Engineering topics
Cincio, Lukasz
Publications and source records attributed to Cincio, Lukasz.
Information Scrambling and Loschmidt Echo
We demonstrate analytically and verify numerically that the out-of-time order correlator is given by the thermal average of Loschmidt echo signals. This provides a direct link between the out-of-time-order correlator—a recently suggested measure of information scrambling in quantum chaotic systems—and the Loschmidt echo, a well-appreciated familiar diagnostic that captures the dynamical aspect of chaotic behavior in the time domain, and is accessible to experimental studies.
Noise amplification at spin-glass bottlenecks of quantum annealing: A solvable model
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Learning to Optimize Variational Quantum Circuits to Solve Combinatorial Problems
Quantum computing is a computational paradigm with the potential to outperform classical methods for a variety of problems. Proposed recently, the Quantum Approximate Optimization Algorithm (QAOA) is considered as one of the leading candidates for demonstrating quantum advantage in the near term. QAOA is a variational hybrid quantum-classical algorithm for approximately solving combinatorial optimization problems. The quality of the solution obtained by QAOA for a given problem instance depends on the performance of the classical optimizer used to optimize the variational parameters. In this paper, we formulate the problem of finding optimal QAOA parameters as a learning task in which the knowledge gained from solving training instances can be leveraged to find high-quality solutions for unseen test instances. To this end, we develop two machine-learning-based approaches. Our first approach adopts a reinforcement learning (RL) framework to learn a policy network to optimize QAOA circuits. Our second approach adopts a kernel density estimation (KDE) technique to learn a generative model of optimal QAOA parameters. In both approaches, the training procedure is performed on small-sized problem instances that can be simulated on a classical computer; yet the learned RL policy and the generative model can be used to efficiently solve larger problems. Furthermore, extensive simulations using the IBM Qiskit Aer quantum circuit simulator demonstrate that our proposed RL- and KDE-based approaches reduce the optimality gap by factors up to 30.15 when compared with other commonly used off-the-shelf optimizers.
Variational Quantum Fidelity Estimation
Computing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelity F ( ρ , σ ) based on the ``truncated fidelity'' F ( ρ m , σ ) , which is evaluated for a state ρ m obtained by projecting ρ onto its m -largest eigenvalues. Our bounds can be refined, i.e., they tighten monotonically with m . To compute our bounds, we introduce a hybrid quantum-classical algorithm, called Variational Quantum Fidelity Estimation, that involves three steps: (1) variationally diagonalize ρ , (2) compute matrix elements of σ in the eigenbasis of ρ , and (3) combine these matrix elements to compute our bounds. Our algorithm is aimed at the case where σ is arbitrary and ρ is low rank, which we call low-rank fidelity estimation, and we prove that no classical algorithm can efficiently solve this problem under reasonable assumptions. Finally, we demonstrate that our bounds can detect quantum phase transitions and are often tighter than previously known computable bounds for realistic situations.
New Heavy Flavor Program for the Future Electron Ion Collider
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Determining topological order from infinite projected entangled pair states
In this work, we present a method of extracting information about the topological order from the ground state of a strongly correlated two-dimensional system computed with the infinite projected entangled pair state (iPEPS). For topologically ordered systems, the iPEPS wrapped on a torus becomes a superposition of degenerate, locally indistinguishable ground states. Projectors in the form of infinite matrix product operators onto states with well-defined anyon flux are used to compute topological S and T matrices (encoding mutual and self-statistics of emergent anyons). The algorithm is shown to be robust against a perturbation driving string-net toric code across a phase transition to a ferromagnetic phase. Our approach provides accurate results near quantum phase transition, where the correlation length is prohibitively large for other numerical methods. Moreover, we used numerically optimized iPEPS describing the ground state of the Kitaev honeycomb model in the toric code phase and obtained topological data in excellent agreement with theoretical prediction.