Talks

We introduce a time-energy uncertainty relation within the context of restarts in monitored quantum dynamics [1] . Previous studies have established that the mean recurrence time, which represents the time taken to return to the initial state, is quantized as an integer multiple of the sampling time, displaying pointwise discontinuous transitions at resonances. Our findings demonstrate that the natural utilization of the restart mechanism in laboratory experiments [2], driven by finite data collection time spans, leads to a broadening effect on the transitions of the mean recurrence time. Our proposed uncertainty relation captures the underlying essence of these phenomena, by connecting the broadening of the mean hitting time near resonances, to the intrinsic energies of the quantum system and to the fluctuations of recurrence time. Our uncertainty relation has also been validated through remote experiments conducted on an International Business Machines Corporation (IBM) quantum computer. We then discuss fractional quantizatization of the recurrence time for interacting spin systems using sub-space measurements [3].
References
[1] R. Yin, Q. Wang, S. Tornow, and E. Barkai, Restart uncertainty relation for monitored quantum dynamics Proceedings of the National Academy of Sciences 122 (1) e2402912121, (2025).
[2] R. Yin, E. Barkai Restart expedites quantum walk hitting times Phys. Rev. Lett. 130, 050802 (2023).
[3] Q. Liu, S. Tornow, D. Kessler, and E. Barkai Properties of Fractionally Quantized Recurrence Times for Interacting Spin Models arXiv:2401.09810 [condmat.stat-mech] (submitted)

1) Introduction to quantum superconducting circuits: resonators, qubits, readout methods
2) Measurement apparatus and their modeling: amplifiers, homodyne and heterodyne measurements, photon detectors, photon counters, quantum efficiency
3) Quantum trajectories of superconducting qubits and cavities: quantum jumps, diffusive trajectories using dispersive measurement and/or fluorescence, past quantum states approach
4) Measurement-based feedback:  stabilization of qubit states and trajectories, stabilization of cavity states, use of neural networks, pros and cons of feedback control compared to reservoir engineering techniques, applications

In this talk, I will discuss how one can use the gravitational path integral to compute the supersymmetric index of black holes as well as other black objects in string theory. The saddles that I shall describe admit a non-zero temperature, consequently lacking an infinitely long AdS throat that separates the horizon from the asymptotic region, and also admit periodic boundary conditions for fermionic fields around the thermal circle, consequently counting bosonic and fermionic states with an opposite sign. Since the microscopic calculation of these indices is oftentimes well understood yet the saddles that I shall describe now lack the conventional decoupling limit taken in AdS/CFT, our analysis represents a first step towards understanding holography for supersymmetric observables in flat space.

Quantum state engineering plays a vital role in various applications in the field of quantum information. Different strategies, including drive-and-dissipation, adiabatic cooling, and measurement-based steering, have been proposed for state generation and manipulation, each with its upsides and downsides. Here, we address a class of measurement-based state engineering protocols where a sequence of generalized measurements is employed to steer a quantum system toward a desired (pure or mixed) target state. Previously studied measurement-based protocols relied on idealized procedures and avoided exploration of the effects of various errors stemming from imperfections of experimental realizations and external noise. We employ the quantum trajectory formalism to provide a detailed analysis of the robustness of these steering protocols against multiple classes of errors. We study a set of realistic errors that can be classified as dynamic or static, depending on whether they remain unchanged while running the protocol. More specifically, we investigate the impact of the erroneous choice of detector-system coupling, erroneous reinitialization of the detector state following a measurement step, fluctuating steering directions, and environmentally induced errors in the detector-system interaction. We show that the protocol remains fully robust against the erroneous choice of detector-system coupling parameters and presents reasonable robustness against other types of errors. Our analysis employs various quantifiers such as fidelity, trace distance, and linear entropy to characterize the protocol’s robustness and provide analytical results for these quantifiers against various errors. We introduce averaging hierarchies of stochastic equations describing individual quantum trajectories associated with detector readouts. Subsequently, we demonstrate the commutation between the classical expectation value and the time-ordering operator of the exponential of a Hamiltonian with multiplicative white noise, as well as the commutation of the expectation value and the partial trace with respect to detector outcomes. Our ideas are implemented and demonstrated for a specific class of steering platforms, addressing a single qubit.

Measurement-induced Phase Transitions (MiPTs) emerge from the interplay between competing local quantum measurements and unitary scrambling dynamics. While monitored quantum trajectories are inherently stochastic, post-selecting specific detector readouts leads to dynamics governed by non-Hermitian Hamiltonians, revealing distinct universal characteristics of MiPTs.

Here, we contrast the quantum dynamics of individual post-selected trajectories with their collective statistics behavior. We introduce a novel partially post-selected stochastic Schrödinger equation that enables the study of controlled subsets of quantum trajectories. Applying this formalism to a Gaussian Majorana fermions model, we employ a two-replica approach combined with renormalization group (RG) techniques to demonstrate that non-Hermitian MiPT universality persists even under limited stochasticity. Notably, we discover that the transition to MiPT occurs at a finite partial post-selection threshold. Our findings establish a framework for leveraging non-Hermitian dynamics to investigate monitored quantum systems while addressing fundamental challenges in post-selection procedures.

It is shown that linearity of classical/quantum/hybrid ensemble dynamics follows from bases of statistics. Hybrid classical- -quantum trajectories and their hybrid master equations are discussed. We stress that the interaction between a classical and a quantum subsystem requires monitoring the quantum subsystem because its action on the classical subsystem can only be realized by the emerging classical signal.

1) Introduction to quantum superconducting circuits: resonators, qubits, readout methods
2) Measurement apparatus and their modeling: amplifiers, homodyne and heterodyne measurements, photon detectors, photon counters, quantum efficiency
3) Quantum trajectories of superconducting qubits and cavities: quantum jumps, diffusive trajectories using dispersive measurement and/or fluorescence, past quantum states approach
4) Measurement-based feedback:  stabilization of qubit states and trajectories, stabilization of cavity states, use of neural networks, pros and cons of feedback control compared to reservoir engineering techniques, applications