ICTS

Quantum thermodynamics is an active research area bridging quantum information and nonequilibrium statistical physics. A key to characterize universal behaviors of entropy production is the fluctuation theorem, which leads to the second law of thermodynamics in the regime far from equilibrium. The fluctuation theorem in classical systems has been thoroughly studied under various feedback control setups by incorporating classical information contents, which sheds modern light on "Maxwell's demon" [1]. However, an intriguing situation in quantum systems, such as continuous (or iterative) measurement and feedback, remains to be investigated.

In this talk, I will first present our theoretical results on the generalized fluctuation theorem and the second law under continuous measurement and feedback [2]. The key ingredient is a newly introduced concept to measure quantum information flow, which we call quantum-classical-transfer (QC-transfer) entropy. QC-transfer entropy can be naturally interpreted as the quantum counterpart of transfer entropy that is commonly used in classical time series analysis.

I will then present our recent collaborating work on an experiment [3]. We employ a state stabilization protocol involving repeated measurement and feedback on an electronic spin qubit associated with a Silicon-Vacancy center in diamond, which is strongly coupled to a diamond nanocavity. This setup allows us to verify the fundamental laws of nonequilibrium quantum thermodynamics, including the second law and the fluctuation theorem, both of which incorporate QC-transfer entropy mentioned above. We further assess the reducible entropy based on the feedback's causal structure and quantitatively demonstrate the thermodynamic advantages of non-Markovian feedback over Markovian feedback. These results reveal a fundamental connection between information and thermodynamics in the quantum regime.

[1] J. M. Parrondo, J. M. Horowitz, and T. Sagawa, Nature Physics 11, 131 (2015).
[2] T. Yada, N. Yoshioka, and T. Sagawa, Phys. Rev. Lett. 128, 170601 (2022).
[3] T. Yada*, P-J. Stas*, A. Suleymanzade, E. Knall, N. Yoshioka, T. Sagawa, and M. Lukin, arXiv:2411.06709 (2024). *: co-first authors

The quantization of gravity is widely believed to result in gravitons -- particles of discrete energy that populate gravitational waves. But their detection has so far been considered impossible. In this talk, I will first show that signatures of single graviton exchanges between matter and gravitational waves can be observed in laboratory experiments. Stimulated and spontaneous single-graviton processes can become relevant for massive quantum acoustic bar resonators, where the stimulated absorption of single gravitons can be resolved through continuous sensing of quantum jumps. In analogy to the discovery of the photo-electric effect for photons, such signatures can provide the first experimental clue of the quantization of gravity.
I will conclude the talk by showing that further statistical tests that probe the quantum mechanical character of radiation fields are also possible, using the counting statistics of observed quantum jumps in resonant detectors. I will present simple statistical tests which provide practical means to test the null hypothesis that a given field is "maximally classical", i.e., accurately described by a coherent state. Our findings suggest circumstances in which that hypothesis plausibly fails, notably including gravitational radiation involving non-linear or stochastic sourcing.

References:
[1] Germain Tobar*, Sreenath K. Manikandan*, Thomas Beitel, and Igor Pikovski. "Detecting single gravitons with quantum sensing."Nature Communications 15, 7229 (2024)

[2] Sreenath K. Manikandan and Frank Wilczek, Detecting Acoherence in Radiation Fields, ArXiv 2409.20378 (2024)

Quantum measurements are described as instantaneous projections in textbooks. They can be stretched out in time using weak measurements, whereby one can observe the evolution of a quantum state towards one of the eigenstates of the measured operator. This evolution is a continuous nonlinear stochastic process, generating an ensemble of quantum trajectories. In particular, the Born rule can be interpreted as a fluctuation-dissipation relation. We experimentally observe the entire quantum trajectory distribution for weak measurements of a superconducting transmon qubit in circuit QED architecture, quantify it, and demonstrate that it agrees very well with the predictions of a single-parameter white-noise stochastic process. This characterisation of quantum trajectories is a powerful clue to unraveling the dynamics of quantum measurement, beyond the conventional axiomatic quantum theory. We emphasise the key quantum features of this framework, and their implications.

We discuss the GKP qubit and how one can mathematically model the decoding task of repeated error correction on a GKP qubit for stochastic displacement noise and coherent finite squeezing noise.

Noise in quantum hardware poses the biggest challenge to realizing robust and scalable quantum computing devices. While conventional quantum error correction (QEC) schemes are relatively resource-intensive, approximate QEC (AQEC) promises a comparable degree of protection from specific noise channels using fewer physical qubits [1 ]. However, unlike standard QEC, the AQEC framework faces hurdles in reliable syndrome measurements due to the overlapping syndrome subspaces leading to the violation of the distinguishability criterion of error subspaces. Our work [2 ] provides an algorithm for discriminating overlapping syndrome subspaces based on the Gram-Schmidt-like orthogonalization routine. In the recovery, we map these orthogonal and disjoint subspaces to the code space followed by a recovery like the perfect recovery [1 , 3 ], or the Petz map [4, 5]. We further prove that this evolved recovery utilizing the Petz map (which we call the canonical Petz map ) gives optimal protection on the information regarding the measure of entanglement fidelity. We show that the performance of the canonical Petz map is similar to that of the Fletcher recovery [ 6 ]. 

[1] D. W. Leung, M. A. Nielsen, I. L. Chuang, and Y. Yamamoto, Approximate quantum error correction can lead to better codes, Physical Review A 56, 2567 (1997).
[2] D. Biswas and P. Mandayam, Efficient syndrome detection for approximate quantum error correction – road towards the optimal recovery, Manuscript is under preparation (2025).
[3] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).
[4 ] H. K. Ng and P. Mandayam, Simple approach to approximate quantum error correction based on the transpose channel, Phys. Rev. A 81, 062342 (2010).
[5] H. Barnum and E. Knill, Reversing quantum dynamics with near- optimal quantum and classical fidelity, Journal of Mathematical Physics 43, 2097 (2002).
[6] A. S. Fletcher, P. W. Shor, and M. Z. Win, Channel-adapted quantum error correction for the amplitude damping channel, IEEE Transactions on Information Theory 54, 5705 (2008).

The thermodynamics of quantum systems driven out of equilibrium has attracted increasing attention in the last decade, in connection with quantum information and statistical physics, and with a focus on non-classical signatures. While a first approach can deal with average thermodynamics quantities over ensembles, in order to establish the impact of quantum and environmental fluctuations during the evolution, a continuous quantum measurement of the open system is required. Such a framework has been developed during the last decade, with recent advances incorporating multiple conserved quantities, the assessment of thermodynamic quantities at stopping times using martingale theory, and the consideration of imperfect and partial monitoring schemes. These advances provide new universal relations in the form of fluctuation theorems and inequalities that refine our understanding of the second-law of thermodynamics in different senses.

We investigate the dynamics of a quantum system subjected to a time-dependent and conditional resetting protocol. Namely, we ask what happens when the unitary evolution of the system is repeatedly interrupted at random time instants with an instantaneous reset to a specified set of reset configurations taking place with a probability that depends on the current configuration of the system at the instant of reset? Analyzing the protocol in the framework of the so-called tight-binding model describing the hopping of a quantum particle to nearest-neighbor sites in a one-dimensional open lattice, we obtain analytical results for the probability of finding the particle on the different sites of the lattice. We explore a variety of dynamical scenarios, including the one in which the resetting time intervals are sampled from an exponential as well as from a power-law distribution. Under exponential resetting, the system relaxes to a stationary state characterized by localization of the particle around the reset sites. The choice of the reset sites plays a defining role in dictating the relative probability of finding the particle at the reset sites as well as in determining the overall spatial profile of the site-occupation probability. Furthermore, analyzing the case of power-law resetting serves to demonstrate that the attainment of the stationary state in this quantum problem is not always evident and depends crucially on whether the distribution of reset time intervals has a finite or an infinite mean. 

Quantum walks, the quantum analogs of classical random walks, have become powerful tools in quantum information processing, offering unique advantages in areas such as quantum computation, search algorithms, and quantum transport. While homogeneous quantum walks with uniform coin operations have been well studied, introducing inhomogeneity - by varying the coin operator or evolution across time and space opens new avenues for controlling the dynamics and properties of quantum systems. Our research has explored the impact of such inhomogeneous quantum walks, yielding two significant results. First, we demonstrated Parrondo's paradox in discrete-time quantum walks using space- and time-dependent coins, achieving paradoxical outcomes without requiring higher-dimensional coins or decoherence, thus enhancing the practicality of implementations [1]. Second, by introducing a Gaussian-profiled coin rotation angle, we showed that this configuration not only improves localization of the walker's probability distribution but also generates maximal entanglement rapidly and a correlation that is robust against decoherence [2]. These findings underscore the potential of inhomogeneous quantum walks for more efficient and resilient quantum technologies.

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We investigate the thermodynamic uncertainty relation (TUR), i.e., a trade-off between entropy production rate and relative power fluctuations, for nondegenerate three-level and degenerate four-level maser heat engines. In the nondegenerate case, we consider two slightly different configurations of the three-level maser heat engine and contrast their degree of violation of the standard TUR. We associate their different TUR-violating properties to the phenomenon of spontaneous emission, which gives rise to an asymmetry between them. Furthermore, in the high-temperature limit, we show that the standard TUR relation is always violated for both configurations. For the degenerate four-level engine, we study the effects of noise-induced coherence on the TUR. We show that, depending on the parametric regime of operation, noise-induced coherence can either suppress or amplify the relative power fluctuations.

Quantum measurements give rise to back-action on the measured system. Tuning the quantum measurement dynamics, and repeating the measurement protocol irrespective of the detectors’ readouts, may be employed to engineer a stable target state. Such a scheme is referred to as a passive quantum steering protocol. The ground state of a given Hamiltonian may or may not be steerable, depending on whether the Hamiltonian is non-frustrated or frustrated. We will discuss how cooling to the ground state may be facilitated even when acting on (measuring) small parts of the system ( “dilute cooling”).
We will also discuss how close to the ground state one can get in the presence of non-steerable frustrated Hamiltonians.

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.

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We describe the smallest quantum error correcting (QEC) code to correct for amplitude-damping (AD) noise, namely, a 3-qubit code that corrects up to first order in the damping strength. We generalize this construction to create a family of codes that correct AD noise up to any fixed order. We underpin the fundamental connection between the structure of our codes and the noise structure via a relaxed form of the Knill-Laflamme conditions, that are different from existing formulations of approximate QEC conditions. Although the recovery procedure for this code is non-deterministic, our codes are optimal with respect to overheads and outperform existing codes to tackle AD noise in terms of entanglement fidelity. This alternate formulation of approximate QEC in fact leads us to a new class of quantum codes tailored to AD noise and also gives rise to a noise-adapted quantum Hamming bound for AD noise.

We introduce a numerical method to sample the distributions of charge, heat, and entropy production in open quantum systems coupled strongly to macroscopic reservoirs, with both temporal and energy resolution and beyond the linear-response regime. Our method exploits the mesoscopic-leads formulation, where macroscopic reservoirs are modeled by a finite collection of modes that are continuously damped toward thermal equilibrium by an appropriate Gorini-Kossakowski-Sudarshan-Lindblad master equation. Focussing on non-interacting fermionic systems, we access the time-resolved full counting statistics through a trajectory unraveling of the master equation. We show that the integral fluctuation theorems for the total entropy production, as well as the martingale and uncertainty entropy production, hold. Furthermore, we investigate the fluctuations of the dissipated heat in finite-time information erasure. Conceptually, our approach extends the continuous-time trajectory description of quantum stochastic thermodynamics beyond the regime of weak system-environment coupling.

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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.

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).

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.

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

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Stochastic thermodynamics analyzes the constraints on the dynamics of small systems (not in the thermodynamic limit) evolving in contact with heat baths and driven, possibly far from equilibrium. In the 90s, it was shown that small systems such as Brownian particles or single proteins could be described by the usual concepts of thermodynamics, and similar laws, with the crucial difference that the 2nd law is valid only for the average over many realizations of a given protocol. In contrast, each single trajectory yields a different value for the work, heat and entropy production, which can exhibit negative entropy production (and, e.g. work extraction from a single heat bath). New thermodynamic relations, the fluctuation theorems, were derived to generalize the 2nd law and encompass new constraints on all the moments of work and heat distributions, not only the average. Those equalities are valid arbitrarily far from equilibrium, significantly pushing forward the application range of thermodynamics.

In the following decades, those results motivated the analysis of quantum open systems with the standpoint of thermodynamics. Indeed, extending stochastic thermodynamics to the quantum domain is a key step towards analyzing engines based on quantum systems, looking for possible quantum advantages with respect to classical engines, or evaluate the resources necessary for quantum control.

In this talk, I will introduce one framework to do so, exploiting the formal analogy between quantum trajectories, generated by measuring the thermal environments coupled to a driven quantum system, and the stochastic trajectories of Brownian particles. I will present the type of quantum fluctuation theorems that can be derived for quantum open systems, as well as the new conceptual issues arising from the nature of measurement in quantum mechanics. I will finish by discussing a few open questions and recent perspectives triggered by this topic.

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

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* Concept of an adaptive measurement and how it is distinct from feedback. 
* Applications of adaptive measurements, including quantum metrology and quantum computing.
* Applications in quantum trajectories in particular, including  
 -- "practical" applications in metrology
 -- potential applications to steering experiments (as introduced in previous lecture)
-- applications to a fundamental question: how big a brain do you need to apply quantum trajectory theory? 

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In this lecture, we provide an introduction to quantum trajectory theory. We present various mathematical problems that arise within this context. In particular, we introduce approaches for analyzing the asymptotic behavior, convergence speed, and stabilization of quantum trajectories toward different states or subspaces through feedback control strategies. Our study includes both quantum non-demolition (QND) measurements and generic (non-QND) measurements in discrete-time and continuous-time settings.

In this talk, I will consider a finite-level quantum system linearly coupled to a bosonic reservoir, that is the prototypical example of an open quantum system. I will present recent results on the reduced dynamics of the finite system when the coupling constant tends to infinity, i.e. in the ultrastrong coupling limit. In particular, I will show that the dynamics corresponds to a nonselective projective measurement followed by a unitary evolution with an effective (Zeno) Hamiltonian. I will also discuss the connection with the usual setting for the quantum Zeno effect, based on repeated measurements.
The rigorous proof of the limit is quite simple and can be generalized to the case of a small system interacting with two reservoirs when one of the couplings is finite and the other one tends to infinity. In this second scenario the reduced dynamics is richer and possibly non-Markovian.
Joint work with Marco Merkli, arXiv:2411.06817.    

State smoothing is a technique to estimate a state at a particular time, conditioned on information obtained both before (past) and after (future) that time. For a classical system, the smoothed state is a normalized product of the filtered state (a state conditioned only on the past measurement information and the initial preparation) and the retrofiltered effect (depending only on the future measurement information). For the quantum case, whilst there are well-established analogues of the filtered state (ρ) and retrofiltered effect (E), their product does not, in general, provide a valid quantum state for smoothing. However, this procedure does seem to work when ρ and E are mutually diagonalizable. This fact has been used to obtain smoothed quantum states — more pure than the filtered states — in a number of experiments on continuously monitored quantum systems, in cavity QED and atomic systems. In this paper we show that there is an implicit assumption underlying this technique: that if all the information were known to the observer, the true system state would be one of the diagonal basis states. This assumption does not necessarily hold, as the missing information is quantum information. It could be known to the observer only if it were turned into a classical measurement record, but then its nature depends on the choice of measurement. We show by a simple model that, depending on that measurement choice, the smoothed quantum state can: agree with that from the classical method; disagree with it but still be co-diagonal with it; or not even be co-diagonal with it. That is, just because filtering and retrofiltering appear classical does not mean classical smoothing theory is applicable in quantum experiments.
Kiarn T. Laverick, Prahlad Warszawski, Areeya Chantasri, and Howard M. Wiseman

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After introducing the basic notions about tensors, I will discuss different aspects of quantum entanglement in the framework of tensor norms. I will show how this point of view can bring new insights to this fundamental notion of quantum theory and how new entanglement criteria can be naturally obtained in this way.

After motivating the need for a study of Open Quantum Systems, I introduce, briefly, some recent developments in the efforts to understand non-Markovian phenomenon.
The discussion about non-Markovian behaviour is made in the backdrop of the Garraway model. This is followed by an introduction to notions such as ergotropy, entropy production, power, in the context of quantum thermodynamics.
Two types of Quantum Thermodynamic devices: Quantum Battery and Quantum Heat Engine are discussed.
These are then illustrated on open system models; (a). the Garraway type, (b). central spin model, (c). Quantum Brownian Motion, (d). two-qubit decoherence.

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