Author(s): Bruno Bertini, Katja Klobas, and Tsung-Cheng Lu

We study the growth of entanglement between two adjacent regions in a tripartite, one-dimensional many-body system after a quantum quench. Combining a replica trick with a space-time duality transformation, we derive an exact, universal relation between the entanglement negativity and Rényi-1/2 mutu…

[Phys. Rev. Lett. 129, 140503] Published Fri Sep 30, 2022

Author(s): J. Klinger, R. Voituriez, and O. Bénichou

We derive a universal, exact asymptotic form of the splitting probability for symmetric continuous jump processes, which quantifies the probability π0,x_(x0) that the process crosses x before 0 starting from a given position x0∈[0,x] in the regime x0≪x. This analysis provides in particular a fully e…

[Phys. Rev. Lett. 129, 140603] Published Fri Sep 30, 2022

Author(s): Alexander Nüßeler, Dario Tamascelli, Andrea Smirne, James Lim, Susana F. Huelga, and Martin B. Plenio

We exploit the properties of chain mapping transformations of bosonic environments to identify a finite collection of modes able to capture the characteristic features, or fingerprint, of the environment. Moreover we show that the countable infinity of residual bath modes can be replaced by a unive…

[Phys. Rev. Lett. 129, 140604] Published Fri Sep 30, 2022

Author(s): David Ehrenstein

When flying, hawkmoths need to delicately balance lift and drag in a way that limits their top speed, according to simulations.

[Physics 15, 152] Published Fri Sep 30, 2022

Categories: Physics

Author(s): Devvrat Tiwari, Shounak Datta, Samyadeb Bhattacharya, and Subhashish Banerjee

In this article we derive the exact dynamics of a two-qubit (spin 1/2) system interacting centrally with separate spin baths composed of qubits in a thermal state. Furthermore, each spin of the bath is coupled to every other spin of the same bath. The corresponding dynamical map is constructed. It i…

[Phys. Rev. A 106, 032435] Published Fri Sep 30, 2022

Author(s): Yongxu Liu, Ruonan Ren, Ping Li, Mingfei Ye, and Yongming Li

Estimating causal relations from observed correlations is a central content of science. Although a comprehensive mathematical framework has been developed to identify cause and effect, it is well known that such methods and techniques are not applicable to quantum systems due to Bell's theorem. Gene…

[Phys. Rev. A 106, 032436] Published Fri Sep 30, 2022

Author(s): Jun-Yi Wu

A linear-optics network is a multimode interferometer system, where indistinguishable photon inputs can create nonclassical interference that cannot be simulated with classical computers. Such nonclassical interference implies the existence of entanglement among its subsystems if we divide its modes…

[Phys. Rev. A 106, 032437] Published Fri Sep 30, 2022

An essential aspect of topological phases of matter is the existence of Wilson loop operators that keep the ground state subspace invariant. Here we present and implement an unbiased numerical optimization scheme to systematically find the Wilson loop operators given a single ground state wave function of a gapped Hamiltonian on a disk. We then show how these Wilson loop operators can be cut and glued through further optimization to give operators that can create, move, and annihilate anyon excitations. We subsequently use these operators to determine the braiding statistics and topological twists of the anyons, yielding a way to fully extract topological order from a single wave function. We apply our method to the ground state of the perturbed toric code and doubled semion models with a magnetic field that is up to a half of the critical value. From a contemporary perspective, this can be thought of as a machine learning approach to discover emergent 1-form symmetries of a ground state wave function. From an application perspective, our approach can be relevant to find Wilson loop operators in current quantum simulators.

The pillars of quantum theory include entanglement and operators' failure to commute. The Page curve quantifies the bipartite entanglement of a many-body system in a random pure state. This entanglement is known to decrease if one constrains extensive observables that commute with each other (Abelian ``charges''). Non-Abelian charges, which fail to commute with each other, are of current interest in quantum thermodynamics. For example, noncommuting charges were shown to reduce entropy-production rates and may enhance finite-size deviations from eigenstate thermalization. Bridging quantum thermodynamics to many-body physics, we quantify the effects of charges' noncommutation -- of a symmetry's non-Abelian nature -- on Page curves. First, we construct two models that are closely analogous but differ in whether their charges commute. We show analytically and numerically that the noncommuting-charge case has more entanglement. Hence charges' noncommutation can promote entanglement.

A test of quantumness is a protocol where a classical user issues challenges to a quantum device to determine if it exhibits non-classical behavior, under certain cryptographic assumptions. Recent attempts to implement such tests on current quantum computers rely on either interactive challenges with efficient verification, or non-interactive challenges with inefficient (exponential time) verification. In this paper, we execute an efficient non-interactive test of quantumness on an ion-trap quantum computer. Our results significantly exceed the bound for a classical device's success.

We present experimental and simulated results to quantify the impact of nonlinear noise in integrated photonic devices relying on spontaneous four-wave mixing. Our results highlight the need for design rule adaptations to mitigate the otherwise intrinsic reduction in quantum state purity. The best strategy in devices with multiple parallel photon sources is to strictly limit photon generation outside of the sources. Otherwise, our results suggest that purity can decrease below 40%.

The physics of a closed quantum mechanical system is governed by its Hamiltonian. However, in most practical situations, this Hamiltonian is not precisely known, and ultimately all there is are data obtained from measurements on the system. In this work, we introduce a highly scalable, data-driven approach to learning families of interacting many-body Hamiltonians from dynamical data, by bringing together techniques from gradient-based optimization from machine learning with efficient quantum state representations in terms of tensor networks. Our approach is highly practical, experimentally friendly, and intrinsically scalable to allow for system sizes of above 100 spins. In particular, we demonstrate on synthetic data that the algorithm works even if one is restricted to one simple initial state, a small number of single-qubit observables, and time evolution up to relatively short times. For the concrete example of the one-dimensional Heisenberg model our algorithm exhibits an error constant in the system size and scaling as the inverse square root of the size of the data set.

In efforts to scale the size of quantum computers, modularity plays a central role across most quantum computing technologies. In the light of fault tolerance, this necessitates designing quantum error-correcting codes that are compatible with the connectivity arising from the architectural layouts. In this paper, we aim to bridge this gap by giving a novel way to view and construct quantum LDPC codes tailored for modular architectures. We demonstrate that if the intra- and inter-modular qubit connectivity can be viewed as corresponding to some classical or quantum LDPC codes, then their hypergraph product code fully respects the architectural connectivity constraints. Finally, we show that relaxed connectivity constraints that allow twists of connections between modules pave a way to construct codes with better parameters.

We present a semidefinite program (SDP) algorithm to find eigenvalues of Schr\"{o}dinger operators within the bootstrap approach to quantum mechanics. The bootstrap approach involves two ingredients: a nonlinear set of constraints on the variables (expectation values of operators in an energy eigenstate), plus positivity constraints (unitarity) that need to be satisfied. By fixing the energy we linearize all the constraints and show that the feasability problem can be presented as an optimization problem for the variables that are not fixed by the constraints and one additional slack variable that measures the failure of positivity. To illustrate the method we are able to obtain high-precision, sharp bounds on eigenenergies for arbitrary confining polynomial potentials in 1-D.

We construct Hamiltonians with only 1- and 2-body interactions that exhibit an exact non-Abelian gauge symmetry (specifically, combinatiorial gauge symmetry). Our spin Hamiltonian realizes the quantum double associated to the group of quaternions. It contains only ferromagnetic and anti-ferromagnetic $ZZ$ interactions, plus longitudinal and transverse fields, and therefore is an explicit example of a spin Hamiltonian with no sign problem that realizes a non-Abelian topological phase. In addition to the spin model, we propose a superconducting quantum circuit version with the same symmetry.

Quantum neural networks have been widely studied in recent years, given their potential practical utility and recent results regarding their ability to efficiently express certain classical data. However, analytic results to date rely on assumptions and arguments from complexity theory. Due to this, there is little intuition as to the source of the expressive power of quantum neural networks or for which classes of classical data any advantage can be reasonably expected to hold. Here, we study the relative expressive power between a broad class of neural network sequence models and a class of recurrent models based on Gaussian operations with non-Gaussian measurements. We explicitly show that quantum contextuality is the source of an unconditional memory separation in the expressivity of the two model classes. Additionally, as we are able to pinpoint quantum contextuality as the source of this separation, we use this intuition to study the relative performance of our introduced model on a standard translation data set exhibiting linguistic contextuality. In doing so, we demonstrate that our introduced quantum models are able to outperform state of the art classical models even in practice.

We consider the application of the pentagon equation in the context of quantum circuit compression. We show that if solutions to the pentagon equation are found, one can transpile a circuit involving non-Heisenberg-type interactions to a circuit involving only Heisenberg-type interactions while, in parallel, reducing the depth of a circuit. In this context, we consider a model of non-local two-qubit operations of Zhang \emph{et. al.} (the $A$ gate), and show that for certain parameters it is a solution of the pentagon equation.

Tensor networks have a gauge degree of freedom on the virtual degrees of freedom that are contracted. A canonical form is a choice of fixing this degree of freedom. For matrix product states, choosing a canonical form is a powerful tool, both for theoretical and numerical purposes. On the other hand, for tensor networks in dimension two or greater there is only limited understanding of the gauge symmetry. Here we introduce a new canonical form, the minimal canonical form, which applies to projected entangled pair states (PEPS) in any dimension, and prove a corresponding fundamental theorem. Already for matrix product states this gives a new canonical form, while in higher dimensions it is the first rigorous definition of a canonical form valid for any choice of tensor. We show that two tensors have the same minimal canonical forms if and only if they are gauge equivalent up to taking limits; moreover, this is the case if and only if they give the same quantum state for any geometry. In particular, this implies that the latter problem is decidable - in contrast to the well-known undecidability for PEPS on grids. We also provide rigorous algorithms for computing minimal canonical forms. To achieve this we draw on geometric invariant theory and recent progress in theoretical computer science in non-commutative group optimization.

In this work, we introduce a quantum-control-inspired method for the characterization of variational quantum circuits using the rank of the dynamical Lie algebra associated with the hermitian generator(s) of the individual layers. Layer-based architectures in variational algorithms for the calculation of ground-state energies of physical systems are taken as the focus of this exploration. A promising connection is found between the Lie rank, the accuracy of calculated energies, and the requisite depth to attain target states via a given circuit architecture, even when using a lot of parameters which is appreciably below the number of separate terms in the generators. As the cost of calculating the dynamical Lie rank via an iterative process grows exponentially with the number of qubits in the circuit and therefore becomes prohibitive quickly, reliable approximations thereto are desirable. The rapidity of the increase of the dynamical Lie rank in the first few iterations of the calculation is found to be a viable (lower bound) proxy for the full calculation, balancing accuracy and computational expense. We, therefore, propose the dynamical Lie rank and proxies thereof as a useful design metric for layer-structured quantum circuits in variational algorithms.

Phonon-induced relaxation within the nitrogen-vacancy (NV) center's electronic ground-state spin triplet limits its coherence times, and thereby impacts its performance in quantum applications. We report measurements of the relaxation rates on the NV center's $| m_{s}=0\rangle \leftrightarrow | m_{s}=\pm 1 \rangle$ and $| m_{s}=-1 \rangle \leftrightarrow | m_{s}=+1 \rangle $ transitions as a function of temperature from 9 to 474 K in high-purity samples. Informed by ab initio calculations, we demonstrate that NV spin-phonon relaxation can be completely explained by the effect of second-order interactions with two distinct groups of quasilocalized phonons. Using a novel analytical model based on this understanding, we determine that the quasilocalized phonon groups are centered at 68.2(17) and 167(12) meV.