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URL:/institute-for-quantum-computing/events/jamal-busna
 ina-phd-thesis-defence
SUMMARY:Jamal Busnaina PhD Thesis Defence
CLASS:PUBLIC
DESCRIPTION:Summary \n\nANALOG QUANTUM SIMULATION VIA PARAMETRIC INTERACTIO
 NS IN\nSUPERCONDUCTING CIRCUITS\n\nWhile universal quantum computers are s
 till years away from being used\nfor simulating complicated quantum system
 s\, analog quantum simulators\nhave become an increasingly attractive appr
 oach to studying\nclassically intractable quantum systems in condensed mat
 ter physics\,\nchemistry\, and high-energy physics. In this dissertation\,
  we utilize\nsuperconducting cavities and qubits to establish analog quant
 um\nsimulation (AQS) platforms to study systems of interest. \n\nAn appro
 ach of AQS that has gained interest lately is the use of\nphotonic lattice
 s to simulate popular lattice models. These systems\nconsist of an array o
 f cavities or resonators arranged on a lattice\nwith some couplings graph 
 between modes. We propose an in situ\nprogrammable platform based on a sup
 erconducting multimode cavity. The\nunique design of the cavity allows us 
 to program arbitrarily connected\nlattices where the coupling strength and
  phase of each individual\ncoupling are highly programmable via parametric
 ally activated\ninteractions. Virtually any quadratic bosonic Hamiltonian 
 can be\nrealized in our platform with a straightforward pumping scheme.\n\
 nThe effectiveness of the cavity-based AQS platform was demonstrated by\nt
 he experimental simulation of two interesting models. First\, we\nsimulate
 d the effect of a fictitious magnetic field on a 4-site\nplaquette of a bo
 sonic Creutz ladder\, a paradigmatic topological model\nfrom high-energy p
 hysics.  Under the right magnetic field conditions\,\nwe observed topolog
 ical features such as emergent edge states and\nlocalized soliton states. 
 The platform's ability is further explored\nby introducing pairing (downco
 nversion) terms to simulate the Bosonic\nKitaev chain (BKC)\, the bosonic 
 version of the famous Fermionic Kitaev\nchain that hosts Majorana fermions
 . We observe interesting properties\nof BKC\, such as chiral transport and
  sensitivity to boundary\nconditions.  \n\nIn the final part of the disse
 rtation\, we propose and implement a\nparametrically activated 3-qubit int
 eraction in a circuit QED\narchitecture as the simplest building block to 
 simulate lattice gauge\ntheories (LGT). LGT is a framework for studying ga
 uge theories in\ndiscretized space-time\, often used when perturbative met
 hods fail.  \nThe gauge symmetries lead to conservation laws\, such as Ga
 uss's law in\nelectrodynamics\, which impose constraints tying the configu
 ration of\nthe gauge field to the configuration of ''matter'' sites.  The
 refore\,\nany quantum simulation approach for LGTs must maintain these\nco
 nservation laws\, with one strategy in AQS being to build them in at\nthe 
 hardware level.  Here\, the gauge constraints are explicitly\nincluded us
 ing a higher-order parametric process between three qubits.\nThe simplest 
 2-site U(1) LGT building block is realized with two\nqubits as matter site
 s and a third qubit as the gauge field mediating\nthe matter-matter intera
 ction\, which is crucial to maintain the\nsymmetry of U(1) LGTs.  \n 
DTSTAMP:20250523T085725Z
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