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Digital quantum simulations of spin models with superconducting circuits

U. Las Heras

Published May 24, 2017• 1 citation
OpenAlex

Abstract

We propose a digital quantum simulation of spin chains with state-of-theart superconducting circuits. Making use of a suitable gate decomposition, we show that it is feasible to implement relevant spin chain models with current technology. We discuss the gate fidelities needed in an experimental set up to achieve this goal. The present work paves the way for the implementation of digital quantum simulation methods in circuit quantum electrodynamics.

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We propose a digital quantum simulation of spin chains with state-of-theart superconducting circuits. Making use of a suitable gate decomposition, we show that it is feasible to implement relevant spin chain models with current technology. We discuss the gate fidelities needed in an experimental set up to achieve this goal. The present work paves the way for the implementation of digital quantum simulation methods in circuit quantum electrodynamics.
We propose the implementation of a digital quantum simulator for prototypical spin models in a circuit quantum electrodynamics architecture. We consider the feasibility of the quantum simulation of Heisenberg and frustrated Ising models in transmon qubits coupled to coplanar waveguide microwave resonators. Furthermore, we analyze the time evolution of these models and compare the ideal spin dynamics with a realistic version of the proposed quantum simulator. Finally, we discuss the key steps for developing a toolbox of digital quantum simulators in superconducting circuits.
We propose a digital-analog quantum simulation of generalized Dicke models with superconducting circuits, including Fermi- Bose condensates, biased and pulsed Dicke models, for all regimes of light-matter coupling. We encode these classes of problems in a set of superconducting qubits coupled with a bosonic mode implemented by a transmission line resonator. Via digital-analog techniques, an efficient quantum simulation can be performed in state-of-the-art circuit quantum electrodynamics platforms, by suitable decomposition into analog qubit-bosonic blocks and collective single-qubit pulses through digital steps. Moreover, just a single global analog block would be needed during the whole protocol in most of the cases, superimposed with fast periodic pulses to rotate and detune the qubits. Therefore, a large number of digital steps may be attained with this approach, providing a reduced digital error. Additionally, the number of gates per digital step does not grow with the number of qubits, rendering the simulation efficient. This strategy paves the way for the scalable digital-analog quantum simulation of many-body dynamics involving bosonic modes and spin degrees of freedom with superconducting circuits.
We propose the analog-digital quantum simulation of the quantum Rabi and Dicke models using circuit quantum electrodynamics (QED). We find that all physical regimes, in particular those which are impossible to realize in typical cavity QED setups, can be simulated via unitary decomposition into digital steps. Furthermore, we show the emergence of the Dirac equation dynamics from the quantum Rabi model when the mode frequency vanishes. Finally, we analyze the feasibility of this proposal under realistic superconducting circuit scenarios.
We propose a method for the efficient quantum simulation of fermionic systems with superconducting circuits. It consists in the suitable use of Jordan-Wigner mapping, Trotter decomposition, and multiqubit gates, be with the use of a quantum bus or direct capacitive couplings. We apply our method to the paradigmatic cases of 1D and 2D Fermi-Hubbard models, involving couplings with nearest and next-nearest neighbours. Furthermore, we propose an optimal architecture for this model and discuss the benchmarking of the simulations in realistic circuit quantum electrodynamics setups.
We propose a method to simulate spin models in trapped ions, using digital-analog techniques. With a suitable multiqubit gate decomposition in terms of analog blocks and digital steps, we show that the dynamics of the spin-1/2 Heisenberg chain can be implemented in a linear ion array. This digital-analog proposal involves substantially less number of gates than a fully digital approach, making it a good candidate for experimental implementations. Our work may be adapted to different quantum platforms.
We propose a method to simulate spin models in trapped ions using a digital-analog approach, consisting in a suitable gate decomposition in terms of analog blocks and digital steps. In this way, we show that the quantum dynamics of an enhanced variety of spin models could be implemented with substantially less number of gates than a fully digital approach. Typically, analog blocks are built of multipartite dynamics providing the complexity of the simulated model, while the digital steps are local operations bringing versatility to it. Finally, we describe a possible experimental implementation in trapped-ion technologies.