{"id":16399,"date":"2026-05-14T11:45:13","date_gmt":"2026-05-14T09:45:13","guid":{"rendered":"https:\/\/qilimanjaro.tech\/?p=16399"},"modified":"2026-06-15T10:37:05","modified_gmt":"2026-06-15T08:37:05","slug":"benchmarking-time-and-energy-inquantum-simulation-a-comparison-ofanalog-and-digital-approaches","status":"publish","type":"post","link":"https:\/\/qilimanjaro.tech\/ca\/benchmarking-time-and-energy-inquantum-simulation-a-comparison-ofanalog-and-digital-approaches\/","title":{"rendered":"Benchmarking Time and Energy in Quantum Simulation: A Comparison of Analog and Digital Approaches"},"content":{"rendered":"<div data-elementor-type=\"wp-post\" data-elementor-id=\"16399\" class=\"elementor elementor-16399\" data-elementor-post-type=\"post\">\n\t\t\t\t<div class=\"elementor-element elementor-element-ce978fe e-flex e-con-boxed e-con e-parent\" data-id=\"ce978fe\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-6b8d461 elementor-widget elementor-widget-text-editor\" data-id=\"6b8d461\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Maig 2026 \u2013 Qilimanjaro<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a0e7f56 elementor-widget elementor-widget-text-editor\" data-id=\"a0e7f56\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p data-start=\"432\" data-end=\"760\">La simulaci\u00f3 de la din\u00e0mica de sistemes qu\u00e0ntics \u00e9s una de les aplicacions a curt termini m\u00e9s prometedores de la computaci\u00f3 qu\u00e0ntica. Tamb\u00e9 \u00e9s una de les tasques m\u00e9s dif\u00edcils per als ordinadors cl\u00e0ssics, cosa que la converteix en un objectiu natural per a l'avantatge qu\u00e0ntic. Dues grans aproximacions competeixen per aconseguir aquest objectiu: <strong>anal\u00f2gic<\/strong> i <strong>digital<\/strong> computaci\u00f3 qu\u00e0ntica. Apunten a la mateixa din\u00e0mica a trav\u00e9s de rutes molt diferents, i el cost de cada ruta tamb\u00e9 resulta ser molt diferent. En un document t\u00e8cnic recent, vam comparar els dos paradigmes en un punt de refer\u00e8ncia simple i representatiu: l'evoluci\u00f3 temporal del model d'Ising de camp transversal en una xarxa bidimensional. Els resultats s\u00f3n sorprenents:<\/p><ul><li data-start=\"432\" data-end=\"760\">Cap ordinador qu\u00e0ntic digital actualment disponible pot reproduir la din\u00e0mica amb la mateixa precisi\u00f3 (dins d&#x27;un pressupost d&#x27;error de 51 TP3T) que un dispositiu anal\u00f2gic aconsegueix directament.<\/li><li data-start=\"432\" data-end=\"760\">Fins i tot assumint que existeixen computadores qu\u00e0ntics digitals tolerants a fallades, els computadores qu\u00e0ntics anal\u00f2gics s\u00f3n aproximadament <strong>\u223c 630 \u00d7 m\u00e9s r\u00e0pid<\/strong> i consume al voltant de <strong>\u223c 90 \u00d7 menys energia<\/strong> en la mateixa tasca.<\/li><li data-start=\"432\" data-end=\"760\">Aconseguir la precisi\u00f3 de l'objectiu digitalment requeriria fidelitats de portes de dos c\u00fabits <strong>tres a sis ordres de magnitud m\u00e9s enll\u00e0 de l'actual maquinari m\u00e9s avan\u00e7at.<\/strong><\/li><\/ul><p>\u00a0<\/p><p>A continuaci\u00f3, desglossem el significat d'aquests n\u00fameros i per qu\u00e8 es compleixen. Per a m\u00e9s informaci\u00f3,\u00a0<strong><a style=\"background-color: #f3f3f3;\" href=\"https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/06\/Benchmarking_Time_and_Energy_in_Quantum_Simulation.pdf\" target=\"_blank\" rel=\"noopener\">consulteu el nostre llibre blanc.<\/a><\/strong><\/p><p><span style=\"color: inherit; font-family: inherit; font-size: 2rem;\">\u00a0<\/span><\/p><h2 data-start=\"432\" data-end=\"760\"><strong>1. Dues maneres de simular un sistema qu\u00e0ntic<\/strong><\/h2><p data-start=\"432\" data-end=\"760\">Una simulaci\u00f3 qu\u00e0ntica respon una simple pregunta de f\u00edsica: <em>Com canvia aquest sistema amb el temps?<\/em>\u00a0 Els dos paradigmes hi donen resposta de maneres fonamentalment diferents.<\/p><p data-start=\"432\" data-end=\"760\"><strong>Ordinadors qu\u00e0ntics anal\u00f2gics<\/strong> Ho respon directament. Creen un sistema f\u00edsic que les seves interaccions naturals coincideixin amb les del problema d'inter\u00e8s, l'encenguin i deixin que la natura faci la resta. L'ordinador \u00e9s la f\u00edsica, de manera que no cal traduir el problema a res m\u00e9s.<\/p><p class=\"p1\"><strong>Computadores qu\u00e0ntics digitals<\/strong> Respon-hi indirectament. Aproximen les mateixes din\u00e0miques a trav\u00e9s d'una llarga seq\u00fc\u00e8ncia d'operacions discretes (ports qu\u00e0ntics), de manera similar a com un integrador num\u00e8ric aproxima una funci\u00f3 cont\u00ednua en un ordinador cl\u00e0ssic. S\u00f3n universals, per\u00f2 paguen per aquesta universalitat en profunditat de circuit.<\/p><p class=\"p1\">Aquesta divisi\u00f3 ha estat el debat arquitect\u00f2nic central en la computaci\u00f3 qu\u00e0ntica durant m\u00e9s d'una d\u00e8cada. El nostre treball quantifica el comprom\u00eds per a una tasca concreta.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-86d3a95 e-con-full e-flex e-con e-child\" data-id=\"86d3a95\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-7bf5dd3 e-con-full e-flex e-con e-child\" data-id=\"7bf5dd3\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-7713619 elementor-widget elementor-widget-image\" data-id=\"7713619\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"781\" height=\"297\" src=\"https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Recurso-4Analog.png\" class=\"attachment-large size-large wp-image-16444\" alt=\"\" srcset=\"https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Recurso-4Analog.png 781w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Recurso-4Analog-300x114.png 300w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Recurso-4Analog-768x292.png 768w\" sizes=\"(max-width: 781px) 100vw, 781px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-2705e71 e-con-full e-flex e-con e-child\" data-id=\"2705e71\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1ace7c3 elementor-widget elementor-widget-image\" data-id=\"1ace7c3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"779\" height=\"297\" src=\"https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Recurso-5Digital.png\" class=\"attachment-large size-large wp-image-16445\" alt=\"\" srcset=\"https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Recurso-5Digital.png 779w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Recurso-5Digital-300x114.png 300w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Recurso-5Digital-768x293.png 768w\" sizes=\"(max-width: 779px) 100vw, 779px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1874627 elementor-widget elementor-widget-text-editor\" data-id=\"1874627\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p class=\"p1\">\u00a0<\/p><h2 data-start=\"432\" data-end=\"760\"><strong>2. El punt de refer\u00e8ncia<\/strong><\/h2><p class=\"p1\">Ens centrem en un model paradigm\u00e0tic en la f\u00edsica de molts cossos qu\u00e0ntics: el <strong>model d'Ising de camp transversal<\/strong>. Els espins es troben als v\u00e8rtexs d'una xarxa, els espins ve\u00efns interactuen i un camp extern actua sobre cada spin individualment. Evolucionem aquest sistema durant un microsegon en tres geometries de xarxa que coincideixen amb les generacions de maquinari de Qilimanjaro:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-dd7e36e elementor-widget elementor-widget-spacer\" data-id=\"dd7e36e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a3199c8 elementor-widget elementor-widget-image\" data-id=\"a3199c8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"768\" height=\"248\" src=\"https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Frame-87455798-1-768x248.png\" class=\"attachment-medium_large size-medium_large wp-image-16460\" alt=\"\" srcset=\"https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Frame-87455798-1-768x248.png 768w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Frame-87455798-1-300x97.png 300w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Frame-87455798-1-1024x330.png 1024w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Frame-87455798-1-1536x496.png 1536w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Frame-87455798-1-2048x661.png 2048w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d2021d2 elementor-widget elementor-widget-spacer\" data-id=\"d2021d2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5c366a3 elementor-widget elementor-widget-text-editor\" data-id=\"5c366a3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p class=\"p1\">La precisi\u00f3 objectiu \u00e9s un pressupost total d&#x27;errors de 51 TP3T. La pregunta, doncs, \u00e9s senzilla:<i> Quant <\/i><i>costa \u2013 en temps, portes, fidelitat i energia \u2013 assolir aquest objectiu en cada paradigma?<\/i><\/p><p>\u00a0<\/p><h2 class=\"p1\"><strong>3. Trotteritzaci\u00f3: com funciona realment la simulaci\u00f3 digital<\/strong><\/h2><p class=\"p2\">Quan un ordinador digital no pot aplicar l'Hamiltoni\u00e0 complet d'una vegada (perqu\u00e8 les diferents parts de l'Hamiltoni\u00e0 no commuten), divideix l'evoluci\u00f3 en molts passos petits. Aix\u00f2 s'anomena <strong>Troteritzaci\u00f3<\/strong>. La idea \u00e9s senzilla: tallem el temps d'evoluci\u00f3 total en intervals petits \u03b4t, i dins de cada interval apliquem les diferents parts de l'Hamiltoni\u00e0 una darrere l'altra.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-a85bada e-con-full e-flex e-con e-child\" data-id=\"a85bada\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-3d003d1 elementor-widget elementor-widget-image\" data-id=\"3d003d1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"768\" height=\"279\" src=\"https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Jan_recursos-04-768x279.png\" class=\"attachment-medium_large size-medium_large wp-image-16406\" alt=\"\" srcset=\"https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Jan_recursos-04-768x279.png 768w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Jan_recursos-04-300x109.png 300w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Jan_recursos-04-1024x372.png 1024w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Jan_recursos-04-1536x558.png 1536w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Jan_recursos-04-2048x744.png 2048w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-06eb6c4 elementor-widget elementor-widget-image\" data-id=\"06eb6c4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"768\" height=\"279\" src=\"https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Jan_recursos-768x279.png\" class=\"attachment-medium_large size-medium_large wp-image-16409\" alt=\"\" srcset=\"https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Jan_recursos-768x279.png 768w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Jan_recursos-300x109.png 300w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Jan_recursos-1024x372.png 1024w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Jan_recursos-1536x558.png 1536w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Jan_recursos-2048x744.png 2048w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-30c45ad elementor-widget elementor-widget-spacer\" data-id=\"30c45ad\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-438d773 elementor-widget elementor-widget-text-editor\" data-id=\"438d773\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p class=\"p1\">Figura 1: Una evoluci\u00f3 cont\u00ednua anal\u00f2gica (esquerra) La Trotteritzaci\u00f3 discretitza una evoluci\u00f3 cont\u00ednua (dreta). Cada pas introdueix un petit error d'aproximaci\u00f3, que disminueix a mesura que creix el nombre de passos.<\/p><p class=\"p1\">Passos m\u00e9s petits signifiquen una aproximaci\u00f3 m\u00e9s precisa, per\u00f2 tamb\u00e9 m\u00e9s portes l\u00f2giques, i en un dispositiu real i soroll\u00f3s, m\u00e9s portes l\u00f2giques signifiquen m\u00e9s error acumulat del maquinari. Per tant, hi ha un punt \u00f2ptim entre \u201cmassa pocs passos, massa error d'aproximaci\u00f3\u201d i \u201cmassa passos, massa error del maquinari\u201d.<\/p><p class=\"p1\">Per millorar aquest comprom\u00eds, es pot utilitzar <strong>f\u00f3rmules de Trotter d'ordre superior<\/strong> (anomenat S<span class=\"s1\">2<\/span>, i<span class=\"s1\">4<\/span>, i<span class=\"s1\">6<\/span>, i aix\u00ed successivament). Redueixen l'error d'aproximaci\u00f3 per pas combinant diversos sub-passos en enginyoses disposicions sim\u00e8triques, fent cada pas m\u00e9s prec\u00eds a costa de ser m\u00e9s car en portes. Com veurem, un ordre m\u00e9s alt no sempre \u00e9s millor.<\/p><h2>\u00a0<\/h2><h2 class=\"p1\"><strong>4. Els ordinadors qu\u00e0ntics digitals actuals no poden executar aquests circuits<\/strong><\/h2><p class=\"p2\">El primer resultat de l&#x27;an\u00e0lisi \u00e9s que cap dels circuits de Trotter necessaris per assolir una precisi\u00f3 de 5% en la xarxa de 5\u00d75 encaixa dins el <strong>temps de coher\u00e8ncia<\/strong> de qubits superconductors actuals, la finestra durant la qual un qubit mant\u00e9 el seu estat qu\u00e0ntic. Prenem els qubits superconductors com a refer\u00e8ncia perqu\u00e8 s\u00f3n la plataforma digital m\u00e9s r\u00e0pida disponible avui dia pel que fa a temps d'operaci\u00f3 de portes. En plataformes m\u00e9s lentes com els ions atrapats, on les portes de dos qubits poden ser ordres de magnitud m\u00e9s lentes, els temps d'execuci\u00f3 del circuit serien corresponentment m\u00e9s llargs i la bretxa respecte als temps de coher\u00e8ncia encara m\u00e9s \u00e0mplia.<\/p><p class=\"p2\">Taula 1: Temps d'execuci\u00f3 del circuit versus temps de coher\u00e8ncia t\u00edpic de m\u00faltiples qubits (T<span class=\"s1\">2 <\/span>\u223c 100 \u03bcs) per a la reixeta de 5\u00d75.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-be3752d elementor-widget elementor-widget-spacer\" data-id=\"be3752d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cdd9cf8 elementor-widget elementor-widget-image\" data-id=\"cdd9cf8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/qilimanjaro.tech\/wp-content\/uploads\/elementor\/thumbs\/Frame-87455799-scaled-rnehhdme31cpphkwgs2bd308jsbud6smjzae595a80.png\" title=\"Marc 87455799\" alt=\"Frame 87455799\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4e033dc elementor-widget elementor-widget-spacer\" data-id=\"4e033dc\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-20a4d25 elementor-widget elementor-widget-text-editor\" data-id=\"20a4d25\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p class=\"p1\">Fins i tot la descomposici\u00f3 m\u00e9s compacta (Trotter de quart ordre) triga aproximadament sis vegades m\u00e9s que el temps de coher\u00e8ncia dels qubits. La descomposici\u00f3 de primer ordre triga m\u00e9s de mil vegades m\u00e9s. Quan el circuit s'acaba, la informaci\u00f3 qu\u00e0ntica ja s'ha descoherentitzat en soroll.<\/p><p class=\"p1\">Equivalentment, assolir la precisi\u00f3 objectiu requeriria taxes d'error de portes de dos qubits entre 10<span class=\"s1\"><sup>\u221210<\/sup> <\/span>i 10<span class=\"s1\"><sup>\u22127<\/sup><\/span>, mentre que el millor maquinari superconductor actual es troba al voltant de 10<span class=\"s1\"><sup>\u22123<\/sup><\/span>. Tancar aquesta bretxa requereix <strong>correcci\u00f3 d'errors qu\u00e0ntics<\/strong>, el r\u00e8gim tolerant a fallades.<\/p><h2>\u00a0<\/h2><h2 class=\"p1\"><strong>5. Fins i tot la simulaci\u00f3 digital tolerant a errors t\u00e9 un cost energ\u00e8tic<\/strong><\/h2><p class=\"p1\">La contraargumentaci\u00f3 natural seria: \u201cd'acord, avui en dia el digital no pot fer-ho, per\u00f2 un cop arribi la toler\u00e0ncia a fallades, la bretxa es tancar\u00e0\u201d. La nostra an\u00e0lisi suggereix el contrari. Fins i tot <em>suposant<\/em> els ordinadors qu\u00e0ntics digitals tolerants a fallades estan disponibles (i ignorant l'overhead substancial de qubits que la toler\u00e0ncia a fallades requereix), el temps d'execuci\u00f3 i el buit energ\u00e8tic persisteixen.<\/p><p class=\"p1\">El motiu \u00e9s estructural. Ambdues parades funcionen dins d'un refrigerador per diluci\u00f3 que consumeix al voltant de 19 kW cont\u00ednuament. La infraestructura de refrigeraci\u00f3 domina el pressupost energ\u00e8tic. El que difereix entre les parades \u00e9s <em>quant de temps necessita funcionar el criostat<\/em> per completar el c\u00e0lcul:<\/p><p class=\"p1\">Taula 2: Energia per experiment complet (malla 5\u00d75, 20 000 tirades, pressupost total d&#x27;errors de 5%). La l\u00ednia de base criog\u00e8nica \u00e9s la mateixa per a ambd\u00f3s paradigmes; nom\u00e9s canvia el temps d&#x27;execuci\u00f3.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cd235de elementor-widget elementor-widget-spacer\" data-id=\"cd235de\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4cd3f62 elementor-widget elementor-widget-image\" data-id=\"4cd3f62\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"230\" src=\"https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Frame-87455800-1024x294.png\" class=\"attachment-large size-large wp-image-16403\" alt=\"\" srcset=\"https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Frame-87455800-1024x294.png 1024w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Frame-87455800-300x86.png 300w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Frame-87455800-768x220.png 768w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Frame-87455800-1536x440.png 1536w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Frame-87455800-2048x587.png 2048w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/Frame-87455800-350x100.png 350w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-eb5002d elementor-widget elementor-widget-spacer\" data-id=\"eb5002d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c125c31 elementor-widget elementor-widget-text-editor\" data-id=\"c125c31\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p class=\"p1\">Traducci\u00f3 al cost operatiu al preu mitj\u00e0 minorista de l&#x27;electricitat als EUA (2025):<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d290504 elementor-widget elementor-widget-spacer\" data-id=\"d290504\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9d1e2b4 elementor-widget elementor-widget-image\" data-id=\"9d1e2b4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/qilimanjaro.tech\/wp-content\/uploads\/elementor\/thumbs\/Frame-87455801-rnehif7xoesgu6qfj9nmedfoi4emk0xhbw4qcsv0g0.png\" title=\"Marc 87455801\" alt=\"Frame 87455801\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c928ba6 elementor-widget elementor-widget-spacer\" data-id=\"c928ba6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-06eb3ee elementor-widget elementor-widget-text-editor\" data-id=\"06eb3ee\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p class=\"p1\">Per a un experiment \u00fanic, el Trotter de quart ordre encara \u00e9s factible. Per\u00f2 els experiments qu\u00e0ntics rarament es fan una vegada: un barrido de par\u00e0metres t\u00edpic t\u00e9 centenars o milers de repeticions independents, de manera que l'avantatge anal\u00f2gic es compon r\u00e0pidament. I creix amb la mida del sistema:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2b8ed5b elementor-widget elementor-widget-spacer\" data-id=\"2b8ed5b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8639b48 elementor-widget elementor-widget-image\" data-id=\"8639b48\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"2560\" height=\"1368\" src=\"https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/energy_comparison-1-scaled.png\" class=\"attachment-full size-full wp-image-16407\" alt=\"\" srcset=\"https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/energy_comparison-1-scaled.png 2560w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/energy_comparison-1-300x160.png 300w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/energy_comparison-1-1024x547.png 1024w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/energy_comparison-1-768x410.png 768w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/energy_comparison-1-1536x821.png 1536w, https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/05\/energy_comparison-1-2048x1095.png 2048w\" sizes=\"(max-width: 2560px) 100vw, 2560px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d8950be elementor-widget elementor-widget-spacer\" data-id=\"d8950be\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f9dd59b elementor-widget elementor-widget-text-editor\" data-id=\"f9dd59b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p class=\"p1\">Figura 2: Cost energ\u00e8tic per experiment en funci\u00f3 de la mida del sistema <em>N<\/em>. El cost anal\u00f2gic (l\u00ednia horitzontal) \u00e9s independent de <em>N<\/em>. Els costos digitals creixen polin\u00f2micament a mesura que <em>N <sup>(1\/p)<\/sup><\/em> per <em>p<\/em>Trotter d'ordre th. L'avantatge an\u00e0leg s'amplia amb la mida per a totes les ordres.<\/p><p class=\"p1\">Anar a ordres de Trotter cada cop m\u00e9s alts no continua millorant el resultat. Passar del primer al segon ordre redueix el temps d'execuci\u00f3 en un factor d'aproximadament 78. Del segon al quart d\u00f3na una millora addicional d'unes 2.8 vegades. Per\u00f2 el sis\u00e8 ordre \u00e9s <em>pitjor<\/em> que la quarta: el circuit triga m\u00e9s i consumeix m\u00e9s energia.<\/p><p class=\"p1\">El motiu \u00e9s que el nombre de portes per pas de Trotter creix aproximadament com 5<sup>(p\/2)<\/sup><span class=\"s1\">\u00a0<\/span>amb la comanda <em>p<\/em>, mentre que el nombre de passos necessaris nom\u00e9s disminueix de manera polin\u00f2mica. Hi ha un ordre \u00f2ptim finit, m\u00e9s enll\u00e0 del qual afegir m\u00e9s &quot;precision per pas&quot; costa m\u00e9s del que estalvia. Per a aquest banc de proves, el Trotter d&#x27;ordre quart \u00e9s el punt \u00f2ptim i superar-lo redueix la precisi\u00f3 del c\u00e0lcul.<\/p><h2>\u00a0<\/h2><h2 class=\"p1\"><strong>6. Implicacions<\/strong><\/h2><p class=\"p2\">Les nostres troballes afirmen que la simulaci\u00f3 qu\u00e0ntica digital de la din\u00e0mica hamiltoniana, amb la precisi\u00f3 necess\u00e0ria per a resultats \u00fatils, no \u00e9s assolible amb l'actual maquinari ni competitiva amb futur maquinari tolerant a fallades. La primera afirmaci\u00f3 es deriva de temps de coher\u00e8ncia i fidelitats de porta que es troben a tres o sis ordres de magnitud del punt on haurien d'estar. La segona es deriva de l'estructura de la simulaci\u00f3 amb f\u00f3rmula de producte: aproxima un proc\u00e9s f\u00edsic continu a trav\u00e9s d'una seq\u00fc\u00e8ncia discreta d'operacions i incorre en un sobrecost de temps d'execuci\u00f3 i energia, aproximadament\u00a0<strong>90x<\/strong> respectivament en el nostre benchmark, que no desapareix en el r\u00e8gim tolerant a falles.<\/p><p class=\"p2\">Aquesta bretxa \u00e9s estructural, no transit\u00f2ria. No es pot tancar amb millors compiladors o millores incrementals de maquinari, perqu\u00e8 es deriva de l'acte de discretitzar la din\u00e0mica en primer lloc. <strong>Un ordinador qu\u00e0ntic anal\u00f2gic executa la f\u00edsica; un ordinador qu\u00e0ntic digital l'aproxima.<\/strong><\/p><p class=\"p2\">Per a la classe \u00e0mplia de problemes centrats en la din\u00e0mica hamiltoniana, la simulaci\u00f3 qu\u00e0ntica de molts cossos, el c\u00e0lcul qu\u00e0ntic adiab\u00e0tic, l'annealing qu\u00e0ntic i la computaci\u00f3 qu\u00e0ntica de reservori, els ordinadors qu\u00e0ntics anal\u00f2gics s\u00f3n la plataforma m\u00e9s eficient en recursos avui dia, i ho continuaran sent fins i tot a mesura que maduri la toler\u00e0ncia a fallades digitals.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-66bd928 elementor-widget elementor-widget-spacer\" data-id=\"66bd928\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fc07a38 elementor-align-center elementor-widget elementor-widget-button\" data-id=\"fc07a38\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/qilimanjaro.tech\/wp-content\/uploads\/2026\/06\/Benchmarking_Time_and_Energy_in_Quantum_Simulation.pdf\" target=\"_blank\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Comprova el nostre whitepaper<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>May 2026 &#8211; Qilimanjaro Simulating the dynamics of quantum systems is one of the most promising near-term applications of quantum computing. It is also one of the hardest tasks for classical computers, which makes it a natural target for quantum advantage. Two main approaches compete for this goal: analog and digital quantum computing. They aim [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":16435,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"footnotes":""},"categories":[8],"tags":[],"class_list":["post-16399","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-science"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Benchmarking Time and Energy in Quantum Simulation: A Comparison of Analog and Digital Approaches - Qilimanjaro<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/qilimanjaro.tech\/ca\/benchmarking-time-and-energy-inquantum-simulation-a-comparison-ofanalog-and-digital-approaches\/\" \/>\n<meta property=\"og:locale\" content=\"ca_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Benchmarking Time and Energy in Quantum Simulation: A Comparison of Analog and Digital Approaches - Qilimanjaro\" \/>\n<meta property=\"og:description\" content=\"May 2026 &#8211; Qilimanjaro Simulating the dynamics of quantum systems is one of the most promising near-term applications of quantum computing. It is also one of the hardest tasks for classical computers, which makes it a natural target for quantum advantage. Two main approaches compete for this goal: analog and digital quantum computing. 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