An efficient quantum algorithm for solving quantum field theory equations can be applied even to difficult cases that include strong particle interactions.
Quantum Leap? Quantum computers are expected to be able to solve some of the most difficult problems in mathematics and physics. It is not known, however, whether quantum field theories (QFTs) can be simulated efficiently with a quantum computer. QFTs are used in particle and condensed matter physics and have an infinite number of degrees of freedom; discretization is necessary to simulate them digitally. Jordan et al. (p. 1130 ; see the Perspective by Hauke et al. ) present an algorithm for the efficient simulation of a particular kind of QFT (with quartic interactions) and estimate the error caused by discretization. Even for the most difficult case of strong interactions, the run time of the algorithm was polynomial (rather than exponential) in parameters such as the number of particles, their energy, and the prescribed precision, making it much more efficient than the best classical algorithms.
Defense Advanced Research Projects Agency (DARPA) is running a program to create an analog quantum-mechanical simulator for strongly interacting quantum particles. It is called an optical lattice emulator, and it involves ultracold neutral atoms moving in a corrugated periodic potential created by an optical lattice. The atoms interact with each other via collisions. In this work, we show how one can apply inhomogenenous dynamical mean-field theory (IDMFT) as an approximate computational tool to study the behavior of just such a system. Ultimately, conventional computation will be employed to benchmark the optical lattice emulator on a numerically tractable problem (a verification and validation study), and then the emulator will be applied to problems that cannot be solved with conventional computation. Here, we demonstrate an efficient massively parallel implementation of the IDMFT algorithm that is transportable, scales to many thousands of processors, and runs at approximately 50% of the theoretical peak speed of the machine.
In the eigen-functional theoretical framework, exact/accurate treatment of high-dimensional strongly correlated electron systems may be realized. The two key steps of this method are that under the path integral formulation we first change a D-dimensional quantum many-particle system into an (D+1)-dimensional (time-dependent) effective "single-particle" problem, then by solving the eigen-equation of the propagator operator of the particles, we can obtain the ground state energy functional and action, respectively. Under the eigen-functional theory, the problems of quantum many-particle systems end in to solve the equation of phase fields that are completely determined by the electron interaction. In practice this equation of the phase fields can be numerically solved for large lattice sites. After replacing the real time by the imaginary time, this method can also be applied for finite temperature cases.