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Quantum Simulators in Other Frames of Reference

Karol Gietka, Ayaka Usui, Jianqiao Deng, Thomas Busch

Published Jul 14, 2020• 0 citations
OpenAlex

Abstract

We show how by exploiting the knowledge of the frame of reference connecting two arbitrary Hamiltonians, one can use one Hamiltonian to simulate the physics of the other one. As an example, we first discuss how one can simulate an infinite-range-interaction one-axis twisting Hamiltonian using a short-range nearest-neighbor-interaction Heisenberg XXX model with a staggered field. Based on this, we show how one can build an alternative version to the existing ideas of digital quantum simulators. As a by-product, we present a method for creating many-body entangled states using only short-range nearest-neighbor interactions.

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We show how by exploiting the knowledge of the frame of reference connecting two arbitrary Hamiltonians, one can use one Hamiltonian to simulate the physics of the other one. As an example, we first discuss how one can simulate an infinite-range-interaction one-axis twisting Hamiltonian using a short-range nearest-neighbor-interaction Heisenberg XXX model with a staggered field. Based on this, we show how one can build an alternative version to the existing ideas of digital quantum simulators. As a by-product, we present a method for creating many-body entangled states using only short-range nearest-neighbor interactions.
We develop a framework and give an example for situations where two distinct Hamiltonians living in the same Hilbert space can be used to simulate the same physics. As an example of an analog simulation, we first discuss how one can simulate an infinite-range-interaction one-axis twisting Hamiltonian using a short-range nearest-neighbor-interaction Heisenberg XXX model with a staggered field. Based on this, we show how one can build an alternative version of a digital quantum simulator. As a by-product, we present a method for creating many-body maximally entangled states using only short-range nearest-neighbor interactions.
Abstract In a digital quantum simulator, basic two-qubit interactions are manipulated by means of fast local control operations to establish a desired target Hamiltonian. Here we consider a quantum simulator based on logical systems, i.e. where several physical qubits are used to represent a single logical two-level system to obtain enhanced and simple control over effective interactions between logical systems. Fixed, distance-dependent pairwise interactions between the physical qubits lead to effective interactions between the logical systems, which can be fully controlled solely by the choice of their internal state. This allows one to directly manipulate the topology and strength of effective interactions between logical systems. We show how to choose and generate the required states of logical systems for any desired interaction pattern and topology, how to perform arbitrary logical measurements, and how to obtain full control over single logical systems using only the intrinsic two-body interactions and control of individual physical qubits. This leads to a universal quantum simulator based on logical systems. We discuss the advantages of such a logical quantum simulator over standard ones, including the possibility to reach target topologies that are only accessible with large overheads otherwise. We provide several examples of how to obtain different target interaction patterns and topologies from initial long-ranged or short-ranged qubit-qubit interactions with a specific distance dependence.
Scalable quantum resources with short-range interacting spin-12\frac1221​ chains
The dynamical generation of quantum resources, such as many-body entanglement, Bell correlations or spin squeezing, can be achieved via one-axis twisting (OAT) dynamics, which require all-to-all couplings. However, current digital and analog quantum simulation platforms natively provide short-range or power-law couplings that decay too quickly for this purpose. We demonstrate that two spin-12\tfrac1221​ chain models -- a staggered nearest-neighbor XXX chain and a long-range XXZ chain -- develop an effective OAT nonlinearity when projected onto the symmetric sector. We show that these dynamics generate metrologically useful spin-squeezed states and Greenberger-Horne-Zeilinger coherences that ensure violation of many-body Bell inequalities. We confirm the accuracy of this mapping by comparing it to the exact dynamics and demonstrate that the generated correlations can be read out using a single probe qubit. The resulting dynamics can be simulated with analog and digital quantum simulators.
Digital-analog quantum computation aims to reduce the currently infeasible resource requirements needed for near-term quantum information processing by replacing sequences of one-and two-qubit gates with a unitary transformation generated by the systems' underlying Hamiltonian.Inspired by this paradigm, we consider superconducting architectures and extend the cross-resonance effect, up to first order in perturbation theory, from a two-qubit interaction to an analog Hamiltonian acting on onedimensional (1D) chains and two-dimensional (2D) square lattices, which, in an appropriate reference frame, results in a purely two-local Hamiltonian.By augmenting the analog Hamiltonian dynamics with single-qubit gates we show how one may generate a larger variety of distinct analog Hamiltonians.We then synthesize unitary sequences, in which we toggle between the various analog Hamiltonians as needed, simulating the dynamics of Ising, XY, and Heisenberg spin models.Our dynamics simulations are Trotter error-free for the Ising and XY models in 1D.We also show that the Trotter errors for 2D XY and 1D Heisenberg chains are reduced, with respect to a digital decomposition, by a constant factor.In order to realize these important near-term speedups, we discuss the practical considerations needed to accurately characterize and calibrate our analog Hamiltonians for use in quantum simulations.We conclude with a discussion of how the Hamiltonian toggling techniques could be extended to derive new analog Hamiltonians, which may be of use in more complex digital-analog quantum simulations for various models of interacting spins.
Remarkable advances in cooling and manipulating atomic gases have opened up new avenues to explore fundamental concepts in quantum many-body physics. Synthetically created potentials and control of atom-atom interactions have made it possible to tailor the properties of experimental systems at a microscopic level. This led to the concept of quantum simulation - here a system capable of reproducing the physics of many-body Hamiltonians. One of the goals of this approach is to provide answers to open questions in the context of condensed matter physics. An equally important frontier is the construction of novel systems, which may at present not be realizable in solid-state or other systems, allowing it to conquer new areas of physics. This path leads to new questions and surprises.