My research is broadly categorized under Quantum Theory. More specifically, I am interested in the following topics:
Analog and Digital Quantum Simulators
With quantum computers being out of reach for now, quantum simulators are the alternative devices for efficient and accurate simulation of problems that are challenging to tackle using conventional computers. There are two main approaches to quantum simulation: digital and analog. Digital quantum simulation exploits the universality of a quantum computer to carry out the simulation, whereas analog quantum simulation requires that one engineers a specific quantum system that generally is only applicable to a small class of problems. There is also the possibility of constructing hybrid simulators by combining both techniques. My research focuses on using different experimental platforms, such as superconducting circuits, trapped ions, or electronic systems for the purpose of quantum simulation.
Dynamics of Complex Open Quantum Systems
Problems associated with quantum many-body systems are notoriously difficult to solve. The resources required for most of the classical computational methods increase exponentially with the number of particles in the simulation and it is challenging to simulate the dynamics of open quantum systems on conventional computers, even using modern parallel processing units. The situation becomes even much more challenging for complex open quantum systems with structured environments, where as yet, only small model systems have been studied theoretically with crude approximations to the system-bath dynamics. However, analog quantum devices may outperform computational approaches on classical machines to emulate the dynamics of complex open quantum systems. Part of my research is focused on using analog quantum devices to mimic the dynamics of complex open quantum systems. The proposed simulators can be constructed using present-day technology, for example, superconducting circuits. With these quantum devices, one can perform more extensive investigation including exciton transport, spectral density, absorption spectra as well as wide range of parameters in complex systems, such as photosynthetic complexes and molecular aggregates.
Frustrated Magnetism (Spin Ice)
Non-equilibrium physics in spin ice is a novel setting which combines kinematic constraints, emergent topological defects, and magnetic long range Coulomb interactions. In spin ice, magnetic frustration leads to highly degenerate yet locally constrained ground states. Together, they form a highly unusual magnetic state – a “Coulomb phase” – whose excitations are pointlike defects – magnetic monopoles – in the absence of which effectively no dynamics is possible. At low temperature, they are sparse and dynamics becomes very sluggish. When quenching the system from a monopole-rich to a monopole-poor state, a wealth of dynamical phenomena occur the exposition of which has been the subject of my research. The interest in this model system is further enhanced by its large degree of tunability, and the ease of probing it in experiment: with varying magnetic fields at different temperatures, geometric properties – including even the effective dimensionality of the system – can be varied. By monitoring magnetisation, spin correlations or zero-field Nuclear Magnetic Resonance, the dynamical properties of the system can be extracted in considerable detail. This establishes spin ice as a laboratory of choice for the study of tunable, slow dynamics.
Quantum Phase Transitions
In contrast to thermal phase transitions occurring when the strength of the thermal fluctuations equals a certain threshold, there is a different class of phase transitions that take place at zero temperature. A non-thermal control parameter such as pressure, magnetic field, or chemical composition is varied to access the transition point. During the sweep through such a phase transition by means of a time-dependent external parameter, small external perturbations or internal fluctuations become strongly amplified, leading to many interesting effects, one of them being the anomalously high susceptibility to decoherence. Due to the convergence of the energy levels at the critical point, even low-energy modes of the environment may cause excitations and thus perturb the system. Exploiting the similarity between adiabatic quantum algorithms and quantum phase transitions, I have studied the impact of decoherence on the sweep through a second-order quantum phase transition for the prototypical example of the Ising chain in a transverse field and compared it to the adiabatic version of Grover’s search algorithm. It turns out that (in contrast to first-order transitions) the impact of decoherence caused by a weak coupling to a rather general environment increases with system size (i.e., number of spins/qubits), which might limit the scalability of the quantum system, PRA 76, 030304(R) (2007); PRA 81, 032305 (2010).
Adiabatic Quantum Computing
With the emergence of the first quantum algorithms, it turned out that quantum computers are in principle much better suited to solving certain classes of problems than classical computers. Prominent examples are Shor’s algorithm for the factorization of large numbers into their prime factors and Grover’s algorithm for searching an unsorted database. The actual realization of usual sequential quantum algorithms goes along with the problem that errors accumulate over many operations and the resulting decoherence tends to destroy the fragile quantum features needed for the computation. An alternative scheme has been suggested, where the solution to a problem is encoded in the (unknown) ground state of a (known) Hamiltonian. This approach is referred to as adiabatic quantum computing which uses the adiabatic theorem, stating that a system will remain near its ground state if the evolution is slow enough. Most investigations devoted to the conditions for adiabatic quantum computing are based on the first-order correction. It is demonstrated that this first-order correction does not yield a good estimate for the computational error. We have proposed a more general criterion, which includes higher-order corrections as well and we show that the computational error can be made exponentially small. Based on this criterion and rather general arguments and assumptions, we have demonstrated that a run-time of order of the inverse minimum energy gap is sufficient and necessary, PRA 73, 062307 (2006).