A field theoretical approach to quantum circuits
Quantum circuits have been widely used as a platform to explore universal properties of generic quantum many-body systems. In this talk, I will present our work in which we construct a field theoretical approach to study quantum circuits. We reformulate the sigma model for time periodic Floquet systems using the replica method, and apply it to the study of spectral statistics of the evolution operator of quantum circuits.
Capacity and Quantum Geometry of Parametrized Quantum Circuits
To harness the potential of noisy intermediate-scale quantum devices, it is paramount to find the best type of circuits to run hybrid quantum-classical algorithms. Key candidates are parametrized quantum circuits that can be effectively implemented on current devices. Here, we evaluate the capacity and trainability of these circuits using the geometric structure of the parameter space via the effective quantum dimension [1]. We find that the capacity exhibits scaling laws and striking differences depending on the type of entangling gates used.
Simulation Complexity of Many-Body Localized Systems
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.
Fundamental effects of noise and error mitigation on the trainability of variational quantum algorithms
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.
Photonic quantum computational advantage
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.
Boson Sampling for Generalized Bosons
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.
Empirical Evaluation of Circuit Approximations on Noisy Quantum Devices
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.
Fault Tolerance and Holography
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.