Talks

A hypothetical primordial black hole population may constitute a fraction of dark matter. These black holes can interact and merge, emitting gravitational waves with rates and source properties that differ from those of astrophysical black hole mergers. I will review the collisional processes that drive the formation and coalescence of primordial black hole binaries in the early and late universe. These processes provide key constraints on the merger rates of these binaries and on the contribution of primordial black holes to the dark matter fraction.

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).

While a generic open quantum system decays to its steady state, continuous time crystals (CTCs) develop spontaneous oscillation and never converge to a stationary state. Just as crystals develop correlations in space, CTCs do so in time. Here, we introduce a Continuous Quasi Time Crystals (CQTC). Despite being characterized by the presence of non-decaying oscillations, this phase does not retain its long-range order, making it the time analogous of quasi-crystal structures. We investigate the emergence of this phase in a system made of two coupled collective spin sub-systems, each developing a CTC phase upon the action of a strong enough drive. The addition of a coupling enables the emergence of different synchronized phases, where both sub-systems oscillate at the same frequency. In the transition between different CTC orders, the system develops chaotic dynamics with aperiodic oscillations. These chaotic features differ from those of closed quantum systems, as the dynamics is not characterized by a unitary evolution. At the same time, the presence of non-decaying oscillations makes this phenomenon distinct from other form of chaos in open quantum system, where the system decays instead. We investigate the connection between chaos and this quasi-crystalline phase using mean-field techniques, and we confirm these results including quantum fluctuations at the lowest order.

We have tried to describe how the interplay between the system environment coupling and external driving frequency shapes the dynamical properties and steady state behavior in a periodically driven transverse field Ising chain subject to measurement. We have analyzed the fate of the steady state entanglement scaling properties as a result of a measurement induced phase transition. We have explained how such steady state entanglement scaling can be computed analytically using asymptotic features of the determinant of associated correlation matrix which turned out to be of block Toeplitz form. We have pointed out the differences from the Hermitian systems in understanding the entanglement scaling behav-ior in regimes where the asymptotic analysis can be performed using Fisher-Hartwig con-jecture. Finally we have discussed how the tuning of the drive frequency controls the do- main of applicability of the Fisher-Hartwig conjecture and the emergence of the long range ordering of the effective Floquet Hamiltonian governing the properties of the system.

What happens when the unitary evolution of a generic closed quantum system is interrupted at random times with non-unitary evolution due to interactions with either the external environment or a measuring apparatus? We adduce a general framework to obtain the average density operator of a generic quantum system experiencing any form of non-unitary interaction. We provide two explicit applications in the context of the tight-binding model for two representative forms of interactions: (i) stochastic resets and (ii) projective measurements at random times. For the resetting case, our exact results show how the particle is localized on the sites at long times, leading to a time-independent mean-squared displacement. For the projective measurement case, repeated projection to the initial state results in an effective suppression of the temporal decay in the probability of the particle being in the initial state. The amount of suppression is comparable to the one in conventional Zeno effect scenarios, where measurements are performed at regular intervals.