We introduce multi-pulse quantum noise spectroscopy protocols for spectral estimation of the noise affecting multiple qubits coupled to Gaussian dephasing environments including both classical and quantum sources. Our protocols are capable of reconstructing all the noise auto- and cross-correlation spectra entering the multiqubit dynamics. We argue that this capability is crucial not only for metrological purposes, as it provides access to the asymmetric spectra associated with non-classical environments, but ultimately for achieving quantum fault-tolerance, as it enables the characterization of bath correlation functions. Our result relies on (i) an exact analytic solution for the reduced multiqubit dynamics that holds in the presence of an arbitrary Gaussian environment and dephasing-preserving control; (ii) the use of specific timing symmetries in the control, which allow for a frequency comb to be engineered for all filter functions of interest, and for the spectra to be related to experimentally accessible qubit observables. We show that quantum spectra have distinctive dynamical signatures, which we explore in two paradigmatic open-system models describing spin and charge qubits coupled to bosonic environments. Complete multiqubit noise spectroscopy is demonstrated numerically in a realistic setting consisting of two-exciton qubits coupled to a phonon bath. The estimated spectra allow us to accurately predict the exciton dynamics as well as extract the temperature and spectral density of the quantum environment.
Imagine that you have several sets of two coupled qubits, but you do not know the parameters of their Hamitonians. How to determine these without resorting to the usual spectroscopy approach to the problem? Based on numerical modeling, we show that all the parameters of a system of two coupled qubits can be determined by applying to it an external classical noise and analysing the Fourier spectrum of the elements of the system's density matrix. In particular, the interlevel spacings as well as the strength and sign of qubit-qubit coupling can be determined this way.
We demonstrate the capability of continuous variable Gaussian states to communicate multipartite quantum information. A quantum teamwork protocol is presented according to which an arbitrary possibly entangled multimode state can be faithfully teleported between two teams each comprising many cooperative users. We prove that N-mode Gaussian weighted graph states exist for arbitrary N, that enable unconditional quantum teamwork implementations for any arrangement of the teams. These perfect continuous variable maximally multipartite entangled resources are typical among pure Gaussian states and…
We show that two capacitively-coupled Josephson junctions, in the quantum limit, form a simple coupled qubit system with effective coupling controlled by the junction bias currents. We compute numerically the energy levels and wave functions for the system, and show how these may be tuned to make optimal qubits. The dependence of the energy levels on the parameters can be measured spectroscopically, providing an important experimental test for the presence of entangled multiqubit states in Josephson-junction based circuits.
Characterizing and understanding the environment affecting quantum systems is critical to elucidate its physical properties and engineer better quantum devices. We develop an approach to reduce the quantum environment causing single-qubit dephasing to a simple yet predictive noise model. Our approach, inspired by quantum noise spectroscopy, is to define a "self-consistent" classical noise spectrum, that is, compatible with all observed decoherence under various qubit dynamics. We demonstrate the power and limits of our approach by characterizing, with nanoscale spatial resolution, the noise ex…
We report on the collapse and revival of Ramsey fringe visibility when a spatially dependent phase is imprinted in the coherences of a trapped ensemble of two-level atoms. The phase is imprinted via the light shift from a Gaussian laser beam which couples the dynamics of internal and external degrees of freedom for the atoms in an echo spectroscopy sequence. The observed revivals are directly linked to the oscillatory motion of atoms in the trap. An understanding of the effect is important for quantum state engineering of trapped atoms.
We introduce open-loop quantum control protocols for characterizing the spectral properties of non-Gaussian noise, applicable to both classical and quantum dephasing environments. The basic idea is to engineer a multi-dimensional frequency comb via repetition of suitably designed pulse sequences, through which the desired high-order noise spectra may be related to observable properties of the qubit probe. We prove that access to a high time resolution is key to achieve spectral reconstruction over an extended bandwidth, overcoming limitations of existing schemes. Non-Gaussian spectroscopy is d…
Accurate characterization of the noise influencing a quantum system of interest has far-reaching implications across quantum science, ranging from microscopic modeling of decoherence dynamics to noise-optimized quantum control. While the assumption that noise obeys Gaussian statistics is commonly employed, noise is generically non-Gaussian in nature. In particular, the Gaussian approximation breaks down whenever a qubit is strongly coupled to discrete noise sources or has a non-linear response to the environmental degrees of freedom. Thus, in order to both scrutinize the applicability of the G…
We propose simple protocols for performing quantum noise spectroscopy based on the method of transfer tensor maps (TTM), [Phys. Rev. Lett. 112, 110401 (2014)]. The TTM approach is a systematic way to deduce the memory kernel of a time-nonlocal quantum master equation via quantum process tomography. With access to the memory kernel it is possible to (1) assess the non-Markovianity of a quantum process, (2) reconstruct the noise spectral density beyond pure dephasing models, and (3) investigate collective decoherence in multiqubit devices. We illustrate the usefulness of TTM spectroscopy on the …
Characterizing and understanding noise affecting quantum states has immense benefits in spectroscopy as well as in realizing quantum devices. Transverse relaxation times under a set of dynamical decoupling (DD) sequences with varying interpulse delays were earlier used for obtaining the noise spectral densities of single-qubit coherences. In this work, using a pair of homonuclear spins and NMR techniques, we experimentally characterize noise in certain decoherence-free subspaces. We also explore the noise of similar states in a heteronuclear spin pair. Further, using a 10-qubit system, we inve…
The fundamental assumption of dynamical decoupling based noise spectroscopy is that the coherence decay rate of qubit (or qubits) driven with a sequence of many pulses, is well approximated by the environmental noise spectrum spanned on frequency comb defined by the sequence. Here we investigate the precise conditions under which this commonly used spectroscopic approach is quantitatively correct. To this end we focus on two representative examples of spectral densities: the long-tailed Lorentzian, and finite-ranged Gaussian---both expected to be encountered when using the qubit for nano-scale…
A qubit subjected to pure dephasing due to classical Gaussian noise can be turned into a spectrometer of this noise by utilizing its readout under properly chosen dynamical decoupling (DD) sequences to reconstruct the power spectral density of the noise. We review the theory behind this DD-based noise spectroscopy technique, paying special attention to issues that arise when the environmental noise is non-Gaussian and/or it has truly quantum properties. While we focus on the theoretical basis of the method, we connect the discussed concepts with specific experiments and provide an overview of …
Classical control noise is ubiquitous in qubit devices, making its accurate spectral characterization essential for designing optimized error suppression strategies at the physical level. Here, we focus on multiplicative Gaussian amplitude control noise on a driven qubit sensor and show that sensing protocols using optimally band-limited Slepian modulation offer substantial benefit in realistic scenarios. Special emphasis is given to laying out the theoretical framework necessary for extending non-parametric multitaper spectral estimation to the quantum setting by highlighting key points of co…
Understanding the physical origin of noise affecting quantum systems is important for nearly every quantum application. Quantum noise spectroscopy has been employed in various quantum systems, such as superconducting qubits, NV centers and trapped ions. Traditional spectroscopy methods are usually efficient in measuring noise spectra with mostly monotonically decaying contributions. However, there are important scenarios in which the noise spectrum is broadband and non-monotonous, thus posing a challenge to existing noise spectroscopy schemes. Here, we compare several methods for noise spectro…
Stochastic treatments of magnetic resonance spectroscopy and optical spectroscopy require evaluations of functions like <exp(i int_0^t Q(s)ds)>, where t is time, Q(s) is the value of a stochastic process at time s, and the angular brackets denote ensemble averaging. This paper gives an exact evaluation of these functions for the case where Q is a continuous-time random walk process. The continuous time random walk describes an environment that undergoes slow, step-like changes in time. It also has a well-defined Gaussian limit, and so allows for non-Gaussian and Gaussian stochastic dynamics to…
Direct characterization of classical dephasing noise for a qubit
State Key Laboratory of Semiconductor Physics and Chip Technologies, Institute of Semiconductors, Chinese Academy of Sciences（中国科学院半导体研究所）；Center of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences（中国科学院大学材料科学与光电技术研究中心）；Department of Applied Physics, University of Science and Technology Beijing（北京科技大学应用物理系）
Molecules are the most demanding quantum systems to be simulated by quantum computers because of their complexity and the emergent role of quantum nature. The recent theoretical proposal of Huh et al. (Nature Photon., 9, 615 (2015)) showed that a multi-photon network with a Gaussian input state can simulate a molecular spectroscopic process. Here, we report the first experimental demonstration of molecular vibrational spectroscopy of SO$_{2}$ with a trapped-ion system. In our realization, the molecular scattering operation is decomposed to a series of elementary quantum optical operations, whi…
We show theoretically how a correlation of multiple measurements on a qubit undergoing pure dephasing can be expressed as environmental noise filtering. The measurement of such correlations can be used for environmental noise spectroscopy, and the family of noise filters achievable in such a setting is broader than the one achievable with a standard approach, in which dynamical decoupling sequences are used. We illustrate the advantages of this approach by considering the case of noise spectrum with sharp features at very low frequencies. We also show how appropriately chosen correlations of a…
I present a theory of environmental noise spectroscopy via dynamical decoupling of a qubit at an optimal working point. Considering a sequence of $n$ pulses and pure dephasing due to quadratic coupling to Gaussian distributed noise $ξ(t)$, I use the linked-cluster (cumulant) expansion to calculate the coherence decay. Solutions allowing for reconstruction of spectral density of noise are given. For noise with correlation time shorter than the timescale on which coherence decays, the noise filtered by the dynamical decoupling procedure can be treated as effectively Gaussian at large $n$, and we…
Phase-sensitive optical parametric amplification of squeezed states helps to overcome detection loss and noise and thus increase the robustness of sub-shot-noise sensing. Because such techniques, e.g., imaging and spectroscopy, operate with multimode light, multimode amplification is required. Here we find the optimal methods for multimode phase-sensitive amplification and verify them in an experiment where a pumped second-order nonlinear crystal is seeded with a Gaussian coherent beam. Phase-sensitive amplification is obtained by tightly focusing the seed into the crystal, rather than seeding…
We study decoherence due to random telegraph and 1/f noise in Josephson qubits. We illustrate differences between gaussian and non gaussian effects at different working points and for different protocols. Features of the intrinsically non-gaussian and non-Markovian low-frequency noise may explain the rich physics observed in the spectroscopy and the dynamics of charge based devices.
We discuss how standard $T_2$-based quantum sensing and noise spectroscopy protocols often give rise to an inadvertent quench of the system or environment being probed: there is an effective sudden change in the environmental Hamiltonian at the start of the sensing protocol. These quenches are extremely sensitive to the initial environmental state, and lead to observable changes in the sensor qubit evolution. We show how these new features can be used to directly access environmental response properties. This enables methods for direct measurement of bath temperature, and methods to diagnose n…
Having accurate tools to describe non-classical, non-Gaussian environmental fluctuations is crucial for designing effective quantum control protocols and understanding the physics of underlying quantum dissipative environments. We show how the Keldysh approach to quantum noise characterization can be usefully employed to characterize frequency-dependent noise, focusing on the quantum bispectrum (i.e., frequency-resolved third cumulant). Using the paradigmatic example of photon shot noise fluctuations in a driven bosonic mode, we show that the quantum bispectrum can be a powerful tool for revea…
Boson sampling (BS) is a multimode linear optical problem that is expected to be intractable on classical computers. It was recently suggested that molecular vibronic spectroscopy (MVS) is computationally as complex as BS. In this review, we discuss the correspondence relation between BS and MVS and briefly introduce the experimental demonstrations of the molecular spectroscopic process using quantum devices. The similarity of the two theories results in another BS setup, which is called "vibronic BS". The hierarchical structure of vibronic BS, which includes the original BS and other Gaussian…
A common task is the determination of system parameters from spectroscopy, where one compares the experimental spectrum with calculated spectra, that depend on the desired parameters. Here we discuss an approach based on a machine learning technique, where the parameters for the numerical calculations are chosen from Gaussian Process Regression (GPR). This approach does not only quickly converge to an optimal parameter set, but in addition provides information about the complete parameter space, which allows for example to identify extended parameter regions where numerical spectra are consist…
The effects of a collection of classical two-level charge fluctuators on the coherence of a dynamically-decoupled qubit are studied. Distinct dynamics are found at different qubit working positions. Exact analytical formulae are derived at pure dephasing and approximate solutions are found at the general working position, for weakly- and strongly-coupled fluctuators. Analysis of these solutions, combined with numerical simulations of the multiple random telegraph processes, reveal the scaling of the noise with the number of fluctuators and the number of control pulses, as well as dependence on…
Nonlinear spectroscopy is widely used for studying physical systems. Conventional nonlinear optical spectroscopy and magnetic resonance spectroscopy, which use classical probes such as electromagnetic waves, can only access certain types of correlations in a quantum system. The idea of quantum nonlinear spectroscopy was recently proposed to use quantum probes such as entangled photons to achieve sensitivities and resolutions beyond the classical limits. It is shown that quantum sensing can extract arbitrary types and orders of correlations in a quantum system by first quantum-entangling a sens…
Molecular vibroic spectroscopy, where the transitions involve non-trivial Bosonic correlation due to the Duschinsky Rotation, is strongly believed to be in a similar complexity class as Boson Sampling. At finite temperature, the problem is represented as a Boson Sampling experiment with correlated Gaussian input states. This molecular problem with temperature effect is intimately related to the various versions of Boson Sampling sharing the similar computational complexity. Here we provide a full description to this relation in the context of Gaussian Boson Sampling. We find a hierarchical str…
