arXiv subjects

Minh C. Tran

Publications and source records attributed to Minh C. Tran.

33 records · Page 2Linked to original sources

arXiv2022

Hierarchy of linear light cones with long-range interactions

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently separated spacetime points approximately commute -- given a many-body state, $\mathcal{O}_x(t) \mathcal{O}_y |ψ\rangle \approx \mathcal{O}_y\mathcal{O}_x(t) |ψ\rangle$ with arbitrarily small errors -- so long as $|x-y|\gtrsim vt$, where $v$ is finite. Yet most non-relativistic physical systems realized in nature have long-range interactions: two degrees of freedom separated by a distance $r$ interact with potential energy $V(r) \propto 1/r^α$. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: at the same $α$, some quantum information processing tasks are constrained by a linear light cone while others are not. In one spatial dimension, this linear light cone exists for every many-body state when $α>3$ (Lieb-Robinson light cone); for a typical state chosen uniformly at random from the Hilbert space when $α>\frac{5}{2}$ (Frobenius light cone); for every state of a non-interacting system when $α>2$ (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones -- and their tightness -- also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that universal quantum state transfer, as well as many-body quantum chaos, are bounded by the Frobenius light cone, and therefore are poorly constrained by all Lieb-Robinson bounds.

quant-ph↗

arXiv2022

Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions

Tracking the dynamics of physical systems in real time is a prime application of digital quantum computers. Using a trapped-ion system with up to six qubits, we simulate the real-time dynamics of a lattice gauge theory in 1+1 dimensions, i.e., the lattice Schwinger model, and demonstrate non-perturbative effects such as pair creation for times much longer than previously accessible. We study the gate requirement of two formulations of the model using the Suzuki-Trotter product formula, as well as the trade-off between errors from the ordering of the Hamiltonian terms, the Trotter step size, and experimental imperfections. To mitigate experimental errors, a recent symmetry-protection protocol for suppressing coherent errors and a symmetry-inspired post-selection scheme are applied. This work demonstrates the integrated theoretical, algorithmic, and experimental approach that is essential for efficient simulation of lattice gauge theories and other complex physical systems.

quant-ph↗

arXiv2021

Clustering of steady-state correlations in open systems with long-range interactions

Lieb-Robinson bounds are powerful analytical tools for constraining the dynamic and static properties of non-relativistic quantum systems. Recently, a complete picture for closed systems that evolve unitarily in time has been achieved. In experimental systems, however, interactions with the environment cannot generally be ignored, and the extension of Lieb-Robinson bounds to dissipative systems which evolve non-unitarily in time remains an open challenge. In this work, we prove two Lieb-Robinson bounds that constrain the dynamics of open quantum systems with long-range interactions that decay as a power-law in the distance between particles. Using a combination of these Lieb-Robinson bounds and mixing bounds which arise from "reversibility" -- naturally satisfied for thermal environments -- we prove the clustering of correlations in the steady states of open quantum systems with long-range interactions. Our work provides an initial step towards constraining the steady-state entanglement structure for a broad class of experimental platforms, and we highlight several open directions regarding the application of Lieb-Robinson bounds to dissipative systems.

quant-ph↗

arXiv2021

XSleepNet: Multi-View Sequential Model for Automatic Sleep Staging

Automating sleep staging is vital to scale up sleep assessment and diagnosis to serve millions experiencing sleep deprivation and disorders and enable longitudinal sleep monitoring in home environments. Learning from raw polysomnography signals and their derived time-frequency image representations has been prevalent. However, learning from multi-view inputs (e.g., both the raw signals and the time-frequency images) for sleep staging is difficult and not well understood. This work proposes a sequence-to-sequence sleep staging model, XSleepNet, that is capable of learning a joint representation from both raw signals and time-frequency images. Since different views may generalize or overfit at different rates, the proposed network is trained such that the learning pace on each view is adapted based on their generalization/overfitting behavior. In simple terms, the learning on a particular view is speeded up when it is generalizing well and slowed down when it is overfitting. View-specific generalization/overfitting measures are computed on-the-fly during the training course and used to derive weights to blend the gradients from different views. As a result, the network is able to retain the representation power of different views in the joint features which represent the underlying distribution better than those learned by each individual view alone. Furthermore, the XSleepNet architecture is principally designed to gain robustness to the amount of training data and to increase the complementarity between the input views. Experimental results on five databases of different sizes show that XSleepNet consistently outperforms the single-view baselines and the multi-view baseline with a simple fusion strategy. Finally, XSleepNet also outperforms prior sleep staging methods and improves previous state-of-the-art results on the experimental databases.

eess.SP↗

arXiv2021

The Lieb-Robinson light cone for power-law interactions

The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as $1/r^α$ at distance $r$? Here, we present a definitive answer to this question for all exponents $α>2d$ and all spatial dimensions $d$. Schematically, information takes time at least $r^{\min\{1, α-2d\}}$ to propagate a distance~$r$. As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.

quant-ph↗

arXiv2021

Faster Digital Quantum Simulation by Symmetry Protection

Simulating the dynamics of quantum systems is an important application of quantum computers and has seen a variety of implementations on current hardware. We show that by introducing quantum gates implementing unitary transformations generated by the symmetries of the system, one can induce destructive interference between the errors from different steps of the simulation, effectively giving faster quantum simulation by symmetry protection. We derive rigorous bounds on the error of a symmetry-protected simulation algorithm and identify conditions for optimal symmetry protection. In particular, when the symmetry transformations are chosen as powers of a unitary, the error of the algorithm is approximately projected to the so-called quantum Zeno subspaces. We prove a bound on this approximation error, exponentially improving a recent result of Burgarth, Facchi, Gramegna, and Pascazio. We apply the symmetry protection technique to the simulations of the XXZ Heisenberg interactions with local disorder and the Schwinger model in quantum field theory. For both systems, the technique can reduce the simulation error by several orders of magnitude over the unprotected simulation. Finally, we provide numerical evidence suggesting that the technique can also protect simulation against other types of coherent, temporally correlated errors, such as the $1/f$ noise commonly found in solid-state experiments.

quant-ph↗

arXiv2021

A Theory of Trotter Error

The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of prior approaches based on truncating the Baker-Campbell-Hausdorff expansion. Our analysis directly exploits the commutativity of operator summands, producing tighter error bounds for both real- and imaginary-time evolutions. Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds in general. We give a host of improved algorithms for digital quantum simulation and quantum Monte Carlo methods, including simulations of second-quantized plane-wave electronic structure, $k$-local Hamiltonians, rapidly decaying power-law interactions, clustered Hamiltonians, the transverse field Ising model, and quantum ferromagnets, nearly matching or even outperforming the best previous results. We obtain further speedups using the fact that product formulas can preserve the locality of the simulated system. Specifically, we show that local observables can be simulated with complexity independent of the system size for power-law interacting systems, which implies a Lieb-Robinson bound as a byproduct. Our analysis reproduces known tight bounds for first- and second-order formulas. Our higher-order bound overestimates the complexity of simulating a one-dimensional Heisenberg model with an even-odd ordering of terms by only a factor of $5$, and is close to tight for power-law interactions and other orderings of terms. This suggests that our theory can accurately characterize Trotter error in terms of both asymptotic scaling and constant prefactor.

quant-ph↗

arXiv2021

Optimal State Transfer and Entanglement Generation in Power-law Interacting Systems

We present an optimal protocol for encoding an unknown qubit state into a multiqubit Greenberger-Horne-Zeilinger-like state and, consequently, transferring quantum information in large systems exhibiting power-law ($1/r^α$) interactions. For all power-law exponents $α$ between $d$ and $2d+1$, where $d$ is the dimension of the system, the protocol yields a polynomial speedup for $α>2d$ and a superpolynomial speedup for $α\leq 2d$, compared to the state of the art. For all $α>d$, the protocol saturates the Lieb-Robinson bounds (up to subpolynomial corrections), thereby establishing the optimality of the protocol and the tightness of the bounds in this regime. The protocol has a wide range of applications, including in quantum sensing, quantum computing, and preparation of topologically ordered states. In addition, the protocol provides a lower bound on the gate count in digital simulations of power-law interacting systems.

quant-ph↗

arXiv2020

A tidal lung simulation to quantify lung heterogeneity with the Inspired Sinewave Test

We have created a lung simulation to quantify lung heterogeneity from the results of the inspired sinewave test (IST). The IST is a lung function test that is non-invasive, non-ionising and does not require patients' cooperation. A tidal lung simulation is developed to assess this test and also a method is proposed to calculate lung heterogeneity from IST results. A sensitivity analysis based on the Morris method and linear regression were applied to verify and to validate the simulation. Additionally, simulated emphysema and pulmonary embolism conditions were created using the simulation to assess the ability of the IST to identify these conditions. Experimental data from five pigs (pre-injured vs injured) were used for validation. This paper contributes to the development of the IST. Firstly, our sensitivity analysis reveals that the IST is highly accurate with an underestimation of about 5% of the simulated values. Sensitivity analysis suggested that both instability in tidal volume and extreme expiratory flow coefficients during the test cause random errors in the IST results. Secondly, the ratios of IST results obtained at two tracer gas oscillation frequencies can identify lung heterogeneity (ELV60/ELV180 and Qp60/Qp180). There was dissimilarity between simulated emphysema and pulmonary embolism (p < 0:0001). In the animal model, the control group had ELV60/ELV180 = 0.58 compared with 0.39 in injured animals (p < 0.0001).

physics.med-ph↗

arXiv2020

Complexity phase diagram for interacting and long-range bosonic Hamiltonians

We classify phases of a bosonic lattice model based on the computational complexity of classically simulating the system. We show that the system transitions from being classically simulable to classically hard to simulate as it evolves in time, extending previous results to include on-site number-conserving interactions and long-range hopping. Specifically, we construct a "complexity phase diagram" with "easy" and "hard" phases, and derive analytic bounds on the location of the phase boundary with respect to the evolution time and the degree of locality. We find that the location of the phase transition is intimately related to upper bounds on the spread of quantum correlations and protocols to transfer quantum information. Remarkably, although the location of the transition point is unchanged by on-site interactions, the nature of the transition point changes dramatically. Specifically, we find that there are two kinds of transitions, sharp and coarse, broadly corresponding to interacting and noninteracting bosons, respectively. Our work motivates future studies of complexity in many-body systems and its interplay with the associated physical phenomena.

quant-ph↗

arXiv2019

Destructive Error Interference in Product-Formula Lattice Simulation

Quantum computers can efficiently simulate the dynamics of quantum systems. In this paper, we study the cost of digitally simulating the dynamics of several physically relevant systems using the first-order product formula algorithm. We show that the errors from different Trotterization steps in the algorithm can interfere destructively, yielding a much smaller error than previously estimated. In particular, we prove that the total error in simulating a nearest-neighbor interacting system of $n$ sites for time $t$ using the first-order product formula with $r$ time slices is $O({nt}/{r}+{nt^3}/{r^2})$ when $nt^2/r$ is less than a small constant. Given an error tolerance $ε$, the error bound yields an estimate of $\max\{O({n^2t}/ε),O({n^2 t^{3/2}}/{ε^{1/2}})\}$ for the total gate count of the simulation. The estimate is tighter than previous bounds and matches the empirical performance observed in Childs et al. [PNAS 115, 9456-9461 (2018)]. We also provide numerical evidence for potential improvements and conjecture an even tighter estimate for the gate count.

quant-ph↗

arXiv2019

Locality and Heating in Periodically Driven, Power-law Interacting Systems

We study the heating time in periodically driven $D$-dimensional systems with interactions that decay with the distance $r$ as a power-law $1/r^α$. Using linear response theory, we show that the heating time is exponentially long as a function of the drive frequency for $α>D$. For systems that may not obey linear response theory, we use a more general Magnus-like expansion to show the existence of quasi-conserved observables, which imply exponentially long heating time, for $α>2D$. We also generalize a number of recent state-of-the-art Lieb-Robinson bounds for power-law systems from two-body interactions to $k$-body interactions and thereby obtain a longer heating time than previously established in the literature. Additionally, we conjecture that the gap between the results from the linear response theory and the Magnus-like expansion does not have physical implications, but is, rather, due to the lack of tight Lieb-Robinson bounds for power-law interactions. We show that the gap vanishes in the presence of a hypothetical, tight bound.

quant-ph↗

arXiv2019

Locality and digital quantum simulation of power-law interactions

The propagation of information in non-relativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance $r$ as a power law, $1/r^α$. The bound implies an effective light cone tighter than all previous bounds. Our approach is based on a technique for approximating the time evolution of a system, which was first introduced as part of a quantum simulation algorithm by Haah et al., FOCS'18. To bound the error of the approximation, we use a known Lieb-Robinson bound that is weaker than the bound we establish. This result brings the analysis full circle, suggesting a deep connection between Lieb-Robinson bounds and digital quantum simulation. In addition to the new Lieb-Robinson bound, our analysis also gives an error bound for the Haah et al. quantum simulation algorithm when used to simulate power-law decaying interactions. In particular, we show that the gate count of the algorithm scales with the system size better than existing algorithms when $α>3D$ (where $D$ is the number of dimensions).

quant-ph↗

arXiv2019

Signaling and Scrambling with Strongly Long-Range Interactions

Strongly long-range interacting quantum systems---those with interactions decaying as a power-law $1/r^α$ in the distance $r$ on a $D$-dimensional lattice for $α\le D$---have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. As a first step towards rectifying this problem, we prove two new Lieb-Robinson-type bounds that constrain the time for signaling and scrambling in strongly long-range interacting systems, for which no tight bounds were previously known. Our first bound applies to systems mappable to free-particle Hamiltonians with long-range hopping, and is saturable for $α\le D/2$. Our second bound pertains to generic long-range interacting spin Hamiltonians, and leads to a tight lower bound for the signaling time to extensive subsets of the system for all $α< D$. This result also lower-bounds the scrambling time, and suggests a path towards achieving a tight scrambling bound that can prove the long-standing fast scrambling conjecture.

quant-ph↗

arXiv2018

Dynamical phase transitions in sampling complexity

We make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a function of time $t$ due to evolution generated by spatially local quadratic bosonic Hamiltonians. We obtain an upper bound on the scaling of $t$ with the number of bosons $n$ for which approximate sampling is classically efficient. We also obtain a lower bound on the scaling of $t$ with $n$ for which any instance of the boson sampling problem reduces to this problem and hence implies that the problem is hard, assuming the conjectures of Aaronson and Arkhipov [Proc. 43rd Annu. ACM Symp. Theory Comput. STOC '11]. This establishes a dynamical phase transition in sampling complexity. Further, we show that systems in the Anderson-localized phase are always easy to sample from at arbitrarily long times. We view these results in the light of classifying phases of physical systems based on parameters in the Hamiltonian. In doing so, we combine ideas from mathematical physics and computational complexity to gain insight into the behavior of condensed matter, atomic, molecular and optical systems.

quant-ph↗