Lorenza Viola - Academia.edu (original) (raw)

Papers by Lorenza Viola

Cambridge University Press eBooks, Sep 5, 2013

Physical review, Sep 12, 2018

Classical control noise is ubiquitous in qubit devices, making its accurate spectral characteriza... more 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 contact and differences with respect to the classical formulation. In particular, we introduce and analyze two approaches (adaptive vs. single-setting) to quantum multitaper estimation, and show how they provide a practical means to both identify fine spectral features not otherwise detectable by existing protocols and to obtain reliable prior estimates for use in subsequent parametric estimation, including high-resolution Bayesian techniques. We quantitatively characterize the performance of both singleand multitaper Slepian estimation protocols by numerically reconstructing representative spectral densities, and demonstrate their advantage over dynamical-decoupling noise spectroscopy approaches in reducing bias from spectral leakage as well as in compensating for aliasing effects while maintaining a desired sampling resolution.

Bulletin of the American Physical Society, Mar 6, 2019

arXiv (Cornell University), Jun 23, 2023

Quantum Information and Computation, 2021

We formalize the problem of dissipative quantum encoding, and explore the advantages of using Mar... more We formalize the problem of dissipative quantum encoding, and explore the advantages of using Markovian evolution to prepare a quantum code in the desired logical space, with emphasis on discrete-time dynamics and the possibility of exact finite-time convergence. In particular, we investigate robustness of the encoding dynamics and their ability to tolerate initialization errors, thanks to the existence of non-trivial basins of attraction. As a key application, we show that for stabilizer quantum codes on qubits, a finite-time dissipative encoder may always be constructed, by using at most a number of quantum maps determined by the number of stabilizer generators. We find that even in situations where the target code lacks gauge degrees of freedom in its subsystem form, dissipative encoders afford nontrivial robustness against initialization errors, thus overcoming a limitation of purely unitary encoding procedures. Our general results are illustrated in a number of relevant example...

Physical Review A, 2019

We show how to achieve full spectral characterization of general multiaxis additive noise. Our pu... more We show how to achieve full spectral characterization of general multiaxis additive noise. Our pulsed spectral estimation technique is based on sequence repetition and frequency-comb sampling and is applicable even to models where a large qubit energy-splitting is present (as is typically the case for spin qubits in semiconductors, for example), as long as the noise is stationary and a second-order (Gaussian) approximation to the controlled reduced dynamics is viable. Our new result is crucial to extending the applicability of these protocols, now standard in dephasing-dominated platforms such as silicon-based qubits, to experimental platforms where both T1 and T2 processes are significant, such as superconducting qubits.

Physical Review A, 2019

We consider the problem of characterizing states of a multipartite quantum system from restricted... more We consider the problem of characterizing states of a multipartite quantum system from restricted, quasi-local information, with emphasis on uniquely determined pure states. By leveraging tools from dissipative quantum control theory, we show how the search for states consistent with an assigned list of reduced density matrices may be restricted to a proper subspace, which is determined solely by their supports. The existence of a quasi-local observable which attains its unique minimum over such a subspace further provides a sufficient criterion for a pure state to be uniquely determined by its reduced states. While the condition that a pure state is uniquely determined is necessary for it to arise as a non-degenerate ground state of a quasi-local Hamiltonian, we prove the opposite implication to be false in general, by exhibiting an explicit analytic counterexample. We show how the problem of determining whether a quasi-local parent Hamiltonian admitting a given pure state as its unique ground state is dual, in the sense of semidefinite programming, to the one of determining whether such a state is uniquely determined by the quasi-local information. Failure of this dual program to attain its optimal value is what prevents these two classes of states to coincide.

Physical Review A, 2018

We quantify the impact of spatio-temporally correlated Gaussian quantum noise on frequency estima... more We quantify the impact of spatio-temporally correlated Gaussian quantum noise on frequency estimation by Ramsey interferometry. While correlations in a classical noise environment can be exploited to reduce uncertainty relative to the uncorrelated case, we show that quantum noise environments with frequency asymmetric spectra generally introduce additional sources of uncertainty due to uncontrolled entanglement of the sensing system mediated by the bath. For the representative case of collective noise from bosonic sources, and experimentally relevant collective spin observables, we find that the uncertainty can increase exponentially with the number of probes. As a concrete application, we show that correlated quantum noise due to a lattice vibrational mode can preclude superclassical precision scaling in current amplitude sensing experiments with trapped ions.

arXiv (Cornell University), Dec 18, 2022

We introduce and experimentally demonstrate a quantum sensing protocol to sample and reconstruct ... more We introduce and experimentally demonstrate a quantum sensing protocol to sample and reconstruct the auto-correlation of a noise process using a single-qubit sensor under digital control modulation. This Walsh noise spectroscopy method exploits simple sequences of spin-flip pulses to generate a complete basis of digital filters that directly sample the power spectrum of the target noise in the sequency domain-from which the auto-correlation function in the time domain, as well as the power spectrum in the frequency domain, can be reconstructed using linear transformations. Our method, which can also be seen as an implementation of frame-based noise spectroscopy, solves the fundamental difficulty in sampling continuous functions with digital filters by introducing a transformation that relates the arithmetic and logical time domains. In comparison to standard, frequency-based dynamical-decoupling noise spectroscopy protocols, the accuracy of our method is only limited by the sampling and discretization in the time space and can be easily improved, even under limited evolution time due to decoherence and hardware limitations. Finally, we experimentally reconstruct the auto-correlation function of the effective magnetic field produced by the nuclear-spin bath on the electronic spin of a single nitrogen-vacancy center in diamond, discuss practical limitations of the method, and avenues for further improving the reconstruction accuracy.

Physical review, Aug 29, 2018

arXiv (Cornell University), May 6, 2013

We investigate some basic scenarios in which a given set of bipartite quantum states may consiste... more We investigate some basic scenarios in which a given set of bipartite quantum states may consistently arise as the set of reduced states of a global N-partite quantum state. Intuitively, we say that the multipartite state "joins" the underlying correlations. Determining whether, for a given set of states and a given joining structure, a compatible N-partite quantum state exists is known as the quantum marginal problem. We restrict to bipartite reduced states that belong to the paradigmatic classes of Werner and isotropic states in d dimensions, and focus on two specific versions of the quantum marginal problem which we find to be tractable. The first is Alice-Bob, Alice-Charlie joining, with both pairs being in a Werner or isotropic state. The second is m-n sharability of a Werner state across N subsystems, which may be seen as a variant of the N-representability problem to the case where subsystems are partitioned into two groupings of m and n parties, respectively. By exploiting the symmetry properties that each class of states enjoys, we determine necessary and sufficient conditions for three-party joinability and 1-n sharability for arbitrary d. Our results explicitly show that although entanglement is required for sharing limitations to emerge, correlations beyond entanglement generally suffice to restrict joinability, and not all unentangled states necessarily obey the same limitations. The relationship between joinability and quantum cloning as well as implications for the joinability of arbitrary bipartite states are discussed.

Bulletin of the American Physical Society, Mar 5, 2018

Physical review, Oct 31, 2019

arXiv (Cornell University), May 1, 2023

arXiv (Cornell University), Dec 18, 2022

We focus on two classes of pure states for a finite-dimensional multipartite quantum system: thos... more We focus on two classes of pure states for a finite-dimensional multipartite quantum system: those that can be identified as unique ground states (UGS) of a locally-constrained Hamiltonian, and those that can be obtained as unique, asymptotically stable equilibria of a Markov quantum dynamics under the same quasi-locality constraints (QLS). While there is an equivalence between (strict) subsets of two classes, namely, states that are UGS of frustration-free Hamiltonians and unique equilibria of purely dissipative dynamics, two paradigmatic entangled states, GHZ and W, offer counterexamples to either implication in the general setting. The intuition that every UGS state can be obtained as the exact steady state of a Markovian cooling process is salvaged only if suitable non-local resources are added. We show that stochastic stabilization of the target UGS state can be achieved if we perform continuous measurement of the global Hamiltonian, while controlling the dynamics with a switching, filtering-based quantum feedback strategy.

Cambridge University Press eBooks, Sep 5, 2013

arXiv (Cornell University), Sep 4, 2000

Theoretical techniques are developed for designing nuclear magnetic resonance (NMR) experiments t... more Theoretical techniques are developed for designing nuclear magnetic resonance (NMR) experiments to simulate a variety of adiabatic decoherence (aka T_2 relaxation) processes, using sequences of pulsed field gradients and diffusion periods. To this end an efficient Hadamard product formalism is introduced and used to derive Lindblad master equations from NMR pulse sequences for both collective and independent phase damping on any number of spins. The Kraus operator sum form is shown to be related to the Hadamard form by diagonalization, and explicit Lindblad and Kraus operators given for arbitrary correlations between two spins. Finally, gradient-diffusion methods are outlined for more complex forms of decoherence, including the three-axis collective model.

This project aimed to address the most significant challenge facing the development of large-scal... more This project aimed to address the most significant challenge facing the development of large-scale quantum computers: suppressing hardware error. Through this work we focused on the realization of a robust, high-fidelity Quantum Control Toolkit that is fully transportable between different quantum computing technology platforms. The techniques encapsulated herein were designed to provide qubit robustness to decoherence during memory (dynamical decoupling-DD), and increase the fidelity of qubit operations undertaken in the presence of random

arXiv (Cornell University), Aug 19, 1999

Cambridge University Press eBooks, Sep 5, 2013

Physical review, Sep 12, 2018

Classical control noise is ubiquitous in qubit devices, making its accurate spectral characteriza... more 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 contact and differences with respect to the classical formulation. In particular, we introduce and analyze two approaches (adaptive vs. single-setting) to quantum multitaper estimation, and show how they provide a practical means to both identify fine spectral features not otherwise detectable by existing protocols and to obtain reliable prior estimates for use in subsequent parametric estimation, including high-resolution Bayesian techniques. We quantitatively characterize the performance of both singleand multitaper Slepian estimation protocols by numerically reconstructing representative spectral densities, and demonstrate their advantage over dynamical-decoupling noise spectroscopy approaches in reducing bias from spectral leakage as well as in compensating for aliasing effects while maintaining a desired sampling resolution.

Bulletin of the American Physical Society, Mar 6, 2019

arXiv (Cornell University), Jun 23, 2023

Quantum Information and Computation, 2021

We formalize the problem of dissipative quantum encoding, and explore the advantages of using Mar... more We formalize the problem of dissipative quantum encoding, and explore the advantages of using Markovian evolution to prepare a quantum code in the desired logical space, with emphasis on discrete-time dynamics and the possibility of exact finite-time convergence. In particular, we investigate robustness of the encoding dynamics and their ability to tolerate initialization errors, thanks to the existence of non-trivial basins of attraction. As a key application, we show that for stabilizer quantum codes on qubits, a finite-time dissipative encoder may always be constructed, by using at most a number of quantum maps determined by the number of stabilizer generators. We find that even in situations where the target code lacks gauge degrees of freedom in its subsystem form, dissipative encoders afford nontrivial robustness against initialization errors, thus overcoming a limitation of purely unitary encoding procedures. Our general results are illustrated in a number of relevant example...

Physical Review A, 2019

We show how to achieve full spectral characterization of general multiaxis additive noise. Our pu... more We show how to achieve full spectral characterization of general multiaxis additive noise. Our pulsed spectral estimation technique is based on sequence repetition and frequency-comb sampling and is applicable even to models where a large qubit energy-splitting is present (as is typically the case for spin qubits in semiconductors, for example), as long as the noise is stationary and a second-order (Gaussian) approximation to the controlled reduced dynamics is viable. Our new result is crucial to extending the applicability of these protocols, now standard in dephasing-dominated platforms such as silicon-based qubits, to experimental platforms where both T1 and T2 processes are significant, such as superconducting qubits.

Physical Review A, 2019

We consider the problem of characterizing states of a multipartite quantum system from restricted... more We consider the problem of characterizing states of a multipartite quantum system from restricted, quasi-local information, with emphasis on uniquely determined pure states. By leveraging tools from dissipative quantum control theory, we show how the search for states consistent with an assigned list of reduced density matrices may be restricted to a proper subspace, which is determined solely by their supports. The existence of a quasi-local observable which attains its unique minimum over such a subspace further provides a sufficient criterion for a pure state to be uniquely determined by its reduced states. While the condition that a pure state is uniquely determined is necessary for it to arise as a non-degenerate ground state of a quasi-local Hamiltonian, we prove the opposite implication to be false in general, by exhibiting an explicit analytic counterexample. We show how the problem of determining whether a quasi-local parent Hamiltonian admitting a given pure state as its unique ground state is dual, in the sense of semidefinite programming, to the one of determining whether such a state is uniquely determined by the quasi-local information. Failure of this dual program to attain its optimal value is what prevents these two classes of states to coincide.

Physical Review A, 2018

We quantify the impact of spatio-temporally correlated Gaussian quantum noise on frequency estima... more We quantify the impact of spatio-temporally correlated Gaussian quantum noise on frequency estimation by Ramsey interferometry. While correlations in a classical noise environment can be exploited to reduce uncertainty relative to the uncorrelated case, we show that quantum noise environments with frequency asymmetric spectra generally introduce additional sources of uncertainty due to uncontrolled entanglement of the sensing system mediated by the bath. For the representative case of collective noise from bosonic sources, and experimentally relevant collective spin observables, we find that the uncertainty can increase exponentially with the number of probes. As a concrete application, we show that correlated quantum noise due to a lattice vibrational mode can preclude superclassical precision scaling in current amplitude sensing experiments with trapped ions.

arXiv (Cornell University), Dec 18, 2022

We introduce and experimentally demonstrate a quantum sensing protocol to sample and reconstruct ... more We introduce and experimentally demonstrate a quantum sensing protocol to sample and reconstruct the auto-correlation of a noise process using a single-qubit sensor under digital control modulation. This Walsh noise spectroscopy method exploits simple sequences of spin-flip pulses to generate a complete basis of digital filters that directly sample the power spectrum of the target noise in the sequency domain-from which the auto-correlation function in the time domain, as well as the power spectrum in the frequency domain, can be reconstructed using linear transformations. Our method, which can also be seen as an implementation of frame-based noise spectroscopy, solves the fundamental difficulty in sampling continuous functions with digital filters by introducing a transformation that relates the arithmetic and logical time domains. In comparison to standard, frequency-based dynamical-decoupling noise spectroscopy protocols, the accuracy of our method is only limited by the sampling and discretization in the time space and can be easily improved, even under limited evolution time due to decoherence and hardware limitations. Finally, we experimentally reconstruct the auto-correlation function of the effective magnetic field produced by the nuclear-spin bath on the electronic spin of a single nitrogen-vacancy center in diamond, discuss practical limitations of the method, and avenues for further improving the reconstruction accuracy.

Physical review, Aug 29, 2018

arXiv (Cornell University), May 6, 2013

We investigate some basic scenarios in which a given set of bipartite quantum states may consiste... more We investigate some basic scenarios in which a given set of bipartite quantum states may consistently arise as the set of reduced states of a global N-partite quantum state. Intuitively, we say that the multipartite state "joins" the underlying correlations. Determining whether, for a given set of states and a given joining structure, a compatible N-partite quantum state exists is known as the quantum marginal problem. We restrict to bipartite reduced states that belong to the paradigmatic classes of Werner and isotropic states in d dimensions, and focus on two specific versions of the quantum marginal problem which we find to be tractable. The first is Alice-Bob, Alice-Charlie joining, with both pairs being in a Werner or isotropic state. The second is m-n sharability of a Werner state across N subsystems, which may be seen as a variant of the N-representability problem to the case where subsystems are partitioned into two groupings of m and n parties, respectively. By exploiting the symmetry properties that each class of states enjoys, we determine necessary and sufficient conditions for three-party joinability and 1-n sharability for arbitrary d. Our results explicitly show that although entanglement is required for sharing limitations to emerge, correlations beyond entanglement generally suffice to restrict joinability, and not all unentangled states necessarily obey the same limitations. The relationship between joinability and quantum cloning as well as implications for the joinability of arbitrary bipartite states are discussed.

Bulletin of the American Physical Society, Mar 5, 2018

Physical review, Oct 31, 2019

arXiv (Cornell University), May 1, 2023

arXiv (Cornell University), Dec 18, 2022

We focus on two classes of pure states for a finite-dimensional multipartite quantum system: thos... more We focus on two classes of pure states for a finite-dimensional multipartite quantum system: those that can be identified as unique ground states (UGS) of a locally-constrained Hamiltonian, and those that can be obtained as unique, asymptotically stable equilibria of a Markov quantum dynamics under the same quasi-locality constraints (QLS). While there is an equivalence between (strict) subsets of two classes, namely, states that are UGS of frustration-free Hamiltonians and unique equilibria of purely dissipative dynamics, two paradigmatic entangled states, GHZ and W, offer counterexamples to either implication in the general setting. The intuition that every UGS state can be obtained as the exact steady state of a Markovian cooling process is salvaged only if suitable non-local resources are added. We show that stochastic stabilization of the target UGS state can be achieved if we perform continuous measurement of the global Hamiltonian, while controlling the dynamics with a switching, filtering-based quantum feedback strategy.

Cambridge University Press eBooks, Sep 5, 2013

arXiv (Cornell University), Sep 4, 2000

Theoretical techniques are developed for designing nuclear magnetic resonance (NMR) experiments t... more Theoretical techniques are developed for designing nuclear magnetic resonance (NMR) experiments to simulate a variety of adiabatic decoherence (aka T_2 relaxation) processes, using sequences of pulsed field gradients and diffusion periods. To this end an efficient Hadamard product formalism is introduced and used to derive Lindblad master equations from NMR pulse sequences for both collective and independent phase damping on any number of spins. The Kraus operator sum form is shown to be related to the Hadamard form by diagonalization, and explicit Lindblad and Kraus operators given for arbitrary correlations between two spins. Finally, gradient-diffusion methods are outlined for more complex forms of decoherence, including the three-axis collective model.

This project aimed to address the most significant challenge facing the development of large-scal... more This project aimed to address the most significant challenge facing the development of large-scale quantum computers: suppressing hardware error. Through this work we focused on the realization of a robust, high-fidelity Quantum Control Toolkit that is fully transportable between different quantum computing technology platforms. The techniques encapsulated herein were designed to provide qubit robustness to decoherence during memory (dynamical decoupling-DD), and increase the fidelity of qubit operations undertaken in the presence of random

arXiv (Cornell University), Aug 19, 1999