Tag - Quantum computation

The prospect of controllable exchange-antisymmetric interactions in atomic fermionic systems could enable new kinds of quantum simulation, topological quantum gates, and exotic few-body states. While p-wave interactions, which are exchange-antisymmetric, may be enhanced via Feshbach resonances, their utilization has been traditionally been limited by three-body loss. In this talk, I will discuss a recent experiment where we create isolated pairs of spin-polarized fermionic atoms in a 3-dimensional optical lattice. In this regime, three-body loss is dramatically reduced, and we can tune and measure the elastic p-wave interaction energy of atom pairs, which can exhibit lifetimes exceeding up to fifty times larger than in free space. This enhanced lifetime allows tuning of the p-wave interaction to the unitary regime. Critically, these on-site interactions may be expressed by a universal single-parameter curve and can be generalized to other cold atoms systems. All experimental results are compared to analytic solutions for two harmonically trapped atoms interacting via a p-wave pseudo potential as well as an ab-initio interaction potential. This result is an important step towards utilizing p-wave interactions in cold atom lattice systems.

Most, if not all, optical elements, such as lenses, diffraction gratings and phase plates, act on the photon’s position. This talk will describe ways to instead manipulate photons via their transverse momentum, i.e., their angle. I will show that this 'non-local' control creates the possibility of completely general spatial optical transformations. I’ll briefly review the use and application of such universal unitary transformations to quantum information and neural networks. I will then introduce our momentum device, which, unlike past universal unitaries implemented in integrated optical systems, works in free space on an array of parallel beams. I will also discuss creating a particularly useful transformation, the transfer-function of free space. By creating nonlocal metamaterial devices, I'll show that we can compress optical propagation into a thin plate, a device we call a 'spaceplate'. If perfected, spaceplates could one day replace the space between a lens and the imaging sensor, enabling thin cameras.

Quantum simulators have advanced significantly in controlling interactions between system and environment, and many platforms can now perform mid-circuit measurements. I will demonstrate how such controllably open quantum systems can give rise to novel forms of quantum criticality in mixed states. In the first half of the talk, I will show how measurements and unitary evolution conditioned on the measurement outcomes ('adaptive quantum circuits') can produce mixed state long-range order and criticality, despite coexisting with extensive entropy. As an illustration, I will show how symmetry-protected topological order can be universally converted into mixed state long-range order, which can undergo a mixed state phase transition with logarithmic scaling of entanglement negativity, a measure of quantum correlations in mixed states. Further applications include fermion occupation measurements and feedback, which are possible in optical lattices, and I will show how these can efficiently transform a gapped pure ground state into a quantum critical mixed state. In the second half, I will discuss how decoherence can remarkably enrich quantum critical pure states, giving rise to renormalization group flows between quantum channels with important implications on the entanglement structure of the resulting critical mixed states.

This talk will investigate the possibility of a Markovian quantum master equation (QME) that consistently describes a finite-dimensional system, a part of which is weakly coupled to a thermal bath. For physical consistency, we will demand that the QME should preserve local conservation laws and be able to show thermalization. After providing some background on QMEs, I will present our three main results:

1. 1. The microscopically derived Redfield equation (RE), which is known to preserve local conservation laws and show thermalization, necessarily violates complete positivity unless in extremely special cases. These special cases can be easily identified.
2. 2. I will then turn to Lindblad QMEs and show that imposing complete positivity and demanding preservation of local conservation laws enforces the Lindblad operators and the lamb-shift Hamiltonian to be 'local', i.e, to be supported only on the part of the system directly coupled to the bath.
3. 3. Finally, I will show how the problem of finding 'local' Lindblad QME which can show thermalization can be turned into a semidefinite program (SDP). This SDP can be solved numerically for any specific example, and its solution conclusively shows whether the desired type of QME is possible up to a given precision. Whenever a QME is possible, it also outputs a form for such a QME.

Taken together, our results indicate that the possibility of a Markovian QME with the desired properties must be taken on a case-by-case basis, since there are setups where such a QME is impossible.

In this talk, I will present some of my past and current works on quantum algorithms. The first part of the talk will be on quantum algorithms for far-future quantum computers with large-scale and perfectly functioning components. The second part will be on employing machine-learning methods for analysing the average-case complexity of algorithms and our vision for applying them to current and near-future noisy quantum computers.

Specifically, in the first part, I will talk about simulating quantum field theories on a quantum computer and an optimal approach for extracting information encoded in a quantum state. Along the way, I will describe how representing quantum fields in multiple scales using wavelets enables more efficient preparation of certain states of a quantum field and dealing with non-linearities in a system. In the second part, I will discuss empirical hardness models, their various applications, and our vision to bring them to the quantum domain. These models allow us to characterize the difficulty of solving a given family of problems using the best available algorithms. These algorithms typically have exponentially varying performances and no attractive theoretical guarantees but work astonishingly well in practice.

The research field that deals with manipulating, controlling and detecting quantum wavepackets possessing specific states is referred to as structured quantum waves. Quantum wavepackets, e.g. electrons or photons, can be labelled with several different degrees of freedom. For instance, photonic states can be described by frequency, polarisation, spatiotemporal modes, and statistical distribution. Apart from the statistics, similar quantisation can be applied to other quantum entities, including electrons, neutrons or atoms. I will discuss different techniques to shape, manipulate and detect photons (electromagnetic fields) and free electrons (in transmission electron microscopy) states. Their applications in quantum information processing (e.g. communication and simulation) and in microscopy will also be the subject of my talk.