Michael Marthaler

Quantum Simulations (United States)

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Gerd Schön

Karlsruhe Institute of Technology

Juha Leppäkangas

Quantum Simulations (United States)

Sebastian Zanker

Quantum Design (Germany)

Lingzhen Guo

Tianjin University

Jan-Michael Reiner

Quantum Simulations (United States)

A. V. Ustinov

National Research University Higher School of Economics

Martin Weides

University of Glasgow

Dmitry S. Golubev

Aalto University

Yasuhiro Utsumi

Mie University

Hannes Rotzinger

Karlsruhe Institute of Technology

Cooperative Institutions

Google (United States)

Karlsruhe Institute of Technology

University of California, Riverside

University of California, Santa Barbara

National Institute of Standards and Technology

National University of Science and Technology

University of California, Berkeley

Russian Quantum Center

Delft University of Technology

Johannes Gutenberg University Mainz

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Describing Trotterized Time Evolutions on Noisy Quantum Computers via Static Effective Lindbladians

arXiv (Cornell University) (2022)

Keith R. Fratus Kirsten Bark Nicolas Vogt Juha Leppäkangas Sebastian Zanker

We consider the extent to which a noisy quantum computer is able to simulate the time evolution of a quantum spin system in a faithful manner. Given a specific set of assumptions regarding the manner in which noise acting on such a device can be modelled at the circuit level, we show how the effects of noise can be reinterpreted as a modification to the dynamics of the original system being simulated. In particular, we find that this modification corresponds to the introduction of static Lindblad noise terms, which act in addition to the original unitary dynamics. The form of these noise terms depends not only on the underlying noise processes occurring on the device, but also on the original unitary dynamics, as well as the manner in which these dynamics are simulated on the device, i.e., the choice of quantum algorithm. We call this effectively simulated open quantum system the noisy algorithm model. Our results are confirmed through numerical analysis.

Quantum noise

Dynamics

10.48550/arxiv.2210.11371

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Citations (3)

Quantum heating of a parametrically modulated oscillator: Spectral signatures

Physical Review A (2011)

M. I. Dykman Michael Marthaler Vittorio Peano

We show that the noise spectrum of a parametrically excited nonlinear oscillator can display a fine structure. It emerges from the interplay of the nonequidistance of the oscillator quasienergy levels and quantum heating that accompanies relaxation. The heating leads to a finite-width distribution over the quasienergy, or Floquet states, even for zero temperature of the thermal reservoir coupled to the oscillator. The fine structure is due to transitions from different quasienergy levels, and thus it provides a sensitive tool for studying the distribution. For larger damping, where the fine structure is smeared out, quantum heating can be detected from the characteristic double-peak structure of the spectrum, which results from transitions accompanied by the increase or decrease of the quasienergy.

Floquet theory

10.1103/physreva.83.052115

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Citations (52)

Spin torque switching of an in-plane magnetized system in a thermally activated region

Physical Review B (2013)

Tomohiro Taniguchi Yasuhiro Utsumi Michael Marthaler Dmitry S. Golubev Hiroshi Imamura

The current dependence of the exponent of the spin torque switching rate of an in-plane magnetized system was investigated by solving the Fokker-Planck equation with low temperature and small damping and current approximations. We derived the analytical expressions of the critical currents, I_{c} and I_{c}^{*}. At I_{c}, the initial state parallel to the easy axis becomes unstable, while at I_{c}^{*} (\simeq 1.27 I_{c}) the switching occurs without the thermal fluctuation. The current dependence of the exponent of the switching rate is well described by (1-I/I_{c}^{*})^{b}, where the value of the exponent b is approximately unity for I < I_{c}, while b rapidly increases up to 2.2 with increasing current for I_{c} < I < I_{c}^{*}. The linear dependence for I < I_{c} agrees with the other works, while the nonlinear dependence for I_{c} < I < I_{c}^{*} was newly found by the present work. The nonlinear dependence is important for analysis of the experimental results, because most experiments are performed in the current region of I_{c} < I < I_{c}^{*}.

Exponent

10.1103/physrevb.87.054406

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Citations (42)

Emission spectrum of the driven nonlinear oscillator

Physical Review A (2012)

Stephan André Lingzhen Guo Vittorio Peano Michael Marthaler Gerd Schön

Motivated by recent ``circuit QED'' experiments we investigate the noise properties of coherently driven nonlinear resonators. By using Josephson junctions in superconducting circuits, strong nonlinearities can be engineered, which lead to the appearance of pronounced effects already for a low number of photons in the resonator. Based on a master equation approach we determine the emission spectrum and observe for typical circuit QED parameters, in addition to the primary Raman-type peaks, second-order peaks. These peaks describe higher harmonics in the slow noise-induced fluctuations of the oscillation amplitude of the resonator and provide a clear signature of the nonlinear nature of the system.

10.1103/physreva.85.053825

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Citations (24)

Physical review. B./Physical review. B (2016)

Juha Leppäkangas M. Fogelström Michael Marthaler Göran Johansson

We study theoretically electromagnetic radiation emitted by inelastic Cooper-pair tunneling. We consider a dc-voltage-biased superconducting transmission line terminated by a Josephson junction. We show that the generated continuous-mode electromagnetic field can be expressed as a function of the time-dependent current across the Josephson junction. The leading-order expansion in the tunneling coupling, similar to the "$P(E)$-theory", has previously been used to investigate the photon emission statistics in the limit of sequential (independent) Cooper-pair tunneling. By explicitly evaluating the system characteristics up to the fourth-order in the tunneling coupling, we account for dynamics between consecutively tunneling Cooper pairs. Within this approach we investigate how temporal correlations in the charge transport can be seen in the first- and second-order coherences of the emitted microwave radiation.

Cooper pair

Coulomb blockade

10.1103/physrevb.93.014506

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Citations (28)

Quantum crossover of the switching rate of a modulated oscillator

Bulletin of the American Physical Society (2012)

Vittorio Peano Lingzhen Guo Michael Marthaler M. I. Dykman Gerd Schoen

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Nonclassical Photon Pair Production in a Voltage-Biased Josephson Junction

Physical Review Letters (2013)

Juha Leppäkangas Göran Johansson Michael Marthaler M. Fogelström

We investigate electromagnetic radiation emitted by a small voltage-biased Josephson junction connected to a superconducting transmission line. At frequencies below the well-known emission peak at the Josephson frequency ($2eV/h$), extra radiation is triggered by quantum fluctuations in the transmission line. For weak tunneling couplings and typical Ohmic transmission lines, the corresponding photon-flux spectrum is symmetric around half the Josephson frequency, indicating that the photons are predominately created in pairs. By establishing an input-output formalism for the microwave field in the transmission line, we give further evidence for this nonclassical photon pair production, demonstrating that it violates the classical Cauchy-Schwarz inequality for two-mode flux cross correlations. In connection to recent experiments, we also consider a stepped transmission line, where resonances increase the signal-to-noise ratio.

Superconducting tunnel junction

10.1103/physrevlett.110.267004

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Citations (49)

Floquet many-body engineering: topology and many-body physics in phase space lattices

New Journal of Physics (2018)

Pengfei Liang Michael Marthaler Lingzhen Guo

Hamiltonians which are inaccessible in static systems can be engineered in periodically driven many-body systems, i.e., Floquet many-body systems. We propose to use interacting particles in a one-dimensional (1D) harmonic potential with periodic kicking to investigate two-dimensional (2D) topological and many-body physics. Depending on the driving parameters, the Floquet Hamiltonian of single kicked harmonic oscillator has various lattice structures in phase space. The noncommutative geometry of phase space gives rise to the topology of the system. We investigate the effective interactions of particles in phase space and find that the point-like contact interaction in quasi-1D real space becomes a long-rang Coulomb-like interaction in phase space, while the hardcore interaction in pure-1D real space becomes a confinement quark-like potential in phase space. We also find that the Floquet exchange interaction does not disappear even in the classical limit, and can be viewed as an effective long-range spin-spin interaction induced by collision. Our proposal may provide platforms to explore new physics and exotic phases by \textit{Floquet many-body engineering}.

Floquet theory

Hamiltonian (control theory)

Lattice (music)

10.1088/1367-2630/aaa7c3

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Citations (39)

Tunneling of a modulated oscillator: quantum interference in the classically forbidden region

Bulletin of the American Physical Society (2008)

Michael Marthaler M. I. Dykman

Quantum interference

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Few-qubit lasing in circuit QED

Physica Scripta (2009)

Stephan André Valentina Brosco Michael Marthaler Alexander Shnirman Gerd Schön

Motivated by recent experiments, which demonstrated lasing and cooling of the electromagnetic modes in a resonator coupled to a superconducting qubit, we describe the specific mechanisms creating the population inversion, and we study the spectral properties of these systems in the lasing state. Different levels of the theoretical description, i.e., the semi-classical and the semi-quantum approximation, as well as an analysis based on the full Liouville equation are compared. We extend the usual quantum optics description to account for strong qubit-resonator coupling and include the effects of low-frequency noise. Beyond the lasing transition we find for a single- or few-qubit system the phase diffusion strength to grow with the coupling strength, which in turn deteriorates the lasing state.

Population inversion

Charge qubit

10.1088/0031-8949/2009/t137/014016

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Citations (23)