52,933 It doesn't guarantee a solver finds them. 31 00:01:54,220 --> 00:01:56,780 We map the QUBO to an Ising Hamiltonian. 32 00:01:56,930 --> 00:01:58,999 The mixer preserves block occupation. 33 00:01:59,149 --> 00:02:04,675 Fixing the rest of the schedule turns global interactions into local fields for VeloxQ. 34 00:02:06,220 --> 00:02:09,178 An outage also changes what happens after repair. 35 00:02:09,326 --> 00:02:10,713 The cooker still needs cleaning. 36 00:02:10,861 --> 00:02:16,488 Here, the worker must finish committed work first, then clean from eleven forty to eleven fifty. 37 00:02:16,636 --> 00:02:18,269 Both resources stay reserved. 38 00:02:18,417 --> 00:02:23,724 Our checker rebuilds those intervals from the schedule, along with freshness and delivery checks. 39 00:02:24,220 --> 00:02:27,804 Let's run the saved depth-three QAOA circuit locally. 40 00:02:27,954 --> 00:02:31,346 Cost and conflict phases alternate with an XY mixer. 41 00:02:31,496 --> 00:02:36,189 The mixer keeps one choice per block, but clashes between blocks still need checking. 42 00:02:36,339 --> 00:02:40,606 We draw four thousand ninety-six fresh samples, using the saved angles. 43 00:02:40,756 --> 00:02:42,825 The result on the right comes from this run. 44 00:02:42,975 --> 00:02:46,623 The kitchen animation is a separate replay of a saved result. 45 00:02:49,220 --> 00:02:50,287 Does training help? 46 00:02:50,437 --> 00:02:56,751 We chose the settings on the small cell and S0/S1, then tested S2/S3. 47 00:02:56,901 --> 00:03:00,208 Training finds the best available plan in all ten seeds. 48 00:03:00,358 --> 00:03:02,961 Random-angle search also hits ten on S2. 49 00:03:03,111 --> 00:03:10,919 At two hundred fifty-six evaluations, training gives roughly eleven and twenty-two times the optimum probability per shot. 50 00:03:11,069 --> 00:03:13,949 We optimize the angles separately for each instance. 51 00:03:14,099 --> 00:03:17,405 And these limited program sets miss better full-grid plans. 52 00:03:18,220 --> 00:03:21,207 VQE now switches from CVaR to Gibbs loss. 53 00:03:21,357 --> 00:03:31,042 Median offered-optimum probability rises from twelve percent to ninety-nine point five percent in both disruption cases, across ten seeds each. 54 00:03:31,192 --> 00:03:32,813 This uses exact gradients. 55 00:03:32,963 --> 00:03:36,953 The staged improvement did not carry over to shot-noise emulation. 56 00:03:38,220 --> 00:03:41,889 For larger plans, VeloxQ sits inside a replanning loop. 57 00:03:42,039 --> 00:03:43,469 It starts from its own plan. 58 00:03:43,619 --> 00:03:51,256 We free two blocks, solve their conditional QUBO, and keep a change only if it passes the checker and improves the objective. 59 00:03:51,406 --> 00:03:57,443 Across three sizes, missed meal lots drop from nine to seven, eleven to six, and thirteen to seven. 60 00:03:57,593 --> 00:03:59,364 That took seventy-one submissions. 61 00:03:59,514 --> 00:04:04,805 Exact neighborhood controls do as well or better, and longer classical runs still win. 62 00:04:06,220 --> 00:04:07,872 The small cell tests correctness. 63 00:04:08,018 --> 00:04:13,578 Larger inputs generate eighteen thousand batch programs with shared resources and demand. 64 00:04:13,724 --> 00:04:17,766 We measure the cost of restricting choices separately from solver quality. 65 00:04:18,220 --> 00:04:19,543 What capacity should we add? 66 00:04:19,693 --> 00:04:22,594 Our best current-capacity plan serves ninety meals. 67 00:04:22,744 --> 00:04:26,008 A third cooker still serves ninety, but removes the waste. 68 00:04:26,158 --> 00:04:28,782 A prep or packing helper reaches one hundred ten. 69 00:04:28,932 --> 00:04:31,279 The same worker currently does both jobs. 70 00:04:31,429 --> 00:04:34,863 Each variant gets the same classical budget and two seeds. 71 00:04:35,013 --> 00:04:37,509 These are feasible plans, not proven optima. 72 00:04:37,659 --> 00:04:40,305 We'd need prices before recommending a purchase. 73 00:04:42,220 --> 00:04:46,803 Our log records why we changed cleaning, meal coverage and idle encoding. 74 00:04:46,952 --> 00:04:49,113 Twenty meals, no waste in the small case. 75 00:04:49,262 --> 00:04:51,732 The demo links to code, proofs and benchmarks.