Compressed simulation of thermal and excited states of the one-dimensionalXYmodel

Abstract

Since several years the preparation and manipulation of a small number of quantum systems in a controlled and coherent way is feasible in many experiments. In fact, these experiments are nowadays commonly used for quantum simulation and quantum computation. As recently shown, such a system can, however, also be utilized to simulate specific behaviors of exponentially larger systems. That is, certain quantum computations can be performed by an exponentially smaller quantum computer. This compressed quantum computation can be employed to observe for instance the quantum phase transition of the 1D XY-model using very few qubits. We extend here this notion to simulate the behavior of thermal as well as excited states of the 1D XY-model. In particular, we consider the 1D XY-model of a spin chain of n qubits and derive a quantum circuit processing only log(n) qubits which simulates the original system. We demonstrate how the behavior of thermal as well as any eigenstate of the system can be efficiently simulated in this compressed fashion and present a quantum circuit on log(n) qubits to measure the magnetization, the number of kinks, and correlations occurring in the thermal as well as any excited state of the original systems. Moreover we derive compressed circuits to study time evolutions.

Compression for quantum population coding

“…From the point of view of quantum simulations, it is also meaningful to consider the compression of tensor network states [42], [43] which provide a variational ansatz for a large number of quantum manybody systems. The extension of quantum compression to this scenario is appealing as a technique to reduce the number of qubits needed to simulate systems of distinguishable quantum particles, in the same spirit of the compressed simulations introduced by Kraus [44] and coauthors [45], [46]. In the long term, the informationtheoretic study of manybody quantum systems may provide a new approach to the simulation of complex systems that are not efficiently simulatable on classical computers.…”

Kibble-Zurek mechanism from different angles: The transverse XY model and subleading scalings

“…We have outlined, how a program can look like to construct a proper drive and reveal the new scaling due to irrelevant couplings for the transverse XY model. Besides its analytical appeal, the transverse XY model is in reach of experimental investigations like trapped ion experiments as in [48,49], where the transverse Ising model was already analyzed, or compressed quantum simulations [85][86][87]. Driving multiple couplings should be possible in the very same framework.…”

Compressed quantum metrology for the Ising Hamiltonian

“…up to the error aforementioned. Another method to prepare the ground state would be to use the exact diagonalization presented before (see also [12,27]). As this diagonalization is achieved via matchgates, the ground state can be generated by applying the corresponding unitary to the initial state |0 .…”