biostudies-literatureUnknown612(7939)Morvan ASystems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles¹. The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multiparticle bound states^2-9. Here we develop a high-fidelity parameterizable fSim gate and implement the periodic quantum circuit of the spin-½ XXZ model in a ring of 24 superconducting qubits. We study the propagation of these excitations and observe their bound nature for up to five photons. We devise a phase-sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the idea that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit.Nature240-245https://www.ebi.ac.uk/biostudies/studies/S-EPMC9729104biostudies-literatureFormation of robust bound states of interacting microwave photons.PMC9729104Crook ALOpremcak ABovaird JSzalay MXing CJeffrey ENersisyan ASchurkus HFBasso JIsakov SVMartin OGrajales Dau AStrain DSu YSmelyanskiy VCurtin BRubin NCMohseni MLaws LZalcman ABurger TSank DGidney CNewman MVillalonga BVidal GBengtsson AHoffmann MKlots ARKorotkov ANLau KMO'Brien TEArute FRoushan PPetukhov AMalone FBabbush RLee JPotter RForati EWhite TBortoli GCourtney WShvarts VJones CLee KWKhezri MNaaman OAsfaw AKlimov PVMorvan AKelly JLocharla AConner PGiang WGross JATorres ADemura SSaei NAtalaya JBurkett BLester BJNeill CKhattar TArya KDebroy DMBourassa AKim SSatzinger KJZhu NShorter AHuang TKieferova MNeeley MIoffe LBKitaev AYSterling GMichailidis AHarrigan MPHong SNiu MYGiustina MKafri DBuckley BBMount EFoxen BAbanin DAChen ZHilton JBroughton MChen YHabegger SLandhuis DMcEwen MJuhas PMegrant AKechedzhi KGilboa DAleiner ILucero EFarhi EMontazeri SShearn MJBacon DBushnell NDel Toro Barba AFlores Burgos LSkruzny JMiao KCLaptev PNeven HBoixo SBuell DAVollgraff-Heidweiller CHuggins WJChiaro BHarrington SDLiu WMi XAcharya RJiang ZKreikebaum JMYao ZMcClean JROlenewa RFaoro LFowler AGErickson CFatemi RHamilton MCSmith WCMruczkiewicz WQuintana CEppens DKostritsa FMeurer Costa BCollins RSchuster CAndersen TINguyen MDunsworth AHuff AIveland JZhang YBardin JCYeh PYoo JNguyen ASankaragomathi KBrill LLill ATfalseFormation of robust bound states of interacting microwave photons.Systems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles¹. The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multiparticle bound states^2-9. Here we develop a high-fidelity parameterizable fSim gate and implement the periodic quantum circuit of the spin-½ XXZ model in a ring of 24 superconducting qubits. We study the propagation of these excitations and observe their bound nature for up to five photons. We devise a phase-sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the idea that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit.2022-01-01T00:00:00Z2022 Dec2025-04-04T20:45:24.478Z2025-04-04T20:45:24.478ZS-EPMC97291043647713310.1038/s41586-022-05348-y