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We present a quantum algorithm to simulate general finite dimensional Lindblad master equations without the requirement of engineering the system-environment interactions. The proposed method is able to simulate both Markovian and non-Markovian quantum dynamics. It consists in the quantum computation of the dissipative corrections to the unitary evolution of the system of interest, via the reconstruction of the response functions associated with the Lindblad operators. Our approach is equally applicable to dynamics generated by effectively non-Hermitian Hamiltonians. We confirm the quality of our method providing specific error bounds that quantify itss accuracy.
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In the present work we investigate the existence of multiple nonequilibrium steady states in a coherently driven XY lattice of dissipative two-level systems. A commonly used mean-field ansatz, in which spatial correlations are neglected, predicts a bistable behavior with a sharp shift between low- and high-density states. In contrast one-dimensional matrix product methods reveal these effects to be artifacts of the mean-field approach, with both disappearing once correlations are taken fully into account. Instead, a bunching-antibunching transition emerges. This indicates that alternative approaches should be considered for higher spatial dimensions, where classical simulations are currently infeasible. Thus we propose a circuit QED quantum simulator implementable with current technology to enable an experimental investigation of the model considered.
Recent advances illustrate the power of reservoir engineering in applications to many-body systems, such as quantum simulators based on superconducting circuits. We present a framework based on kinetic equations and noise spectra that can be used to understand both the transient and long-time behavior of many particles coupled to an engineered reservoir in a number-conserving way. For the example of a bosonic array, we show that the non-equilibrium steady state can be expressed, in a wide parameter regime, in terms of a modified Bose-Einstein distribution with an energy-dependent temperature.
Simulating quantum physics with a device which itself is quantum mechanical, a notion Richard Feynman originated, would be an unparallelled computational resource. However, the universal quantum simulation of fermionic systems is daunting due to their particle statistics, and Feynman left as an open question whether it could be done, because of the need for non-local control. Here, we implement fermionic interactions with digital techniques in a superconducting circuit. Focusing on the Hubbard model, we perform time evolution with constant interactions as well as a dynamic phase transition with up to four fermionic modes encoded in four qubits. The implemented digital approach is universal and allows for the efficient simulation of fermions in arbitrary spatial dimensions. We use in excess of 300 single-qubit and two-qubit gates, and reach global fidelities which are limited by gate errors. This demonstration highlights the feasibility of the digital approach and opens a viable route towards analog-digital quantum simulation of interacting fermions and bosons in large-scale solid state systems.
We describe the dynamics of a qubit interacting with a bosonic mode coupled to a zero-temperature bath in the deep strong coupling (DSC) regime. We provide an analytical solution for this open system dynamics in the off-resonance case of the qubit-mode interaction. Collapses and revivals of parity chain populations and the oscillatory behavior of the mean photon number are predicted. At the same time, photon number wave packets, propagating back and forth along parity chains, become incoherently mixed. Finally, we investigate numerically the effect of detuning on the validity of the analytical solution.
Reaching the strong coupling regime of light-matter interaction has led to an impressive development in fundamental quantum physics and applications to quantum information processing. Latests advances in different quantum technologies, like superconducting circuits or semiconductor quantum wells, show that the ultrastrong coupling regime (USC) can also be achieved, where novel physical phenomena and potential computational benefits have been predicted. Nevertheless, the lack of effective decoupling mechanism in this regime has so far hindered control and measurement processes. Here, we propose a method based on parity symmetry conservation that allows for the generation and reconstruction of arbitrary states in the ultrastrong coupling regime of light-matter interactions. Our protocol requires minimal external resources by making use of the coupling between the USC system and an ancillary two-level quantum system.
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