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- Project Team :Noah Stevenson, Gerwin Koolstra, Karthik Siva, Akel Hashim
- Collaborators :Justin Dressel, Shiva Barzili, Sacha Greenfield (Chapman University)
- Start Date :January 2019
- Status :In Process
- Presentations :2019, 2020 APS March Meetings

All quantum systems couple to their surrounding environment, itself composed of unmonitored quantum-coherent degrees of freedom. Often the environment exhibits a memory of the system’s state, resulting in Non-Markovian return of quantum information to the system at later times. Since current techniques to reconstruct a system’s state from experimental data, such as stochastic master equations (SME’s), rely on Markovianity, understanding how quantum-coherent devices evolve in the presence of non-Markovian effects remains an outstanding problem. We use continuous quantum state tracking with weak measurement to experimentally investigate non-Markovianity in transmon superconducting qubits and train recurrent neural network models to reconstruct quantum trajectories, motivated by such models’ demonstrated ability to learn long-time correlations in sequential data. Accurately reconstructed quantum trajectories in turn enable us to determine the degree to which a system is non-Markovian, estimate time-dependent SME parameters, and map heterodyne backaction.

- Driven qubit-cavity system: Precise quantum control of superconducting qubits necessitates determining the time-dependent Hamiltonian of control pulses with high fidelity. While continuous state tracking has proved effective for determining single-qubit time-evolution in regimes with Markovian dynamics, fast control pulses used for native quantum gates and entanglement generation can result in non-Markovian transient dynamics. We use quantum state tracking with continuous weak measurement to experimentally investigate non-Markovianity in a transmon superconducting qubit coupled to a readout resonator. By weakly measuring the qubit state during a Rabi oscillation sequence on a timescale comparable to the cavity decay rate, we isolate dynamics that are difficult to describe with single-qubit trajectory theory. We are currently studying the effect of qubit-cavity hybridization and heterodyne backaction.
- Multi-qubit system:We investigate an analog quantum simulation of a qubit strongly coupled to an unmonitored, coherent environment with two qubits on a multi-qubit chip coupled by an always-on cross-resonance (CR) and ZZ interaction, where one qubit acts as the system and the other as the environment. As the two-qubit state oscillates between a separable and entangled state due to the CR interaction, the system qubit oscillates between a pure and mixed state, simulating decoherence to the environment and non-Markovian information backflow.

Current research activities revolve around analysis of single-qubit evolution in the presence of non-Markovian quantum memory with the goal of estimating time-dependent SME parameters and characterizing memory properties such as correlation time. Future directions include investigating other systems that host non-Markovian effects, characterizing the properties of non-Markovian memory, investigating methods of general non-Markovian trajectory reconstruction beyond recurrent neural networks, diagnosing gate errors with continuous weak measurement, and measuring quantum trajectories of three level systems.
### Relevant Publications:

E. Flurin, L.S. Martin, S. Hacohen-Gourgy, I.Siddiqi, Using a Recurrent Neural Network to Reconstruct Quantum Dynamics of a Superconducting Qubit from Physical Observations Phys. Rev. X 10, 011006 (2020)

S. J. Weber, A. Chantasri, J. Dressel, A. N. Jordan, K. W. Murch, I. Siddiqi. Mapping the optimal route between two quantum states. Nature, 511 (7511), pp. 570–573, (2014)

S. J. Weber, A. Chantasri, J. Dressel, A. N. Jordan, K.J. Cerrillo and J. Cao, Non-Markovian Dynamical Maps: Numerical Processing of Open Quantum Trajectories. Phys. Rev. Lett. 112, 110401 (2014)

S. J. Weber, A. Chantasri, J. Dressel, A. N. Jordan, K.K. W. Murch, S. J. Weber, C. Macklin, I. Siddiqi. Observing single quantum trajectories of a superconducting quantum bit. Nature, 502 (7470), pp. 211–214, (2013)