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arXiv:1608.08025 · Scientific Reports

Digital-analog quantum simulation of generalized Dicke models with superconducting circuits

Lucas Lamata

Published Mar 3, 2017• 46 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/srep43768

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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 concept of mixed analog–digital quantum simulation of the Dicke model with ensembles of superconducting qubits coupled to the single-mode microwave resonators. Using both single-qubit and twoqubit quantum logic gates, it should be possible to engineer different initial conditions for the ensemble of qubits. Since qubits can interact through the photon field of a common quantum resonator, it is attractive to examine the time evolution of this system depending on various characteristics of the initial state, including entanglement and symmetry. We here study theoretically the dynamics of such systems taking into account energy dissipation, pure decoherence as well as disorder in qubits excitation frequencies, which are unavoidable for macroscopic artificial quantum systems. We reveal unusual effects of these imperfections on the dynamics.
The Dicke model provides a fundamental description of collective light-matter interactions and has long served as a testbed for exploring a wide range of physical phenomena in quantum optics and condensed matter physics. In this work, we develop a variational framework for investigating the finite-size Dicke model on both fully qubit-based (digital) and hybrid qubit boson based (digital-analogue) quantum computing platforms. We show that the resulting model reproduces the characteristic critical behavior of the Dicke model in the appropriate large-spin limit while remaining suitable for implementation on both classical emulators of quantum computers and actual trapped ion quantum computers, albeit in the case of latter somewhat limited by noise. Finally, we introduce a complementary hybrid qubit-bosonic variational ansatz that directly exploits the bosonic degree of freedom to reduce quantum resources and discuss its potential implementation on hybrid quantum hardware. Our results establish a scalable, symmetry-aware framework for variational quantum simulations of collective light-matter systems and provide a pathway toward efficient simulations of more general spin-boson models on near-term quantum devices.
In recent years, there has been a significant progress in the development of digital quantum processors. The state-of-the-art quantum devices are imperfect, and fully algorithmic fault-tolerant quantum computing is a matter of future. Until technology develops to the state with practical error correction, computational approaches other than the standard digital one can be used to avoid execution of the most noisy quantum operations. We demonstrate how a hybrid digital-analog approach allows simulating dynamics of a transverse-field Ising model without standard two-qubit gates, which are currently one of the most problematic building blocks of quantum circuits. We use qubit-qubit crosstalks (couplings) of IBM superconducting quantum processors to simulate Trotterized dynamics of spin clusters and then we compare the obtained results with the results of conventional digital computation based on two-qubit gates from the universal set. The comparison shows that digital-analog approach significantly outperforms standard digital approach for this simulation problem, despite of the fact that crosstalks in IBM quantum processors are small. We argue that the efficiency of digital-analog quantum computing can be improved with the help of more specialized processors, so that they can be used to efficiently implement other quantum algorithms. This indicates the prospect of a digital-to-analog strategy for near-term noisy intermediate-scale quantum computers.
We propose an efficient protocol for digital quantum simulation of quantum chemistry problems and enhanced digital-analog quantum simulation of transport phenomena in biomolecules with superconducting circuits. Along these lines, we optimally digitize fermionic models of molecular structure with single-qubit and two-qubit gates, by means of Trotter-Suzuki decomposition and Jordan-Wigner transformation. Furthermore, we address the modelling of system-environment interactions of biomolecules involving bosonic degrees of freedom with a digital-analog approach. Finally, we consider gate-truncated quantum algorithms to allow the study of environmental effects.
Abstract We propose a digital-analog quantum algorithm for simulating the Hubbard-Holstein model, describing strongly-correlated fermion-boson interactions, in a suitable architecture with superconducting circuits. It comprises a linear chain of qubits connected by resonators, emulating electron-electron (e-e) and electron-phonon (e-p) interactions, as well as fermion tunneling. Our approach is adequate for a digital-analog quantum computing (DAQC) of fermion-boson models including those described by the Hubbard-Holstein model. We show the reduction in the circuit depth of the DAQC algorithm, a sequence of digital steps and analog blocks, outperforming the purely digital approach. We exemplify the quantum simulation of a half-filling two-site Hubbard-Holstein model. In such example we obtain fidelities larger than 0.98, showing that our proposal is suitable to study the dynamical behavior of solid-state systems. Our proposal opens the door to computing complex systems for chemistry, materials, and high-energy physics.