arXiv subjects

Yu Tong

Publications and source records attributed to Yu Tong.

At least 55 records · Page 3Linked to original sources

arXiv2022

Entanglement area law for 1D gauge theories and bosonic systems

We prove an entanglement area law for a class of 1D quantum systems involving infinite-dimensional local Hilbert spaces. This class of quantum systems include bosonic models such as the Hubbard-Holstein model, and both U(1) and SU(2) lattice gauge theories in one spatial dimension. Our proof relies on new results concerning the robustness of the ground state and spectral gap to the truncation of Hilbert space, applied within the approximate ground state projector (AGSP) framework from previous work. In establishing this area law, we develop a system-size independent bound on the expectation value of local observables for Hamiltonians without translation symmetry, which may be of separate interest. Our result provides theoretical justification for using tensor network methods to study the ground state properties of quantum systems with infinite local degrees of freedom.

quant-ph↗

arXiv2022

Ground state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices

Under suitable assumptions, the algorithms in [Lin, Tong, Quantum 2020] can estimate the ground state energy and prepare the ground state of a quantum Hamiltonian with near-optimal query complexities. However, this is based on a block encoding input model of the Hamiltonian, whose implementation is known to require a large resource overhead. We develop a tool called quantum eigenvalue transformation of unitary matrices with real polynomials (QET-U), which uses a controlled Hamiltonian evolution as the input model, a single ancilla qubit and no multi-qubit control operations, and is thus suitable for early fault-tolerant quantum devices. This leads to a simple quantum algorithm that outperforms all previous algorithms with a comparable circuit structure for estimating the ground state energy. For a class of quantum spin Hamiltonians, we propose a new method that exploits certain anti-commutation relations and further removes the need of implementing the controlled Hamiltonian evolution. Coupled with Trotter based approximation of the Hamiltonian evolution, the resulting algorithm can be very suitable for early fault-tolerant quantum devices. We demonstrate the performance of the algorithm using IBM Qiskit for the transverse field Ising model. If we are further allowed to use multi-qubit Toffoli gates, we can then implement amplitude amplification and a new binary amplitude estimation algorithm, which increases the circuit depth but decreases the total query complexity. The resulting algorithm saturates the near-optimal complexity for ground state preparation and energy estimating using a constant number of ancilla qubits (no more than 3).

quant-ph↗

arXiv2022

Learning many-body Hamiltonians with Heisenberg-limited scaling

Learning a many-body Hamiltonian from its dynamics is a fundamental problem in physics. In this work, we propose the first algorithm to achieve the Heisenberg limit for learning an interacting $N$-qubit local Hamiltonian. After a total evolution time of $\mathcal{O}(ε^{-1})$, the proposed algorithm can efficiently estimate any parameter in the $N$-qubit Hamiltonian to $ε$-error with high probability. The proposed algorithm is robust against state preparation and measurement error, does not require eigenstates or thermal states, and only uses $\mathrm{polylog}(ε^{-1})$ experiments. In contrast, the best previous algorithms, such as recent works using gradient-based optimization or polynomial interpolation, require a total evolution time of $\mathcal{O}(ε^{-2})$ and $\mathcal{O}(ε^{-2})$ experiments. Our algorithm uses ideas from quantum simulation to decouple the unknown $N$-qubit Hamiltonian $H$ into noninteracting patches, and learns $H$ using a quantum-enhanced divide-and-conquer approach. We prove a matching lower bound to establish the asymptotic optimality of our algorithm.

quant-ph↗

arXiv2022

Provably accurate simulation of gauge theories and bosonic systems

Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the truncation error, we develop methods for bounding the rate of growth of local quantum numbers such as the occupation number of a mode at a lattice site, or the electric field at a lattice link. Our approach applies to various models of bosons interacting with spins or fermions, and also to both abelian and non-abelian gauge theories. We show that if states in these models are truncated by imposing an upper limit $Λ$ on each local quantum number, and if the initial state has low local quantum numbers, then an error at most $ε$ can be achieved by choosing $Λ$ to scale polylogarithmically with $ε^{-1}$, an exponential improvement over previous bounds based on energy conservation. For the Hubbard-Holstein model, we numerically compute a bound on $Λ$ that achieves accuracy $ε$, obtaining significantly improved estimates in various parameter regimes. We also establish a criterion for truncating the Hamiltonian with a provable guarantee on the accuracy of time evolution. Building on that result, we formulate quantum algorithms for dynamical simulation of lattice gauge theories and of models with bosonic modes; the gate complexity depends almost linearly on spacetime volume in the former case, and almost quadratically on time in the latter case. We establish a lower bound showing that there are systems involving bosons for which this quadratic scaling with time cannot be improved. By applying our result on the truncation error in time evolution, we also prove that spectrally isolated energy eigenstates can be approximated with accuracy $ε$ by truncating local quantum numbers at $Λ=\textrm{polylog}(ε^{-1})$.

quant-ph↗

arXiv2022

$T_2$-limited dc Quantum Magnetometry via Flux Modulation

High-sensitivity magnetometry is of critical importance to the fields of biomagnetism and geomagnetism. However, the magnetometry for the low-frequency signal detection meets the challenge of sensitivity improvement, due to multiple types of low-frequency noise sources. In particular, for the solid-state spin quantum magnetometry, the sensitivity of low frequency magnetic field has been limited by short $T_2^*$. Here, we demonstrate a $T_2$-limited dc quantum magnetometry based on the nitrogen-vacancy centers in diamond. The magnetometry, combining the flux modulation and the spin-echo protocol, promotes the sensitivity from being limited by $T_2^*$ to $T_2$ of orders of magnitude longer. The sensitivity of the dc magnetometry of 32 $\rm pT/Hz^{1/2}$ has been achieved, overwhelmingly improved by 100 folds over the Ramsey-type method result of 4.6 $\rm nT/Hz^{1/2}$. Further enhancement of the sensitivity have been systematically analyzed, although challenging but plenty of room is achievable. Our result sheds light on realization of room temperature dc quantum magnetomerty with femtotesla-sensitivity in the future.

quant-ph↗

arXiv2022

Heisenberg-limited ground state energy estimation for early fault-tolerant quantum computers

Under suitable assumptions, the quantum phase estimation (QPE) algorithm is able to achieve Heisenberg-limited precision scaling in estimating the ground state energy. However, QPE requires a large number of ancilla qubits and large circuit depth, as well as the ability to perform inverse quantum Fourier transform, making it expensive to implement on an early fault-tolerant quantum computer. We propose an alternative method to estimate the ground state energy of a Hamiltonian with Heisenberg-limited precision scaling, which employs a simple quantum circuit with one ancilla qubit, and a classical post-processing procedure. Besides the ground state energy, our algorithm also produces an approximate cumulative distribution function of the spectral measure, which can be used to compute other spectral properties of the Hamiltonian.

quant-ph↗

arXiv2021

Fast inversion, preconditioned quantum linear system solvers, and fast evaluation of matrix functions

Preconditioning is the most widely used and effective way for treating ill-conditioned linear systems in the context of classical iterative linear system solvers. We introduce a quantum primitive called fast inversion, which can be used as a preconditioner for solving quantum linear systems. The key idea of fast inversion is to directly block-encode a matrix inverse through a quantum circuit implementing the inversion of eigenvalues via classical arithmetics. We demonstrate the application of preconditioned linear system solvers for computing single-particle Green's functions of quantum many-body systems, which are widely used in quantum physics, chemistry, and materials science. We analyze the complexities in three scenarios: the Hubbard model, the quantum many-body Hamiltonian in the planewave-dual basis, and the Schwinger model. We also provide a method for performing Green's function calculation in second quantization within a fixed particle manifold and note that this approach may be valuable for simulation more broadly. Besides solving linear systems, fast inversion also allows us to develop fast algorithms for computing matrix functions, such as the efficient preparation of Gibbs states. We introduce two efficient approaches for such a task, based on the contour integral formulation and the inverse transform respectively.

quant-ph↗

arXiv2021

Collision-induced spin noise

Collision phenomena are ubiquitous and of importance in determining the microscopic structures and intermolecular interactions of atoms and molecules. The existing approaches are mostly based on atomic or molecular scatterings, which are hindered by the inconvenience of using ultra-high vacuum and low temperature systems. Here we demonstrate a new spin-noise spectroscopic approach by measuring optical polarization rotation noise of the probe light, which operates with simple apparatus and ambient conditions. Our approach features tens of gigahertz bandwidth and one part-per-million resolution, outperforming existing spin-noise techniques. Enabled by the new technique, we observe the collision-induced spin noise of alkali atoms, and precisely determine key collision parameters, such as collision diameter, well depth, and dominant interaction type. Our work provides a new tool to study a broad range of collision phenomena under ambient conditions.

quant-ph↗

arXiv2021

News Image Steganography: A Novel Architecture Facilitates the Fake News Identification

A larger portion of fake news quotes untampered images from other sources with ulterior motives rather than conducting image forgery. Such elaborate engraftments keep the inconsistency between images and text reports stealthy, thereby, palm off the spurious for the genuine. This paper proposes an architecture named News Image Steganography (NIS) to reveal the aforementioned inconsistency through image steganography based on GAN. Extractive summarization about a news image is generated based on its source texts, and a learned steganographic algorithm encodes and decodes the summarization of the image in a manner that approaches perceptual invisibility. Once an encoded image is quoted, its source summarization can be decoded and further presented as the ground truth to verify the quoting news. The pairwise encoder and decoder endow images of the capability to carry along their imperceptible summarization. Our NIS reveals the underlying inconsistency, thereby, according to our experiments and investigations, contributes to the identification accuracy of fake news that engrafts untampered images.

cs.CV↗

arXiv2021

Privacy-sensitive Objects Pixelation for Live Video Streaming

With the prevailing of live video streaming, establishing an online pixelation method for privacy-sensitive objects is an urgency. Caused by the inaccurate detection of privacy-sensitive objects, simply migrating the tracking-by-detection structure into the online form will incur problems in target initialization, drifting, and over-pixelation. To cope with the inevitable but impacting detection issue, we propose a novel Privacy-sensitive Objects Pixelation (PsOP) framework for automatic personal privacy filtering during live video streaming. Leveraging pre-trained detection networks, our PsOP is extendable to any potential privacy-sensitive objects pixelation. Employing the embedding networks and the proposed Positioned Incremental Affinity Propagation (PIAP) clustering algorithm as the backbone, our PsOP unifies the pixelation of discriminating and indiscriminating pixelation objects through trajectories generation. In addition to the pixelation accuracy boosting, experiments on the streaming video data we built show that the proposed PsOP can significantly reduce the over-pixelation ratio in privacy-sensitive object pixelation.

cs.CV↗

arXiv2020

Near-optimal ground state preparation

Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We assume that an initial state with non-trivial overlap with the ground state can be efficiently prepared, and the spectral gap between the ground energy and the first excited energy is bounded from below. With these assumptions we design an algorithm that prepares the ground state when an upper bound of the ground energy is known, whose runtime has a logarithmic dependence on the inverse error. When such an upper bound is not known, we propose a hybrid quantum-classical algorithm to estimate the ground energy, where the dependence of the number of queries to the initial state on the desired precision is exponentially improved compared to the current state-of-the-art algorithm proposed in [Ge et al. 2019]. These two algorithms can then be combined to prepare a ground state without knowing an upper bound of the ground energy. We also prove that our algorithms reach the complexity lower bounds by applying it to the unstructured search problem and the quantum approximate counting problem.

quant-ph↗

arXiv2020

Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems

We present a quantum eigenstate filtering algorithm based on quantum signal processing (QSP) and minimax polynomials. The algorithm allows us to efficiently prepare a target eigenstate of a given Hamiltonian, if we have access to an initial state with non-trivial overlap with the target eigenstate and have a reasonable lower bound for the spectral gap. We apply this algorithm to the quantum linear system problem (QLSP), and present two algorithms based on quantum adiabatic computing (AQC) and quantum Zeno effect respectively. Both algorithms prepare the final solution as a pure state, and achieves the near optimal $\mathcal{\widetilde{O}}(dκ\log(1/ε))$ query complexity for a $d$-sparse matrix, where $κ$ is the condition number, and $ε$ is the desired precision. Neither algorithm uses phase estimation or amplitude amplification.

quant-ph↗

arXiv2020

Thickness-Dependence of Exciton-Exciton Annihilation in Halide Perovskite Nanoplatelets

Exciton-exciton annihilation (EEA) and Auger recombination are detrimental processes occurring in semiconductor optoelectronic devices at high carrier densities. Despite constituting one of the main obstacles for realizing lasing in semiconductor nanocrystals (NCs), the dependencies on NC size are not fully understood, especially for those with both weakly and strongly confined dimensions. Here, we use differential transmission spectroscopy to investigate the dependence of EEA on the physical dimensions of thickness-controlled 2D halide perovskite nanoplatelets (NPls). We find the EEA lifetimes to be extremely short on the order of 7-60 ps. Moreover, they are strongly determined by the NPl thickness with a power-law dependence according to τ_2~d^5.3. Additional measurements show that the EEA lifetimes also increase for NPls with larger lateral dimensions. These results show that a precise control of the physical dimensions is critical for deciphering the fundamental laws governing the process especially in 1D and 2D NCs.

cond-mat.mes-hall↗

arXiv2020

Identifying and reducing interfacial losses to enhance color-pure electroluminescence in blue-emitting perovskite nanoplatelet light-emitting diodes

Perovskite nanoplatelets (NPls) hold great promise for light-emitting applications, having achieved high photoluminescence quantum efficiencies (PLQEs) approaching unity in the blue wavelength range, where other metal-halide perovskites have typically been ineffective. However, the external quantum efficiency (EQE) of blue-emitting NPl light-emitting diodes (LEDs) have only reached 0.12%, with typical values well below 0.1%. In this work, we show that the performance of NPl LEDs is primarily hindered by a poor electronic interface between the emitter and hole-injector. Through Kelvin Probe and X-ray photoemission spectroscopy measurements, we reveal that the NPls have remarkably deep ionization potentials (>=6.5 eV), leading to large barriers for hole injection, as well as substantial non-radiative decay at the interface between the emitter and hole-injector. We find that an effective way to reduce these non-radiative losses is by using poly(triarylamine) interlayers. This results in an increase in the EQE of our blue LEDs emitting at 464 nm wavelength to 0.3%. We find that our results can be generalized to thicker sky-blue-emitting NPls, where we increase the EQE to 0.55% using the poly(triarylamine) interlayer. Our work also identifies the key challenges for further efficiency increases.

physics.optics↗

arXiv2020

Boosting tunable blue luminescence of halide perovskite nanoplatelets through post-synthetic surface trap repair

The easily tunable emission of halide perovskite nanocrystals throughout the visible spectrum makes them an extremely promising material for light-emitting applications. Whereas high quantum yields and long-term colloidal stability have already been achieved for nanocrystals emitting in the red and green spectral range, the blue region currently lags behind, with low quantum yields, broad emission profiles and insufficient colloidal stability. In this work, we present a facile synthetic approach for obtaining two-dimensional CsPbBr3 nanoplatelets with monolayer-precise control over their thickness, resulting in sharp photoluminescence and electroluminescence peaks with a tunable emission wavelength between 432 and 497 nm due to quantum confinement. Subsequent addition of a PbBr2-ligand solution repairs surface defects likely stemming from bromide and lead vacancies in a sub-ensemble of weakly emissive nanoplatelets. The overall photoluminescence quantum yield of the blue-emissive colloidal dispersions is consequently enhanced up to a value of 73+-2 %. Transient optical spectroscopy measurements focusing on the excitonic resonances further confirm the proposed repair process. Additionally, the high stability of these nanoplatelets in films and to prolonged UV light exposure is shown.

cond-mat.mes-hall↗

arXiv2020

Enhancing robustness and efficiency of density matrix embedding theory via semidefinite programming and local correlation potential fitting

Density matrix embedding theory (DMET) is a powerful quantum embedding method for solving strongly correlated quantum systems. Theoretically, the performance of a quantum embedding method should be limited by the computational cost of the impurity solver. However, the practical performance of DMET is often hindered by the numerical stability and the computational time of the correlation potential fitting procedure, which is defined on a single-particle level. Of particular difficulty are cases in which the effective single-particle system is gapless or nearly gapless. To alleviate these issues, we develop a semidefinite programming (SDP) based approach that can significantly enhance the robustness of the correlation potential fitting procedure compared to the traditional least squares fitting approach. We also develop a local correlation potential fitting approach, which allows one to identify the correlation potential from each fragment independently in each self-consistent field iteration, avoiding any optimization at the global level. We prove that the self-consistent solutions of DMET using this local correlation potential fitting procedure are equivalent to those of the original DMET with global fitting. We find that our combined approach, called L-DMET, in which we solve local fitting problems via semidefinite programming, can significantly improve both the robustness and the efficiency of DMET calculations. We demonstrate the performance of L-DMET on the 2D Hubbard model and the hydrogen chain. We also demonstrate with theoretical and numerical evidence that the use of a large fragment size can be a fundamental source of numerical instability in the DMET procedure.

physics.comp-ph↗

arXiv2019

Low-rank representation of tensor network operators with long-range pairwise interactions

Tensor network operators, such as the matrix product operator (MPO) and the projected entangled-pair operator (PEPO), can provide efficient representation of certain linear operators in high dimensional spaces. This paper focuses on the efficient representation of tensor network operators with long-range pairwise interactions such as the Coulomb interaction. For MPOs, we find that all existing efficient methods exploit a peculiar "upper-triangular low-rank" (UTLR) property, i.e. the upper-triangular part of the matrix can be well approximated by a low-rank matrix, while the matrix itself can be full-rank. This allows us to convert the problem of finding the efficient MPO representation into a matrix completion problem. We develop a modified incremental singular value decomposition method (ISVD) to solve this ill-conditioned matrix completion problem. This algorithm yields equivalent MPO representation to that developed in [Stoudenmire and White, Phys. Rev. Lett. 2017]. In order to efficiently treat more general tensor network operators, we develop another strategy for compressing tensor network operators based on hierarchical low-rank matrix formats, such as the hierarchical off-diagonal low-rank (HODLR) format, and the $\mathcal{H}$-matrix format. Though the pre-constant in the complexity is larger, the advantage of using the hierarchical low-rank matrix format is that it is applicable to both MPOs and PEPOs. For the Coulomb interaction, the operator can be represented by a linear combination of $\mathcal{O}(\log(N)\log(N/ε))$ MPOs/PEPOs, each with a constant bond dimension, where $N$ is the system size and $ε$ is the accuracy of the low-rank truncation. Neither the modified ISVD nor the hierarchical low-rank algorithm assumes that the long-range interaction takes a translation-invariant form.

physics.comp-ph↗

arXiv2019

Projected Density Matrix Embedding Theory with Applications to the Two-Dimensional Hubbard Model

Density matrix embedding theory (DMET) is a quantum embedding theory for strongly correlated systems. From a computational perspective, one bottleneck in DMET is the optimization of the correlation potential to achieve self-consistency, especially for heterogeneous systems of large size. We propose a new method, called projected density matrix embedding theory (p-DMET), which achieves self-consistency without needing to optimize a correlation potential. We demonstrate the performance of p-DMET on the two-dimensional Hubbard model.

physics.chem-ph↗