Quantum Simulation

While quantum computers are, in principle, extremely powerful than today's digital computers, noise and lack-of-scalability severely limits their true potential. Quantum simulation with with current generation quantum hardware requires customisation so that the use of noisy multiparty-gates can be minimised. Promising candidates in this direction are the so-called variational quantum algorithms. These consist of a classical optimiser together with a parametrised quantum circuit, and have been shown to be universal for quantum computation. In particular, quantum approximate optimisation algorithm (QAOA) have been proven to be an efficient tool to simulate many-body system. The canonical version of the protocol cannot be applied directly to any many-body systems especially for longer range systems since an exponentially large number of parameters need to be optimised over multiple iterations and therefore the simulation becomes inefficient. We look for ways to customise these protocols such that efficient simulation becomes reality.

Related Publications:
Lakkaraju, Ghosh, Sadhukhan and Sen(De), Mimicking quantum correlation of a long-range Hamiltonian by finite-range interactions, Phys. Rev. A 106, 052425 (2022)

Quantum Error Mitigation

Because of the hefty overhead cost of the quantum error correction, the era of the fault-tolerant quantum computation may still be rather distant and the best choice that we have today to push the current limits, at least for the currently available limited-size quantum hardwares, is probably quantum error mitigation where the overhead is not in the system size but in the sample size of the quantum data which is relatively easy to generate using the current generation of quantum architectures. We look for ways to suppress the error as much as possible playing around with the post-selection strategies and try to guess the noiseless expectation value of an observable without actively correcting the noisy quantum state.

Related Publication:

Mills, Sadhukhan and Kashefi, Simplifying errors by symmetry and randomisation, arXiv:2303.02712 (2023)

Open Quantum Systems

Since exact isolation is impossible in practice, it is crucial to study the effect of environmental interactions on genuine quantum correlations such as entanglement. Entanglement, being a fragile quantity, is known to decohere rapidly in an open system evolution. A constant search is going on in the community to identify the situations where entanglement, under environmental decoherence, do not decay for a sufficiently large amount of time. One of the key motivation is to study Markovian dynamics of quantum correlations in many-body systems under environmental interactions and identify such scenarios where entanglement is robust against decoherence.

Related Publication:
Chanda, Das, Sadhukhan, Pal, Sen(De) and Sen, Scale-invariant freezing of entanglement, Phys. Rev. A 97, 062324 (2018)

Adiabatic Quantum Computing

One of the key resource to the efficient quantum technologies is the preparation of a quantum system in a well-controlled initial state (ground state, without defects) and then optimise the adiabatic control of its time evolution to an interesting target state, both of which are crucial features for adiabatic quantum computing. Since the initial state and target state could be separated by a quantum critical point, it is pivotal to have a deeper understanding and direct control of the out-of-equilibrium phenomena in quantum many-body systems which are driven across phase transitions. We are interested in systematic characterization of out-of-equilibrium dynamics of quantum systems which is crucial to develop protocols for quantum simulation, going beyond the established paradigms of adiabatic dynamics.

Related Publications:
Sinha, Sadhukhan, Rams and Dziarmaga, Inhomogeneity induced shortcut to adiabaticity in Ising chains with long-range interactions, Phys. Rev. B 102, 214203 (2020)

Non-equilibrium Dynamics of Long-Range Quantum Systems

The realization of adiabatic dynamics in many-body quantum systems is severely limited by the existence of gapless phases and the possible presence of critical points. The so-called Kibble-Zurek mechanism offers an elegant theoretical framework for describing the statistical properties of a system which is slowly driven across a critical point. However, there are several limitations which are mainly based on the lack of knowledge of the relaxation dynamics during and following the quench. This scenario is even more challenged for phase transitions whose critical properties cannot be cast in terms of power law divergences of the correlation length and of the relaxation time at criticality e.g. long range systems. Our goal has been to achieve a comprehensive understanding of non-equilibrium dynamics of long-range quantum systems bringing together ideas from quantum information theory to many-body systems to shed new lights on the less-understood co-operative phenomena.

Related Publications:
1. Lakkaraju, Ghosh, Sadhukhan and Sen(De), Total correlation as a touchstone of dynamical quantum phase transition, arXiv:2305.02945 (2023)
2. Sadhukhan and Dziarmaga, Is there a correlation length in a model with long-range interactions? arXiv:2107.02508 (2021)
3. Sadhukhan, Sinha, Francuz, Stefaniak, Rams, Dziarmaga and Zurek, Phys. Rev. B 101, 144429 (2020)

Multipartite Entanglement

In the bipartite scenario, the structure of the quantum states is well understood. However, in the multipartite scenario, this is not the case, especially for the mixed states. We aim to provide a deeper understanding of the complex structure of the multiparty entangled states in many-body systems and try to identify the fundamental protocols where truly multipartite states are useful.

Related Publications:

Sadhukhan, Singha Roy, Pal, Rakshit, Sen(De) and Sen, Multipartite entanglement accumulation in quantum states: Localizable generalized geometric measure, Phys. Rev. A 95, 022301 (2017)

Quantum Correlations

Is entanglement the only nontrivial form of quantum correlation that do not have a classical counterpart?

In other words, can we confirm whether entanglement is the only way to quantify quantum correlations present in a shared quantum state, and or there are resources independent of entanglement that can be used to implement quantum protocols with nonclassical efficiencies.

It turns out that the non-separability sieve can indeed be seen as leaving out some states that are quantum correlated in a different way. One can fine-grain the sieve, via several approaches, and conceptualize disparate measures of quantum correlations beyond the entanglement-separability paradigm, and they are useful too!

For more, check out: Bera, Das, Sadhukhan, Singha Roy, Sen(De) and Sen, Rep. Prog. Phys. 81, 024001 (2018)