Theory of variational quantum simulation

The variational method is a versatile tool for classical simulation of a variety of quantum systems. Great efforts have recently been devoted to its extension to quantum computing for efficiently solving static many-body problems and simulating real and imaginary time dynamics. In this work, we first review the conventional variational principles, including the Rayleigh-Ritz method for solving static problems, and the Dirac and Frenkel variational principle, the McLachlan's variational principle, and the time-dependent variational principle, for simulating real time dynamics. We focus on the simulation of dynamics and discuss the connections of the three variational principles. Previous works mainly focus on the unitary evolution of pure states. In this work, we introduce variational quantum simulation of mixed states under general stochastic evolution. We show how the results can be reduced to the pure state case with a correction term that takes accounts of global phase alignment. For variational simulation of imaginary time evolution, we also extend it to the mixed state scenario and discuss variational Gibbs state preparation. We further elaborate on the design of ansatz that is compatible with post-selection measurement and the implementation of the generalised variational algorithms with quantum circuits. Our work completes the theory of variational quantum simulation of general real and imaginary time evolution and it is applicable to near-term quantum hardware.Comment: 41 pages, accepted by Quantu

Fast, accurate, and transferable many-body interatomic potentials by symbolic regression

The length and time scales of atomistic simulations are limited by the computational cost of the methods used to predict material properties. In recent years there has been great progress in the use of machine learning algorithms to develop fast and accurate interatomic potential models, but it remains a challenge to develop models that generalize well and are fast enough to be used at extreme time and length scales. To address this challenge, we have developed a machine learning algorithm based on symbolic regression in the form of genetic programming that is capable of discovering accurate, computationally efficient manybody potential models. The key to our approach is to explore a hypothesis space of models based on fundamental physical principles and select models within this hypothesis space based on their accuracy, speed, and simplicity. The focus on simplicity reduces the risk of overfitting the training data and increases the chances of discovering a model that generalizes well. Our algorithm was validated by rediscovering an exact Lennard-Jones potential and a Sutton Chen embedded atom method potential from training data generated using these models. By using training data generated from density functional theory calculations, we found potential models for elemental copper that are simple, as fast as embedded atom models, and capable of accurately predicting properties outside of their training set. Our approach requires relatively small sets of training data, making it possible to generate training data using highly accurate methods at a reasonable computational cost. We present our approach, the forms of the discovered models, and assessments of their transferability, accuracy and speed

Variational quantum simulation of general processes

Variational quantum algorithms have been proposed to solve static and dynamic problems of closed many-body quantum systems. Here we investigate variational quantum simulation of three general types of tasks---generalised time evolution with a non-Hermitian Hamiltonian, linear algebra problems, and open quantum system dynamics. The algorithm for generalised time evolution provides a unified framework for variational quantum simulation. In particular, we show its application in solving linear systems of equations and matrix-vector multiplications by converting these algebraic problems into generalised time evolution. Meanwhile, assuming a tensor product structure of the matrices, we also propose another variational approach for these two tasks by combining variational real and imaginary time evolution. Finally, we introduce variational quantum simulation for open system dynamics. We variationally implement the stochastic Schr\"odinger equation, which consists of dissipative evolution and stochastic jump processes. We numerically test the algorithm with a six-qubit 2D transverse field Ising model under dissipation.Comment: 18 page

Berry Phases, Quantum Phase Transitions and Chern Numbers

We study the relation between Chern numbers and Quantum Phase Transitions (QPT) in the XY spin-chain model. By coupling the spin chain to a single spin, it is possible to study topological invariants associated to the coupling Hamiltonian. These invariants contain global information, in addition to the usual one (obtained by integrating the Berry connection around a closed loop). We compute these invariants (Chern numbers) and discuss their relation to QPT. In particular we show that Chern numbers can be used to label regions corresponding to different phases.Comment: Proceedings of The International Conference on Strongly Correlated Electron Systems (SCES'07). Accepted for publication in Physica

Specific Involvement of G Proteins in Regulation of Serum Response Factor-mediated Gene Transcription by Different Receptors

Regulation of serum response factor (SRF)-mediated gene transcription by G protein subunits and G protein-coupled receptors was investigated in transfected NIH3T3 cells and in a cell line that was derived from mice lacking G_(αq) and G_(α11). We found that the constitutively active forms of the α subunits of the G_q and G_(12) class of G proteins, including Gα_q, Gα_(11), Gα_(14), Gα_(16), Gα_(12), and Gα_(13), can activate SRF in NIH3T3 cells. We also found that the type 1 muscarinic receptor (m1R) and α_1-adrenergic receptor (AR)-mediated SRF activation is exclusively dependent on Gα_(q/11), while the receptors for thrombin, lysophosphatidic acid (LPA), thromboxane A2, and endothelin can activate SRF in the absence of Gα_(q/11). Moreover, RGS12 but not RGS2, RGS4, or Axin was able to inhibit Gα_(12) and Gα_(13)-mediated SRF activation. And RGS12, but not other RGS proteins, blocked thrombin- and LPA-mediated SRF activation in the Gα_(q/11)-deficient cells. Therefore, the thrombin, LPA, thromboxane A2, and endothelin receptors may be able to couple to Gα_(12/13). On the contrary, receptors including β_2- and α_2-ARs, m2R, the dopamine receptors type 1 and 2, angiotensin receptors types 1 and 2, and interleukin-8 receptor could not activate SRF in the presence or absence of Gα_(q/11), suggesting that these receptors cannot couple to endogenous G proteins of the G_(12) or G_q classes

Variational ansatz-based quantum simulation of imaginary time evolution

Imaginary time evolution is a powerful tool for studying quantum systems. While it is possible to simulate with a classical computer, the time and memory requirements generally scale exponentially with the system size. Conversely, quantum computers can efficiently simulate quantum systems, but not non-unitary imaginary time evolution. We propose a variational algorithm for simulating imaginary time evolution on a hybrid quantum computer. We use this algorithm to find the ground-state energy of many-particle systems; specifically molecular hydrogen and lithium hydride, finding the ground state with high probability. Our method can also be applied to general optimisation problems and quantum machine learning. As our algorithm is hybrid, suitable for error mitigation and can exploit shallow quantum circuits, it can be implemented with current quantum computers.Comment: 14 page

Multi-robot-based nanoassembly planning with automated path generation

In this paper, a novel approach of automated multirobot nanoassembly planning is presented. This approach uses an improved self-organizing map to coordinate assembly tasks of nanorobots while generating optimized motion paths at run time with a modified shunting neural network. It is capable of synchronizing multiple nanorobots working simultaneously and efficiently on the assembly of swarms of objects in the presence of obstacles and environmental uncertainty. Operation of the presented approach is demonstrated with experiments at the end of the paper