arXiv subjects

Hakan E. Türeci

Publications and source records attributed to Hakan E. Türeci.

At least 37 records · Page 2Linked to original sources

arXiv2023

Quantifying the Expressive Capacity of Quantum Systems: Fundamental Limits and Eigentasks

The expressive capacity of quantum systems for machine learning is limited by quantum sampling noise incurred during measurement. Although it is generally believed that noise limits the resolvable capacity of quantum systems, the precise impact of noise on learning is not yet fully understood. We present a mathematical framework for evaluating the available expressive capacity of general quantum systems from a finite number of measurements, and provide a methodology for extracting the extrema of this capacity, its eigentasks. Eigentasks are a native set of functions that a given quantum system can approximate with minimal error. We show that extracting low-noise eigentasks leads to improved performance for machine learning tasks such as classification, displaying robustness to overfitting. We obtain a tight bound on the expressive capacity, and present analyses suggesting that correlations in the measured quantum system enhance learning capacity by reducing noise in eigentasks. These results are supported by experiments on superconducting quantum processors. Our findings have broad implications for quantum machine learning and sensing applications.

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arXiv2023

DEC-QED: A flux-based 3D electrodynamic modeling approach to superconducting circuits and materials

Modeling the behavior of superconducting electronic circuits containing Josephson junctions is crucial for the design of superconducting information processors and devices. In this paper, we introduce DEC-QED, a computational approach for modeling the electrodynamics of superconducting electronic circuits containing Josephson junctions in arbitrary three-dimensional electromagnetic environments. DEC-QED captures the non-linear response and induced currents in BCS superconductors and accurately captures phenomena such as the Meissner effect, flux quantization and Josephson effects. Using a spatial coarse-graining formulation based on Discrete Exterior Calculus (DEC), DEC-QED can accurately simulate transient and long-time dynamics in superconductors. The expression of the entire electrodynamic problem in terms of the gauge-invariant flux field and charges makes the resulting classical field theory suitable for second quantization.

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arXiv2022

Radiative Properties of an Artificial Atom coupled to a Josephson Junction Array

We study the radiative properties -- the Lamb shift, Purcell decay rate and the spontaneous emission dynamics -- of an artificial atom coupled to a long, multimode cavity formed by an array of Josephson junctions. Introducing a tunable coupling element between the atom and the array, we demonstrate that such a system can exhibit a crossover from a perturbative to non-perturbative regime of light-matter interaction as one strengthens the coupling between the atom and the Josephson junction array (JJA). As a consequence, the concept of spontaneous emission as the occupation of the local atomic site being governed by a single complex-valued exponent breaks down. This breakdown, we show, can be interpreted in terms of formation of hybrid atom-resonator modes with radiative losses that are non-trivially related to the effective coupling between individual modes. We develop a singular function expansion approach for the description of the open quantum system dynamics in such a multimode non-perturbative regime. This modal framework generalizes the normal mode description of quantum fields in a finite volume, incorporating exact radiative losses and incident quantum noise at the delimiting surface. Our results are pertinent to recent experiments with Josephson atoms coupled to high impedance Josephson junction arrays.

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arXiv2021

Physical reservoir computing using finitely-sampled quantum systems

The paradigm of reservoir computing exploits the nonlinear dynamics of a physical reservoir to perform complex time-series processing tasks such as speech recognition and forecasting. Unlike other machine-learning approaches, reservoir computing relaxes the need for optimization of intra-network parameters, and is thus particularly attractive for near-term hardware-efficient quantum implementations. However, the complete description of practical quantum reservoir computers requires accounting for their placement in a quantum measurement chain, and its conditional evolution under measurement. Consequently, training and inference has to be performed using finite samples from obtained measurement records. Here we describe a framework for reservoir computing with nonlinear quantum reservoirs under continuous heterodyne measurement. Using an efficient truncated-cumulants representation of the complete measurement chain enables us to sample stochastic measurement trajectories from reservoirs of several coupled nonlinear bosonic modes under strong excitation. This description also offers a mathematical basis to directly compare the computational capabilities of a given physical reservoir operated across classical and quantum regimes. Applying this framework to the classification of quantum states of systems that are part of the same measurement chain as the quantum reservoir computer, we assess and explain measurement-contingent advantages and disadvantages of reservoir processing in quantum regimes. Our results also identify the vicinity of bifurcation points as presenting optimal nonlinear processing regimes of an oscillator-based quantum reservoir. The considered models are directly realizable in modern circuit QED experiments, while the framework is applicable to more general quantum nonlinear reservoirs.

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arXiv2021

Reservoir Computing Approach to Quantum State Measurement

Efficient quantum state measurement is important for maximizing the extracted information from a quantum system. For multi-qubit quantum processors in particular, the development of a scalable architecture for rapid and high-fidelity readout remains a critical unresolved problem. Here we propose reservoir computing as a resource-efficient solution to quantum measurement of superconducting multi-qubit systems. We consider a small network of Josephson parametric oscillators, which can be implemented with minimal device overhead and in the same platform as the measured quantum system. We theoretically analyze the operation of this Kerr network as a reservoir computer to classify stochastic time-dependent signals subject to quantum statistical features. We apply this reservoir computer to the task of multinomial classification of measurement trajectories from joint multi-qubit readout. For a two-qubit dispersive measurement under realistic conditions we demonstrate a classification fidelity reliably exceeding that of an optimal linear filter using only two to five reservoir nodes, while simultaneously requiring far less calibration data \textendash{} as little as a single measurement per state. We understand this remarkable performance through an analysis of the network dynamics and develop an intuitive picture of reservoir processing generally. Finally, we demonstrate how to operate this device to perform two-qubit state tomography and continuous parity monitoring with equal effectiveness and ease of calibration. This reservoir processor avoids computationally intensive training common to other deep learning frameworks and can be implemented as an integrated cryogenic superconducting device for low-latency processing of quantum signals on the computational edge.

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arXiv2021

Nearly quantum-limited Josephson-junction Frequency Comb synthesizer

While coherently-driven Kerr microcavities have rapidly matured as a platform for frequency comb formation, such microresonators generally possess weak Kerr coefficients; consequently, triggering comb generation requires millions of photons to be circulating inside the cavity. This suppresses the role of quantum fluctuations in the comb's dynamics. In this paper, we realize a minimal version of coherently-driven Kerr-mediated microwave frequency combs in the circuit QED architecture, where the quantum vacuum's fluctuations are the primary limitation on comb coherence. We achieve a comb phase coherence of up to 35~$μ$s, approaching the theoretical device quantum limit of 55~$μ$s, and vastly longer than the modes' inherent lifetimes of 13~ns. The ability within cQED to engineer stronger nonlinearities than optical microresonators, together with operation at cryogenic temperatures, and excellent agreement of comb dynamics with quantum theory indicates a promising platform for the study of complex dynamics of quantum nonlinear systems

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arXiv2019

Lifetime renormalization of weakly anharmonic superconducting qubits: I. Role of number non-conserving terms

The dynamics of a weakly anharmonic superconducting qubit in a complex electromagnetic environment is generally well-described by an effective multimode Kerr Hamiltonian at sufficiently weak excitation. This Hamiltonian can be embedded in a master equation with losses determined by the details of the electromagnetic environment. Recent experiments indicate, however, that when a superconducting circuit is driven with microwave signals the observed relaxation rates appear to be substantially different from expectations based on the electromagnetic environment of the qubit alone. This issue is a limiting factor in the optimization of superconducting qubit readout schemes. We claim here that an effective master equation with drive-power dependent parameters is an efficient approach to model such quantum dynamics. In this sequence of papers, we derive effective master equations, whose parameters exhibit nonlinear dependence on the excitation level of the circuit as well as the electromagnetic environment of the qubit. We show that the number non-conserving terms in the qubit nonlinearity generally lead to a renormalization of dissipative parameters of the effective master equation, while the number conserving terms give rise to a renormalization of the system frequencies. Here, in Part I, we consider the excitation-relaxation dynamics of a transmon qubit that is prepared in a certain initial state, but is not driven otherwise. A unitary transformation technique is introduced to study the renormalization of i) qubit relaxation due to coupling to a generic bath and ii) Purcell decay. Analytic expressions are provided for the dependence of the nonlinear dissipative terms on the details of the electromagnetic environment of the qubit. The perturbation technique based on unitary transformations developed here is generalized to the continuously driven case in Part II.

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arXiv2019

Lifetime renormalization of driven weakly anharmonic superconducting qubits: II. The readout problem

Recent experiments in superconducting qubit systems have shown an unexpectedly strong dependence of the qubit relaxation rate on the readout drive power. This phenomenon limits the maximum measurement strength and thus the achievable readout speed and fidelity. We address this problem here and provide a plausible mechanism for drive-power dependence of relaxation rates. To this end we introduce a two-parameter perturbative expansion in qubit anharmonicity and the drive amplitude through a unitary transformation technique introduced in Part I. This approach naturally reveals number non-conserving terms in the Josephson potential as a fundamental mechanism through which applied microwave drives can activate additional relaxation mechanisms. We present our results in terms of an effective master equation with renormalized state- and drive-dependent transition frequency and relaxation rates. Comparison of numerical results from this effective master equation to those obtained from a Lindblad master equation which only includes number-conserving terms (i.e. Kerr interactions) shows that number non-conserving terms can lead to significant drive-power dependence of the relaxation rates. The systematic expansion technique introduced here is of general applicability to obtaining effective master equations for driven-dissipative quantum systems that contain weakly non-linear degrees of freedom.

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arXiv2018

Frequency Combs in a Lumped-Element Josephson-Junction Circuit

We investigate the dynamics of a microwave-driven Josephson junction capacitively coupled to a lumped element LC oscillator. In the regime of driving where the Josephson junction can be approximated as a Kerr oscillator, this minimal nonlinear system has been previously shown to exhibit a bistability in phase and amplitude. In the present study, we characterize the full phase diagram and show that besides a parameter regime exhibiting bistability, there is also a regime of self-oscillations characterized by a frequency comb in its spectrum. We discuss the mechanism of comb generation which appears to be different from those studied in microcavity frequency combs and mode-locked lasers. We then address the fate of the comb-like spectrum in the regime of strong quantum fluctuations, reached when nonlinearity becomes the dominant scale with respect to dissipation. We find that the nonlinearity responsible for the emergence of the frequency combs also leads to its dephasing, leading to broadening and ultimate disappearance of sharp spectral peaks. Our study explores the fundamental question of the impact of quantum fluctuations for quantum systems which do not possess a stable fixed point in the classical limit.

cond-mat.mes-hall↗

arXiv2017

Fluxon-Based Quantum Simulation in Circuit QED

Long-lived fluxon excitations can be trapped inside a superinductor ring, which is divided into an array of loops by a periodic sequence of Josephson junctions in the quantum regime, thereby allowing fluxons to tunnel between neighboring sites. By tuning the Josephson couplings, and implicitly the fluxon tunneling probability amplitudes, a wide class of 1D tight-binding lattice models may be implemented and populated with a stable number of fluxons. We illustrate the use of this quantum simulation platform by discussing the Su-Schrieffer-Heeger model in the 1-fluxon subspace, which hosts a symmetry protected topological phase with fractionally charged bound states at the edges. This pair of localized edge states could be used to implement a superconducting qubit increasingly decoupled from decoherence mechanisms.

cond-mat.mes-hall↗

arXiv2017

Competing role of interactions in synchronization of exciton-polariton condensates

We present a theoretical study of synchronization dynamics in incoherently pumped exciton-polariton condensates in coupled polariton traps. Our analysis is based on a coupled-mode theory for the generalized Gross-Pitaevskii equation, which employs an expansion in non-Hermitian, pump-dependent modes appropriate for the pumped geometry. We find that polariton-polariton and reservoir-polariton interactions play competing roles and lead to qualitatively different synchronized phases of the coupled polariton modes as pumping power is increased. Crucially, these interactions can also act against each other to hinder synchronization. We map out a phase diagram and discuss the general characteristics of these phases using a generalized Adler equation.

cond-mat.mes-hall↗

arXiv2017

Studying Light-Harvesting Models with Superconducting Circuits

The process of photosynthesis, the main source of energy in the animate world, converts sunlight into chemical energy. The surprisingly high efficiency of this process is believed to be enabled by an intricate interplay between the quantum nature of molecular structures in photosynthetic complexes and their interaction with the environment. Investigating these effects in biological samples is challenging due to their complex and disordered structure. Here we experimentally demonstrate a new approach for studying photosynthetic models based on superconducting quantum circuits. In particular, we demonstrate the unprecedented versatility and control of our method in an engineered three-site model of a pigment protein complex with realistic parameters scaled down in energy by a factor of $10^5$. With this system we show that the excitation transport between quantum coherent sites disordered in energy can be enabled through the interaction with environmental noise. We also show that the efficiency of the process is maximized for structured noise resembling intramolecular phononic environments found in photosynthetic complexes.

quant-ph↗

arXiv2017

Cutoff-free Circuit Quantum Electrodynamics

Any quantum-confined electronic system coupled to the electromagnetic continuum is subject to radiative decay and renormalization of its energy levels. When coupled to a cavity, these quantities can be strongly modified with respect to their values in vacuum. Generally, this modification can be accurately captured by including only the closest resonant mode of the cavity. In the circuit quantum electrodynamics architecture, where the coupling strengths can be substantial, it is however found that the radiative decay rates are strongly influenced by far off-resonant modes. A multimode calculation accounting for the infinite set of cavity modes leads to divergences unless a cutoff is imposed. It has so far not been identified what the source of divergence is. We show here that unless gauge invariance is respected, any attempt at the calculation of circuit QED quantities is bound to diverge. We then present a theoretical approach to the calculation of a finite spontaneous emission rate and the Lamb shift that is free of cutoff.

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arXiv2017

Non-Markovian dynamics of a superconducting qubit in an open multimode resonator

We study the dynamics of a transmon qubit that is capacitively coupled to an open multimode superconducting resonator. Our effective equations are derived by eliminating resonator degrees of freedom while encoding their effect in the Green's function of the electromagnetic background. We account for the dissipation of the resonator exactly by employing a spectral representation for the Green's function in terms of a set of non-Hermitian modes and show that it is possible to derive effective Heisenberg-Langevin equations without resorting to the rotating wave, two level or Markov approximations. A well-behaved time domain perturbation theory is derived to systematically account for the nonlinearity of the transmon. We apply this method to the problem of spontaneous emission, capturing accurately the non-Markovian features of the qubit dynamics, valid for any qubit-resonator coupling strength.

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arXiv2016

Non-Hermitian coupled-mode theory for incoherently pumped exciton-polariton condensates

The generalized Gross-Pitaevskii equation (gGPE) is an effective phenomenological description for the dynamics of incoherently pumped exciton-polariton condensates. However, a brute force numerical simulation of the gGPE provides little physical insight into condensate formation under arbitrary pumping configurations, and is demanding in terms of computational resources. We introduce in this paper a modal description of polariton condensation under incoherent pumping of arbitrary spatial profile, based on eigenmodes of the non-Hermitian generator of the linearized dynamics. A pump-dependent basis is then introduced to formulate a temporal coupled-mode theory that captures condensate dynamics in the presence of all nonlinear interactions. Simulations using a single set of modes for a given pumping and trapping configuration agree very well with a full integration of the gGPE in diverse dynamical regimes, supporting the validity of this modal description, while also providing a speedup in simulation times.

cond-mat.mes-hall↗

arXiv2016

Purification and switching protocols for dissipatively stabilized entangled qubit states

Pure dephasing processes limit the fidelities achievable in driven-dissipative schemes for stabilization of entangled states of qubits. We propose a scheme which, combined with already existing entangling methods, purifies the desired entangled state by driving out of equilibrium auxiliary dissipative cavity modes coupled to the qubits. We lay out the specifics of our scheme and compute its efficiency in the particular context of two superconducting qubits in a cavity-QED architecture, where the strongly coupled auxiliary modes provided by collective cavity excitations can drive and sustain the qubits in maximally entangled Bell states with fidelities reaching 90% for experimentally accessible parameters.

quant-ph↗

arXiv2016

Photon-mediated interactions: a scalable tool to create and sustain entangled states of N atoms

We propose and study the use of photon-mediated interactions for the generation of long-range steady-state entanglement between N atoms. Through the judicious use of coherent drives and the placement of the atoms in a network of Cavity QED systems, a balance between their unitary and dissipative dynamics can be precisely engineered to stabilize a long-range correlated state of qubits in the steady state. We discuss the general theory behind such a scheme, and present an example of how it can be used to drive a register of N atoms to a generalized W state and how the entanglement can be sustained indefinitely. The achievable steady-state fidelities for entanglement and its scaling with the number of qubits are discussed for presently existing superconducting quantum circuits. While the protocol is primarily discussed for a superconducting circuit architecture, it is ideally realized in any Cavity QED platform that permits controllable delivery of coherent electromagnetic radiation to specified locations.

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arXiv2014

Steady-state entanglement of spatially separated qubits via quantum bath engineering

We propose a scheme for driving a dimer of spatially separated qubits into a maximally entangled non-equilibrium steady state. A photon-mediated retarded interaction between the qubits is realized by coupling them to two tunnel-coupled leaky cavities where each cavity is driven by a coherent microwave tone. The proposed cooling mechanism relies on striking the right balance between the unitary and driven-dissipative dynamics of the qubit subsystem. We map the dimer to an effective transverse-field XY model coupled to a non-equilibrium bath that can be suitably engineered through the choice of drive frequencies and amplitudes. We show that both singlet and triplet states can be obtained with remarkable fidelities. The proposed protocol can be implemented with a superconducting circuit architecture that was recently experimentally realized and paves the way to achieving large-scale entangled systems that are arbitrarily long lived.

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