ICTS

We will discuss the phenomenology of integer and fractional quantum Hall states, paying particular attention to edge modes in abelian quantum Hall states. These modes are one platform for quantum information processing. 

Bulk-boundary correspondence licenses us to probe the bulk topological order by studying the transport properties of the edge modes. However, edge modes in a fractional quantum Hall (FQH) state can undergo edge reconstruction and, on top of that, can be in the coherent regime or exhibit varying degrees of charge and thermal equilibrations, giving rise to a zoo of intriguing models. Distinguishing the different models and equilibration regimes is an outstanding problem, which can not be resolved by finding only conductance plateaus in a quantum point contact (QPC). In this work we show that electrical shot noise at a QPC conductance plateau can serve as such diagnostics. As a prototypical example we consider the ν = 2/3 FQH state, and show that different inequalities between the auto- and cross-correlation electrical shot noise hold for different edge models. In particular, our results offer several possible scenarios for the QPC conductance plateaus e^2/3h (observed previously), e^2/2h (recently observed), and 5e^2/9h (our prediction), as well as how to distinguish among them via shot noise.

Quantum mechanics is characterized by some NO-Go principles like uncertainty principle, no-cloning of unknown quantum state,  indistinguishability of non-orthogonal states, Impossibility of definite quantum state for subsystem for definite entangled state of the composite system, impossibility of local realistic description of QM etc. Quantum information threory is based on some information processing tasks by exploiting these No-Go theorems in a creative way , which are otherwise impossible in classical world. In these lecture series (three talks), after some discussion on fromalism of QM, basic information processing tasks like dense coding, teleportation, quantum key generation will be introdued along with manipulation of entanglement which is the most important resource in quantum information theory. Basic ideas of quantum nonlocality and quantum computation will also be discussed. 

Two-dimensional systems can host exotic quasiparticles, called anyons, which obey intermediate quantum statistics characterized by an exchange phase φ varying between 0 and π. As a consequence, contrary to fermions and bosons, anyons keep a robust memory of braiding operations, which consist in moving one anyon around another one. In the fractional quantum Hall regime, obtained by applying a strong magnetic field perpendicular to a two-dimensional electron gas, elementary excitations carry a fractional charge and have been predicted to obey fractional statistics with an exchange phase φ=π/m (where m is an odd integer). I will present how fractional statistics of anyons can be demonstrated in this system by implementing and studying anyon collisions at a beam-splitter. In the low magnetic field regime, where the elementary excitations are electrons obeying fermionic statistics, fermion antibunching shows up as a suppression of the current cross-correlations at the output of the beam-splitter, reflecting the fact that two electrons systematically exit in two different arms of the beam-splitter. In the case of anyons in the fractional quantum Hall regime, specific anyon bunching mechanisms occur, which are directly sensititve to the anyon braiding phase 2φ. They result in the observation of strong negative cross-correlations of the electrical currents at the output of the beam-splitter that can be used to extract the braiding properties of anyons. The presentation will review experimental investigations of the fractional statistics of anyons using the anyon collider geometry.

Quantum mechanics is characterized by some NO-Go principles like uncertainty principle, no-cloning of unknown quantum state,  indistinguishability of non-orthogonal states, Impossibility of definite quantum state for subsystem for definite entangled state of the composite system, impossibility of local realistic description of QM etc. Quantum information threory is based on some information processing tasks by exploiting these No-Go theorems in a creative way , which are otherwise impossible in classical world. In these lecture series (three talks), after some discussion on fromalism of QM, basic information processing tasks like dense coding, teleportation, quantum key generation will be introdued along with manipulation of entanglement which is the most important resource in quantum information theory. Basic ideas of quantum nonlocality and quantum computation will also be discussed. 

We will discuss the phenomenology of integer and fractional quantum Hall states, paying particular attention to edge modes in abelian quantum Hall states. These modes are one platform for quantum information processing. 

We will discuss the phenomenology of integer and fractional quantum Hall states, paying particular attention to edge modes in abelian quantum Hall states. These modes are one platform for quantum information processing. 

In these three lectures I will cover the theoy of the non-Abelian fractional quantum Hall states. I will cover ideal wave functions and conformal field theory, edge states of non-Abelian fractional quantum Hall states and non-Abelian fractional statistics, edge states and coset constructions, quantum interferometers, effective field theories of non-Abelian states and Fibonacci states.

Quantum dots have emerged as one of the contenders for a future quantum information processor. Bilayer graphene is now established as a material that allows high quality bi-polar Coulomb blockade measurement, time-dependent transport measurements and first relaxation time measurements. In contrast to the more conventional GaAs and Si-based systems, several exiting and unexpected observations in graphene have been explained by the peculiar graphene bandstructure, which is gate-tunable, the additional valley degree of freedom, and spin-valley coupling. Here we demonstrate shell filling of electronic states in graphene quantum dots and derive the spin and valley Hund rules for the first 24 carriers occupying the quantum dots. Lifetimes of single single spins are measured using the Elzermann read-out. For two carriers occupying a single or double quantum dot we find a complex charge stability diagram with transitions governed by Pauli spin and/or valley blockade. Using these two carrier states we measure spin lifetimes of about 50 ms and valley lifetimes approaching 1s.
In superconducting graphene fabricated using two layers twisted by the magic angle we investigate Josephson junctions as well as a SQUID, where the critical current in the two arms can be independently controlled by gate electrodes.
This work was done in collaboration with Lisa Maria Gächter, Rebekka Garreis, Chuyao Tong, Max Josef Ruckriegel, Benedikt Kratochwil, Folkert Kornelis de Vries, Annika Kurzmann, Wister Wei Huang, Elías Portolés, Shuichi Iwakiri, Giulia Zheng, Peter Rickhaus and Thomas Ihn.

Fractional quantum Hall state at 5/2 filling is intriguing. A typical magnetic field for observing 5/2 state in GaAs systems contributes to sizable Landau level mixing. This mixing can be quantified with a parameter κ as ratio between the Coulomb and cyclotron energy scales. While the theories are developed for zero or small values of κ, the experiments are generally performed for κ∼1. We numerically find [1] that a topological phase transition occurs nearly at κ=0.7. The ground state wave function for the topological phase occurring for κ∼1 is orthogonal to all the well-known wavefunctions, namely, Moore-Read Pfaffian and its particle-hole conjugate anti-Pfaffian, and particle-hole symmetric Pfaffian. Our proposed wave function has very high overlap with this ground state. This wavefunction reproduces state counting of low-lying entanglement spectra with that of the exact ground state. It further describes a Majorana edge mode as manifestation of hidden Z_2 symmetry. The edge modes are consistent with experimentally [2] found 2.5 unit of thermal Hall conductance. 

[1] S. Das, S. Das, and S. S. Mandal, Phys. Rev. Lett. 131, 056202 (2023),
[2] M. Banerjee, M. Heiblum, V. Umansky, D. E. Feldman,Y. Oreg, and A. Stern, Nature 559, 205 (2018).

In these three lectures I will cover the theoy of the non-Abelian fractional quantum Hall states. I will cover ideal wave functions and conformal field theory, edge states of non-Abelian fractional quantum Hall states and non-Abelian fractional statistics, edge states and coset constructions, quantum interferometers, effective field theories of non-Abelian states and Fibonacci states.

In these three lectures I will cover the theoy of the non-Abelian fractional quantum Hall states. I will cover ideal wave functions and conformal field theory, edge states of non-Abelian fractional quantum Hall states and non-Abelian fractional statistics, edge states and coset constructions, quantum interferometers, effective field theories of non-Abelian states and Fibonacci states.

Projective measurements in random quantum circuits lead to a rich breadth of entanglement phases and extend the realm of non-unitary quantum dynamics. Here we explore the connection between measurement-only quantum circuits in one spatial dimension and the statistical mechanics of loop models in two dimensions. We introduce a fundamental symmetry of loop models: the orientability of world lines. We discuss how orientability enters in the measurement framework, acting as a separatrix for the universal long-wavelength behavior in a circuit. When it is broken, the circuit falls into the universality class of closely packed loops with crossings (CPLC) and features a Goldstone phase with a peculiar, universally enhanced growth of the entanglement entropy. In turn, when orientability is preserved, the long-wavelength behavior of the circuit mimics that of (coupled) two-dimensional Potts models. A rich circuit dynamics is observed, ranging from CPLC to the -state Potts model (percolation), the -state Potts model (Ising) and coupled Potts models (BKT) universality class.

We'll explore quantum error correction fundamentals, starting with decoherence and key principles of QEC codes. Our discussion will extend to stabilizer and topological codes, as well as more advanced coding schemes. Time permitting, we'll also review the current state of quantum computing across different technologies.

We present new facets in the domain of photonic quantum information processing (QIP). A major part of the talk focuses on our recent works in higher dimensional QIP.
We provide a novel scheme for direct determination of different entanglement monotones used to quantify entanglement in arbitrary system dimensions using only one pair of complementary observables, as opposed to the standard d^2 measurements needed in d dimensions. In our scheme, we analytically relate statistical measures of correlations i.e. Pearson Correlation Coefficient, Mutual Predictability and Mutual Information with the standard measures of entanglement i.e. Negativity and Entanglement of Formation for arbitrary dimensional states. In [1], we theoretically formulate, experimentally implement and explore implications of the  scheme for actually determining values of the  entanglement measures for the first time making use of the standard  statistical correlators, essentially for two-qudit pure states. The extension to mixed states is thoroughly studied in [2], showing that the efficacy of this scheme is restricted to not only distillable entangled states, but extends to bound entangled states as well. 
Next we discuss our novel approach to higher dimensional quantum state estimation, using interference as a tool [3]. Here we present an interferometric method, in which any qubit state, whether mixed or pure, can be inferred from the visibility, phase shift, and average intensity of an interference pattern using a single-shot measurement—hence, we call it Quantum State Interferography [3]. This provides us with a “black box” approach to quantum state estimation, wherein, between the incidence and extraction of state information, we are not changing any conditions within the setup, thus giving us a true single shot estimation of the quantum state. An extension of the scheme to pure states involving d−1 interferograms for d-dimensional systems (qudits) is also presented. The scaling gain is even more dramatic in the qudit scenario for our method, where, in contrast, standard QST, scales roughly as d2.
In the final part, we briefly present the first loophole-free experiment wherein both the LGI and the WLGI inequalities have been decisively violated using single photons[4], thus providing a comprehensive refutation of the classical realist worldview along with measurements ensured to be non-invasive. This provides a powerful platform for harnessing this most general unambiguous signature of nonclassicality of single photon states towards various information theoretic applications wherein the single photon is a ubiquitous workhorse.
[1] Direct determination of entanglement monotones for arbitrary dimensional bipartite states using statistical correlators and one set of complementary measurements, D. Ghosh, T.Jennewein, U.Sinha, Quantum Science and Technology, 7 045037, 2022.
[2] Relating an entanglement measure with statistical correlators for two-qudit mixed states using only a pair of complementary observables, S. Sadana, S. Kanjilal, D.Home, U.Sinha, arXiv: 2201.06188, 2022.
[3] Quantum State Interferography, S.Sahoo, S. Chakraborti, A.K.Pati, U.Sinha, Phys. Rev. Lett. 125 123601, 2020.
[4] Loophole free interferometric test of macrorealism using heralded single photons, K.Joarder, D.Saha, D.Home, U.Sinha, PRX Quantum, 3, 010307, 2022.

From the perspective of many-body physics, the transmon qubit architectures currently developed for quantum computing are systems of coupled nonlinear quantum resonators. A significant amount of intentional frequency detuning (disorder) is required to protect individual qubit states against the destabilizing effects of nonlinear resonator coupling. In this talk, we will discuss the stability of this variant of a many-body localized phase for system parameters relevant to current quantum processors.  An essential element in of our diagnostic toolbox are classical simulations, which can be run, e.g., for upcoming IBM designs comprising hundreds of qubits. The overall conclusion of this study is that it will take considerable engineering efforts to protect transmon quantum computers from the destructive influence of chaotic fluctuations. 

Bilayer graphene exhibits a rich phase diagram in the quantum Hall (QH) regime, arising from a multitude of internal degrees of freedom, including spin, valley, and orbital indices. The variety of fractional QH states between filling factors 1 and 2 suggests, among other things, a quantum phase transition between valley-polarized and unpolarized states at a perpendicular electric-field D*. We find that the behavior of D* with filling factor changes markedly as the magnetic field B is reduced. We present a theoretical model for lattice-scale interactions, which explains these observations; contrary to earlier studies, it involves finite-ranged terms comprising both repulsive and attractive components.  Within this model, we analyze the nature of the phase at filling factor 2, and predict that valley-coherence may emerge at high B fields. This suggests that the system may support bond-ordered phases which may be amenable to experimental verification. 

We'll explore quantum error correction fundamentals, starting with decoherence and key principles of QEC codes. Our discussion will extend to stabilizer and topological codes, as well as more advanced coding schemes. Time permitting, we'll also review the current state of quantum computing across different technologies.

I will show how the analysis of electron waiting times and the correlation between them help in understanding topological Andreev bound states in an Andreev interferometer where a superconducting loop with a controllable phase difference is connected to a quantum spin Hall edge. The edge state helicity enables the transfer of electrons and holes into separate leads controlled by the phase difference of the loop. In this setup, the topological phase transition with emerging topological bound states occurs at $\phi=\pi$ and electron waiting times are sensitive to it. However, the waiting times for the Andreev-reflected holes remain insensitive. These two different waiting times show opposite behaviors when we consider the correlation between them. Some of the cross-distributions also show unique features indicating the appearance of topological Andreev bound states.

Two-dimensional systems at low temperatures and high magnetic field can host exotic particles “anyons” with elementary excitations, very different from bosonic and fermionic excitations. They carry fractional charge and have fractional statistics. The fractional charge of these anyons has been studied successfully using low-frequency shot noise measurement. However, no universal method for sensing them unambiguously exists. Here we exploited the Josephson relation of these anyonic states to determine the fractional charge of excited quasiparticles. The microwave photons emitted by voltage biased anyonic system obey the Josephson relation, like Josephson junction but with the charge q = e* rather than e. This provides direct evidence of fractional charge in fractional quantum Hall effect. I will conclude the talk with recent advancement in experiments on fractional statistics in mesoscopic anyonic collider, see talk by Gwendal Fevé.

Recent years have seen the discovery of and a surge of interest in a phenomenon dubbed “chiral state conversion”. Under cyclic adiabatic non-Hermitian evolution, all system states get converted to one eigenstate of the Hamiltonian. When the evolution path encircles an exceptional point of the Hamiltonian, the conversion is chiral: depending on the path orientation, the final state is different.

At the same time, a number of (theoretical and experimental) examples have emerged, demonstrating that the conversion may be chiral without encircling an exceptional point or non-chiral despite encircling one.

I will present a newly-developed general theory of this phenomenon, which explains the mechanism behind the phenomenon, as well as all the unusual examples.