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URL:https://uwaterloo.ca/institute-for-quantum-computing/events/jamal-busna
 ina-phd-thesis-defence
SUMMARY:Jamal Busnaina PhD Thesis Defence
CLASS:PUBLIC
DESCRIPTION:ANALOG QUANTUM SIMULATION VIA PARAMETRIC INTERACTIONS IN\nSUPER
 CONDUCTING CIRCUITS\n\nWhile universal quantum computers are still years a
 way from being used\nfor simulating complicated quantum systems\, analog q
 uantum simulators\nhave become an increasingly attractive approach to stud
 ying\nclassically intractable quantum systems in condensed matter physics\
 ,\nchemistry\, and high-energy physics. In this dissertation\, we utilize\
 nsuperconducting cavities and qubits to establish analog quantum\nsimulati
 on (AQS) platforms to study systems of interest. \n\nAn approach of AQS t
 hat has gained interest lately is the use of\nphotonic lattices to simulat
 e popular lattice models. These systems\nconsist of an array of cavities o
 r resonators arranged on a lattice\nwith some couplings graph between mode
 s. We propose an in situ\nprogrammable platform based on a superconducting
  multimode cavity. The\nunique design of the cavity allows us to program a
 rbitrarily connected\nlattices where the coupling strength and phase of ea
 ch individual\ncoupling are highly programmable via parametrically activat
 ed\ninteractions. Virtually any quadratic bosonic Hamiltonian can be\nreal
 ized in our platform with a straightforward pumping scheme.\n\nThe effecti
 veness of the cavity-based AQS platform was demonstrated by\nthe experimen
 tal simulation of two interesting models. First\, we\nsimulated the effect
  of a fictitious magnetic field on a 4-site\nplaquette of a bosonic Creutz
  ladder\, a paradigmatic topological model\nfrom high-energy physics.  Un
 der the right magnetic field conditions\,\nwe observed topological feature
 s such as emergent edge states and\nlocalized soliton states. The platform
 's ability is further explored\nby introducing pairing (downconversion) te
 rms to simulate the Bosonic\nKitaev chain (BKC)\, the bosonic version of t
 he 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 dissertation\, we
  propose and implement a\nparametrically activated 3-qubit interaction in 
 a circuit QED\narchitecture as the simplest building block to simulate lat
 tice gauge\ntheories (LGT). LGT is a framework for studying gauge theories
  in\ndiscretized space-time\, often used when perturbative methods fail. 
  \nThe gauge symmetries lead to conservation laws\, such as Gauss's law i
 n\nelectrodynamics\, which impose constraints tying the configuration of\n
 the gauge field to the configuration of ''matter'' sites.  Therefore\,\na
 ny quantum simulation approach for LGTs must maintain these\nconservation 
 laws\, with one strategy in AQS being to build them in at\nthe hardware le
 vel.  Here\, the gauge constraints are explicitly\nincluded using a highe
 r-order parametric process between three qubits.\nThe simplest 2-site U(1)
  LGT building block is realized with two\nqubits as matter sites and a thi
 rd qubit as the gauge field mediating\nthe matter-matter interaction\, whi
 ch is crucial to maintain the\nsymmetry of U(1) LGTs.  
DTSTAMP:20260420T191831Z
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