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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

The Fisher information quantifies to what precision an unknown parameter can be learned from stochastic data. In the case of independent and identically-distributed random variables the precision scales linearly with their number. The i.i.d. assumption, however, is not always justified especially for temporal data where correlations are to be expected, such as in the outcomes of continuous measurement of a quantum system. In this talk, I will show how estimation precision behaves in the presence of temporal correlations and show that the scaling remains linear for processes with finite Markov order and with what rate. The second part of the talk will focus on parameter estimation in the quantum jump unravelling of a quantum master equation.
This talk is based on:
Radaelli, M., Landi, G. T., Modi, K., & Binder, F. C. Fisher information of correlated stochastic processes. New Journal of Physics 25, 053037 (2023). https://doi.org/10.1088/1367-2630/acc01d
Radaelli, M., Smiga, J. A., Landi, G. T., & Binder, F. C. Parameter estimation for quantum jump unraveling. ArXiv:2402.06556 (2024). https://doi.org/10.48550/arXiv.2402.06556
Radaelli, M., Landi, G. T., & Binder, F. C. Gillespie algorithm for quantum jump trajectories. Physical Review A 110, 062212 (2024). https://doi.org/10.1103/PhysRevA.110.062212

With the advent of digital and analog quantum simulation experiments, it is now possible to experimentally simulate the dynamics of quantum many-body lattice systems and make site-resolved measurements. These experiments make it pertinent to consider the probability of getting any specific measurement outcome, which we call the signal, on placing multiple detectors at various sites while simulating the dynamics of a quantum many-body lattice system. In this work we formulate and investigate this problem, introducing the concept of quantum many-body detection probability (QMBDP), which refers to the probability of detecting a chosen signal at least once in a given time. We show that, on tuning some Hamiltonian parameters, there can be sharp transition from a regime where the QMBDP is approximately equal to one to a regime where the QMBDP is approximately equal to zero. Most notably, the effects of such a transition can be observed at a single trajectory level. This is not a measurement-induced transition, but rather a nonequilibrium transition reflecting opening of a specific type of gap in the many-body spectrum. We demonstrate this in a single-impurity nonintegrable model, where changing the many-body interaction strength brings about such a transition. Our findings suggest that instead of measuring expectation values, single-shot stroboscopic measurements could be used to observe nonequilibrium transitions.

 In the early 1960's Roy Glauber presented a theory to characterize the temporal fluctuations in photo-detection signals.  Such fluctuations can be signatures of non-classical properties, and the theory of photo-detection gave rise to the field of quantum optics with visions to control atomic light emitters to prepare and apply a variety of quantum states of light in experiments. In the past decades, "bits and pieces" of solid-state materials were manufactured with high purity and precision, enabling observation of similar phenomena with solid state spin systems and superconducting circuits, microwaves and acoustic waves as had been studied with single atoms and photons in quantum optics.
The talk will review more recent methods that refine and elaborate on Glauber's theories to describe the dynamics of open quantum systems, i.e., systems subject to interactions with their environment. These methods reintroduce, but with a plot twist, Niels Bohr's quantum jumps in modern quantum physics, and while being employed for quantum technology applications they imply delightful encounters with the famous discussions between Niels Bohr and Albert Einstein on the interpretation of quantum theory.

In the original Matrix movie, the bulk of the human population lives not in the real world but inside a computer simulation called the Matrix. They are unable to detect this situation, except for the fact that certain agents can transcend the normal rules of physics. In this talk, I will explain how this is eerily similar to the world we live in. Certain people (quantum physicists) can transcend the normal rules by using entangled particles to do things that "should be" impossible. This makes the world a very puzzling place, even for quantum physicists. These “super-powers” are also central to the emerging field of quantum information technology. Finally, I will explain very recent work by myself and co-workers [1] that ties all of this together in order to show that the world is even more puzzling than we had thought. Much like the latest Matrix movie.

[1] K.-W. Bong, A. Utreras-Alarcón, et al., Nature Physics 16, 1199 (2020); E. G. Cavalcanti and H.M. Wiseman, Entropy 23, 925 (2021); H. M. Wiseman, E. G. Cavalcanti, and E.G Rieffel, Quantum 7, 1112 (2023).

Hybrid quantum systems based on collective states of a spin ensemble have served as exciting platforms for quantum technology ranging from quantum communication protocols to processing and storage of quantum information. In this talk, we present a theoretical approach to study the open dynamics of states of the spin ensemble-cavity system based on tensor-network methods. We show how these methods allow us to design and demonstrate high-fidelity transfer and protection of information in collective states of a hybrid quantum system.

Is it possible to simulate efficiently using classical means the workings of a quantum computer that used mixed states if no non-classical correlations are generated in the mixed state? We discuss this question in the context of the DQC1 model of quantum computation and sketch path for efficient classical simulation of the DQC1 circuit that estimates the trace of an implementable unitary under the zero quantum discord condition is presented and the challenges in doing such a simulation are elucidated. This result reinforces the status of non-classical correlations quantified by quantum discord and related measures as the key resource enabling exponential speedups in mixed state quantum computation.

I will briefly review the operational and algorithmic approach for digital quantum simulation using different forms of quantum walk and present the example for simulating Dirac equations [1], many-body systems dynamics, complex quantum networks and open quantum systems [2]. I will also present the progress made in experimentally realizing and controlling quantum walks which with a promise for performing universal quantum computation[3].

[1] Nature Communications 11, 3720 (2020)
[2] New J. Phys. 22, 123027 (2020) ; New Journal of Physics 23, 113013 (2021)
[3] EPJ Quantum Technology 10, 43 (2023); Physical Review A 110 (3), 032615 (2024)

In the last decade, we have witnessed remarkable progress in quantum computing aided by an ever increasing number of qubits, enhanced error correction methods, and advances in hardware. One of the major obstacles that quantum computing must deal with is environmental effects on quantum dynamics. The obstacle originates from quantum systems being – unavoidably – a part of nature and, thereby, not isolated and noise-free. Thoroughly understanding the dynamics of quantum systems connected to the environment, or open quantum systems remains one of the critical research areas.

The primary focus of our research at Spin Lab is the dynamics of open quantum systems. The research relies on home-grown theoretical tools and experimental work using Nuclear Magnetic Resonance spectroscopy. The theoretical part involves the formulation and applications of a novel form of quantum master equation that takes into account the fluctuations in the local environment. To completely incorporate their effects, a propagator is designed to include finite evolution due to the fluctuations and infinitesimal evolution due to system Hamiltonians. The resulting quantum master equation (named, fluctuation-regularized quantum master equation or FRQME) is characterized by the presence of an exponential kernel in the dissipator and – most importantly – by the inclusion of dissipators from external drives and coupling. The later dissipators have been shown to play a major role in explaining many of the hitherto enigmatic features of spin dynamics, such as the emergence of prethermal plateau in spin-locking experiments, the emergence of superradiance in dipolar systems. The new master equation was used to show optimal behavior in various quantum control experiments. FRQME had been used in quantum optics to show the nonlinear behavior of light shifts and in quantum sensing. FRQME has also been used to explore foundational aspects of quantum mechanics.
In the presentation, the FRQME and some of its applications in wide-ranging areas will be highlighted.