Quantum solver of contracted eigenvalue equations for scalable molecular simulations on quantum computing devices
The accurate computation of ground and excited states of many-fermion quantum systems is one of the most important challenges in the physical and computational sciences whose solution stands to benefit significantly from the advent of quantum computing devices. Existing methodologies using phase estimation or variational algorithms have potential drawbacks such as deep circuits requiring substantial error correction or non-trivial high-dimensional classical optimization.
Floquet vortex states induced by light carrying the orbital angular momentum
We propose a scheme to create electronic Floquet vortex states by irradiating the circularly-polarized laser light carrying non-zero orbital angular momentum on the two-dimensional semiconductor. We study the properties of the Floquet vortex states analytically and numerically using methods analogous to the techniques used for the analysis of superconducting vortex states, while we exhibit that the Floquet vortex created in the current system has the wider tunability.
Limitations of optimization algorithms on noisy quantum devices
Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is whether their noise can be overcome or it fundamentally restricts any potential quantum advantage.
Quantum information processing with nuclear spins in diamond
Spins associated to defects in solids are promising qubits for quantum information processing. We have developed novel control gates for an electron spin coupled to nuclear spins, and applied this scheme to realise a universally connected 10-qubit register using an NV-centre in diamond [1]. Moreover, we employed dynamical decoupling of the register to realise coherence times up to 63(2) seconds. Building upon these techniques, we have also recently demonstrated the 3D imaging of a system of 27 coupled nuclear spins with atomic scale resolution [2].
Hofstadter butterfly and Floquet topological insulators in minimally twisted bilayer graphene
We theoretically study the Hofstadter butterfly of a triangular network model in minimally twisted bilayer graphene. The band structure manifests periodicity in energy, mimicking that of Floquet systems. The butterfly diagrams provide fingerprints of the model parameters and reveal the hidden band topology. In a strong magnetic field, we establish that minimally twisted bilayer graphene realizes low-energy Floquet topological insulators (FTIs) carrying zero Chern number, while hosting chiral edge states in bulk gaps.
Degree vs. Approximate Degree and Quantum Implications of Huang’s Sensitivity Theorem
Based on the recent breakthrough of Huang (2019), we show that for any total Boolean function f, deg(f) = O(~deg(f)^2): The degree of f is at most quadratic in the approximate degree of f.
Fundamental aspects of solving quantum problems with machine learning
Machine learning (ML) provides the potential to solve challenging quantum many-body problems in physics and chemistry. Yet, this prospect has not been fully justified. In this work, we establish rigorous results to understand the power of classical ML and the potential for quantum advantage in an important example application: predicting outcomes of quantum mechanical processes.