Gate-based digital quantum simulations offer an exciting new paradigm for studying the many-body physics of strongly correlated systems. In this context, electron-phonon models are challenging for qubit-only quantum simulators, as bosonic degrees of freedom require costly finite-dimensional encodings. Here, we elaborate on an alternative approach based on a digital-analog circuit QED architecture, where fermions are encoded in transmon qubits while bosons are represented directly by microwave resonators. The central building block of this framework is a qubit-resonator Rabi gate that emulates strong electron-phonon coupling and can be implemented through a sequence of resonant Jaynes-Cummings gates interleaved with layers of single-qubit rotations. Using this Rabi gate as the fundamental unitary operation, we construct quantum circuits for the Hubbard-Holstein and Yukawa-Sachdev-Ye-Kitaev models, which describe, respectively, strongly correlated electrons coupled to phonons and phonon-mediated interactions among Majorana fermions. We further demonstrate how nonclassical phonon physics and signatures of quantum chaos in these models can be probed through circuit simulations, and develop measurement and variational protocols tailored to near-term superconducting quantum hardware.
Gate-based digital quantum simulations offer an exciting new paradigm for studying the many-body physics of strongly correlated systems. In this context, electron-phonon models are challenging for qubit-only quantum simulators, as bosonic degrees of freedom require costly finite-dimensional encodings. Here, we elaborate on an alternative approach based on a digital-analog circuit QED architecture, where fermions are encoded in transmon qubits while bosons are represented directly by microwave resonators. The central building block of this framework is a qubit-resonator Rabi gate that emulates strong electron-phonon coupling and can be implemented through a sequence of resonant Jaynes-Cummings gates interleaved with layers of single-qubit rotations. Using this Rabi gate as the fundamental unitary operation, we construct quantum circuits for the Hubbard-Holstein and Yukawa-Sachdev-Ye-Kitaev models, which describe, respectively, strongly correlated electrons coupled to phonons and phonon-mediated interactions among Majorana fermions. We further demonstrate how nonclassical phonon physics and signatures of quantum chaos in these models can be probed through circuit simulations, and develop measurement and variational protocols tailored to near-term superconducting quantum hardware.
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.
Abstract The Jaynes‐Cummings model describes the coupling between photons and a single two‐level atom in a simplified representation of light‐matter interactions. In circuit QED, this model is implemented by combining microwave resonators and superconducting qubits on a microchip with unprecedented experimental control. Arranging qubits and resonators in the form of a lattice realizes a new kind of Hubbard model, the Jaynes‐Cummings‐Hubbard model, in which the elementary excitations are polariton quasi‐particles. Due to the genuine openness of photonic systems, circuit QED lattices offer the possibility to study the intricate interplay of collective behavior, strong correlations and non‐equilibrium physics. Thus, turning circuit QED into an architecture for quantum simulation, i.e., using a well‐controlled system to mimic the intricate quantum behavior of another system too daunting for a theorist to tackle head‐on, is an exciting idea which has served as theorists’ playground for a while and is now also starting to catch on in experiments. This review gives a summary of the most recent theoretical proposals and experimental efforts.
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.
Key to solving many societally relevant problems in materials science, quantum chemistry, and nuclear physics is understanding their fundamental microscopic quantum behavior. All of these problems can be phrased as fermionic (e.g., electrons, quarks) and bosonic particles (e.g., lattice vibrations, photons) interacting with each other. However, solving these systems of strongly interacting fermions and bosons is out of reach for classical computers and also non-error-corrected qubit-only quantum computers. In this paper, we introduce a hybrid qubit and bosonic-oscillator quantum-simulation framework, which is so efficient that it could simulate some of these strongly correlated problems even without error correction. Specifically, we leverage the available universal bosonic gate set with O ( 1 ) operations per gate as a function of the bosonic cutoff. This enables our framework to provide exact decompositions of higher-order fermion-boson interactions, including notoriously challenging terms such as ( 2 + 1 ) D gauge theories. We show how to compile dynamics, ancilla-free partial error detection, nonlocal observable measurements, and ground-state energy estimation using both qubit-boson variational quantum eigensolvers and quantum signal processing. We introduce a “post-qubit quantum advantage” experiment which is out of reach for both near-term qubit-only quantum computers and classical computers. We justify this proposal by estimating bosonic gate fidelities through high–boson-occupation Lindblad simulation and by comparing to qubit-only algorithms. For the latter, we develop a new qubit-based algorithm for simulating a beam splitter with a boson number cutoff N max , which scales as O ˜ ( N max 1 + o ( 1 ) ) , asymptotically outperforming previously known qubit methods. However, to reach the same circuit fidelity as qubit-boson hardware with 99.9% per-gate fidelity, a qubit quantum computer using the best-known method would still need fidelities of at least 99.9999%, likely requiring substantial error correction. Our framework can be used in superconducting hardware, which we focus on, as well as trapped-ion and neutral-atom hardware. This work establishes digital hybrid qubit-boson quantum simulation as a promising and advantageous method for solving the many challenging, strongly correlated, fermion-boson models of relevance to science and technology.
Motivated by the compelling need to understand the nonequilibrium dynamics of small-polaron formation following an electron-phonon interaction quench, in this work we propose a digital quantum simulator of a one-dimensional lattice model describing an itinerant fermionic excitation (e.g. an electron) nonlocally coupled to zero-dimensional bosons (e.g. Einstein-type phonons). Quantum circuits implementing the dynamics of this model, which includes Peierls- and breathing-mode-type excitation-boson interactions, are designed here, their complexity scaling linearly with the system size. A circuit that generates the natural initial (pre-quench) state of this system -- a bare-excitation Bloch state, equivalent to a W state of a qubit register -- is also presented. To facilitate comparisons with the proposed simulator, once experimentally realized, the system dynamics are also evaluated numerically and characterized through the Loschmidt echo and various correlation functions.
Analog quantum simulators can be used to study quantum correlation in novel many-body systems by emulating the Hamiltonian of these systems. One essential question in quantum simulation is to probe the properties of an emulated many-body system. Here we present a circuit QED scheme for probing such properties by measuring the spectrum of a superconducting resonator coupled to a quantum simulator. We first study a general framework of this approach and show that the spectrum of the resonator is directly related to the correlation function of the coupling operator between the resonator and the simulator. We then apply this scheme to a simulator of the transverse field Ising model implemented with superconducting qubits, where the resonance peaks in the resonator spectrum correspond to the frequencies of the elementary excitations. The effects of resonator damping, qubit decoherence, and resonator backaction are also discussed. This setup can be used to probe a broad range of many-body models.