Seminar

We investigate the difficulty of classically simulating evolution under many-body localized (MBL) Hamiltonians. Using the defining feature that MBL systems have a complete set of local integrals of motion (LIOMs), we demonstrate a transition in the classical complexity of simulating such systems as a function of evolution time. On one side, we construct a quasipolynomial-time tensor-network-inspired algorithm that can simulate MBL systems evolved for any time polynomial in the system size.

Variational Quantum Algorithms (VQAs) are viewed as amongst the best hope for near-term quantum advantage. A natural question is whether noise places fundamental limitations on VQA performance. In the first part of this talk, we show that noise can severely limit the trainability of VQAs by exponentially flattening the optimization landscape and suppressing the magnitudes of cost gradients.

The main challenge for scaling up photonic quantum technologies is the lack of perfect quantum light sources. We have pushed the parametric down-conversion to its physical limit and produce two-photon source with simultaneously a collection efficiency of 97% and an indistinguishability of 96% between independent photons. Using a single quantum dot in microcavities, we have produced on-demand single photons with high purity (>99%), near-unity indistinguishability, and high extraction efficiency—all combined in a single device compatibly and simultaneously.

We generalized the standard Boson sampling task including Linear Boson Sampling the Gaus- sian Boson Sampling from photons to what we call generalized boson system which the computation relation between the creation and annihilation operators is not a constant. We showed that in such a system, one still has the standard hardness results including Hafnian and Permanents. We also use the spin system as our example and provide an experimental setup.
 

Noisy Intermediate-Scale Quantum (NISQ) devices fail to produce outputs with sufficient fidelity for deep circuits with many gates today. Such devices suffer from read-out, multi-qubit gate and cross-talk noise combined with short decoherence times limiting circuit depth. This work develops a methodology to generate shorter circuits with fewer multi-qubit gates whose unitary transformations approximate the original reference one. It explores the benefit of such generated approximations under NISQ devices.

We give a direct product theorem for the entanglement-assisted interactive quantum communication complexity in terms of the quantum partition bound for product distributions. The quantum partition or efficiency bound is a lower bound on communication complexity, a non-distributional version of which was introduced by Laplante, Lerays and Roland (2012). For a two-input boolean function, the best result for interactive quantum communication complexity known previously was due to Sherstov (2018), who showed a direct product theorem in terms of the generalized discrepancy.

Quantum process tomography is a critical capability for building quantum computers, enabling quantum networks, and understanding quantum sensors. Like quantum state tomography, the process tomography of an arbitrary quantum channel requires a number of measurements that scale exponentially in the number of quantum bits affected. However, the recent field of shadow tomography, applied to quantum states, has demonstrated the ability to extract key information about a state with only polynomially many measurements.

Many schemes for obtaining a computational advantage with near-term quantum hardware are motivated by mathematical results proving the computational hardness of sampling from near-term quantum circuits. Near-term quantum circuits are often modeled as geometrically-local, shallow-depth (GLSD) quantum circuits. That is, circuits consisting of two qubit gates that can act only on neighboring qubits, and that have polylogarithmic depth in the number of qubits.

In this talk I will study the extension of fault tolerance techniques to holographic quantum error correcting codes in the context of the ads/cft correspondence. I will seek to argue that the threshold here corresponds to that of the confinement/de confinement phase transition here, analogously to the situation in topological quantum error correcting codes based on Tqft’s.

What does it mean to simulate a quantum field theory? This is a challenging question because a majority of the quantum field theories relevant to fundamental physics lack a fully rigourous mathematical definition. Thus it is impossible in general to compare the predictions of discretised theories with their continuum counterparts.