Friday Quantum Seminar

We argue that all locality-preserving mappings between fermionic observables and Pauli matrices on a two-dimensional lattice can be generated from the exact bosonization (arXiv:1711.00515), whose gauge constraints project onto the subspace of the toric code with emergent fermions. Starting from the exact bosonization and applying Clifford finite-depth generalized local unitary (gLU) transformation, we can achieve all possible fermion-to-qubit mappings (up to the re-pairing of Majorana fermions).

Dirac Spin Liquids (DSLs) are gapless symmetric states in 2+1 dimensions with no magnetic order. They are featureless, yet interesting because their low energy physics is believed to be described by QED-3, an effective field theory in terms of gapless Dirac fermions coupled to an emergent U(1) gauge field. They also serve as a parent state for seemingly unrelated magnetically ordered states, where the ordered states arise from condensation of ``monopole excitations” of the DSL. Can such a description have experimentally observable consequences?

We derive a family of optimal protocols, in the sense of saturating the quantum Cramér-Rao bound, for measuring a linear combination of d field amplitudes with quantum sensor networks, a key subprotocol of general quantum sensor networks applications. We demonstrate how to select different protocols from this family under various constraints via linear programming. Focusing on entanglement-based constraints, we prove the surprising result that highly entangled states are not necessary to achieve optimality for many problems.

To realize a digital quantum processor based on superconducting qubits, gate error rates must be further reduced by raising coherence times and increasing anharmonicity. I report our group's progress in improving coherence and control of fluxonium superconducting qubits by optimizing the circuit's spectrum and enhancing fabrication methods.

Gauge theory is a powerful theoretical framework for understanding the fundamental forces in the standard model. Simulating the real time dynamics of gauge theory, especially in the strong coupling regime, is a challenging classical problem.  Quantum computers offer a solution to this problem by taking advantage of the intrinsic quantum nature of the systems. The Schwinger model, that is the 1+1 dimensional U(1) gauge theory coupled to fermions, has served as a testbed for different methods of quantum simulation.

Monitored random unitary circuits with intermittent measurements can host a phase transition between a pure and a mixed phase with different entanglement entropy behaviors with the system size. Recently, it was demonstrated that these phase transitions can be locally probed via entangling reference qubits to the quantum circuit and studying the purification dynamics of the reference qubits. After disentangling from the circuit, the state of the reference qubit can be determined according to the measurement outcomes of the qubits in the circuit.

Nuclear magnetic resonance (NMR) spectroscopy is a useful tool in understanding molecular composition and dynamics, but simulating NMR spectra of large molecules becomes intractable on classical computers as the spin correlations in these systems can grow exponentially with molecule size. In contrast, quantum computers are well suited to simulate NMR spectra of molecules, particularly zero- to ultralow field (ZULF) NMR where the spin-spin interactions in the molecules dominate.

Lieb-Robinson bounds are powerful analytical tools for constraining the dynamic and static properties of non-relativistic quantum systems. Recently, a complete picture for closed systems that evolve unitarily in time has been achieved. In experimental systems, however, interactions with the environment cannot generally be ignored, and the extension of Lieb-Robinson bounds to dissipative systems which evolve non-unitarily in time remains an open challenge.

We investigate the difficulty of classically simulating evolution under many-body localized (MBL) Hamiltonians. Using the defining feature that MBL systems have a complete set of local integrals of motion (LIOMs), we demonstrate a transition in the classical complexity of simulating such systems as a function of evolution time. On one side, we construct a quasipolynomial-time tensor-network-inspired algorithm that can simulate MBL systems evolved for any time polynomial in the system size.

We generalized the standard Boson sampling task including Linear Boson Sampling the Gaus- sian Boson Sampling from photons to what we call generalized boson system which the computation relation between the creation and annihilation operators is not a constant. We showed that in such a system, one still has the standard hardness results including Hafnian and Permanents. We also use the spin system as our example and provide an experimental setup.