The relevance of shallow-depth quantum circuits has recently increased, mainly due to their applicability to near-term devices. In this context, one of the main goals of quantum circuit complexity is to find problems that can be solved by quantum shallow circuits but require more computational resources classically. Our first contribution in this work is to prove new separations between classical and quantum constant-depth circuits. Firstly, we show a separation between constant-depth quantum circuits with quantum advice $\mathsf{QNC}^0/\mathsf{qpoly}$, and $\mathsf{AC}^0[p]$, which is the class of classical constant-depth circuits with unbounded-fan in and $\pmod{p}$ gates. In addition, we show a separation between $\mathsf{QAC}^0$, which additionally has Toffoli gates with unbounded control, and $\mathsf{AC}^0[p]$. This establishes the first such separation for a shallow-depth quantum class that does not involve quantum fan-out gates. Secondly, we consider $\mathsf{QNC}^0$ circuits with infinite-size gate sets. We show that these circuits, along with (classical or quantum) prime modular gates, can implement threshold gates, showing that $\mathsf{QNC}^0[p]=\mathsf{QTC}^0$. Finally, we also show that in the infinite-size gateset case, these quantum circuit classes for higher-dimensional Hilbert spaces do not offer any advantage to standard qubit implementations.
We propose an implementation of bivariate bicycle codes (Nature \bf 627, 778 (2024)) based on long-range Rydberg gates between stationary neutral atom qubits. An optimized layout of data and ancilla qubits reduces the maximum Euclidean communication distance needed for non-local parity check operators. An optimized Rydberg gate pulse design enables $\sf CZ$ entangling operations with fidelity ${\mathcal F}>0.999$ at a distance greater than $12~\mu\rm m$. The combination of optimized layout and gate design leads to a quantum error correction cycle time of $\sim 1.2~\rm ms$ for a $[[144,12,12]]$ code, an order of magnitude improvement over previous designs.
Geometric locality is an important theoretical and practical factor for quantum low-density parity-check (qLDPC) codes which affects code performance and ease of physical realization. For device architectures restricted to 2D local gates, naively implementing the high-rate codes suitable for low-overhead fault-tolerant quantum computing incurs prohibitive overhead. In this work, we present an error correction protocol built on a bilayer architecture that aims to reduce operational overheads when restricted to 2D local gates by measuring some generators less frequently than others. We investigate the family of bivariate bicycle qLDPC codes and show that they are well suited for a parallel syndrome measurement scheme using fast routing with local operations and classical communication (LOCC). Through circuit-level simulations, we find that in some parameter regimes bivariate bicycle codes implemented with this protocol have logical error rates comparable to the surface code while using fewer physical qubits.
Quantum error correction is necessary for large-scale quantum computing. A promising quantum error correcting code is the surface code. For this code, fault-tolerant quantum computing (FTQC) can be performed via lattice surgery, i.e., splitting and merging patches of code. Given the frequent use of certain lattice-surgery subroutines (LaS), it becomes crucial to optimize their design in order to minimize the overall spacetime volume of FTQC. In this study, we define the variables to represent LaS and the constraints on these variables. Leveraging this formulation, we develop a synthesizer for LaS, LaSsynth, that encodes a LaS construction problem into a SAT instance, subsequently querying SAT solvers for a solution. Starting from a baseline design, we can gradually invoke the solver with shrinking spacetime volume to derive more compact designs. Due to our foundational formulation and the use of SAT solvers, LaSsynth can exhaustively explore the design space, yielding optimal designs in volume. For example, it achieves 8% and 18% volume reduction respectively over two states-of-the-art human designs for the 15-to-1 T-factory, a bottleneck in FTQC.
In this paper, we investigate the relationship between entanglement and non-stabilizerness (also known as magic) in matrix product states (MPSs). We study the relation between magic and the bond dimension used to approximate the ground state of a many-body system in two different contexts: full state of magic and mutual magic (the non-stabilizer analogue of mutual information, thus free of boundary effects) of spin-1 anisotropic Heisenberg chains. Our results indicate that obtaining converged results for non-stabilizerness is typically considerably easier than entanglement. For full state magic at critical points and at sufficiently large volumes, we observe convergence with $1/\chi^2$, with $\chi$ being the MPS bond dimension. At small volumes, magic saturation is so quick that, within error bars, we cannot appreciate any finite-$\chi$ correction. Mutual magic also shows a fast convergence with bond dimension, whose specific functional form is however hindered by sampling errors. As a by-product of our study, we show how Pauli-Markov chains (originally formulated to evaluate magic) resets the state of the art in terms of computing mutual information for MPS. We illustrate this last fact by verifying the logarithmic increase of mutual information between connected partitions at critical points. By comparing mutual information and mutual magic, we observe that, for connected partitions, the latter is typically scaling much slower - if at all - with the partition size, while for disconnected partitions, both are constant in size.
We give a simple description of rectangular matrices that can be implemented by a post-selected stabilizer circuit. Given a matrix with entries in dyadic cyclotomic number fields $\mathbb{Q}(\exp(i\frac{2\pi}{2^m}))$, we show that it can be implemented by a post-selected stabilizer circuit if it has entries in $\mathbb{Z}[\exp(i\frac{2\pi}{2^m})]$ when expressed in a certain non-orthogonal basis. This basis is related to Barnes-Wall lattices. Our result is a generalization to a well-known connection between Clifford groups and Barnes-Wall lattices. We also show that minimal vectors of Barnes-Wall lattices are stabilizer states, which may be of independent interest. Finally, we provide a few examples of generalizations beyond standard Clifford groups.
The performance of quantum algorithms for eigenvalue problems, such as computing Hamiltonian spectra, depends strongly on the overlap of the initial wavefunction and the target eigenvector. In a basis of Slater determinants, the representation of energy eigenstates of systems with $N$ strongly correlated electrons requires a number of determinants that scales exponentially with $N$. On classical processors, this restricts simulations to systems where $N$ is small. Here, we show that quantum computers can efficiently simulate strongly correlated molecular systems by directly encoding the dominant entanglement structure in the form of spin-coupled initial states. This avoids resorting to expensive classical or quantum state preparation heuristics and instead exploits symmetries in the wavefunction. We provide quantum circuits for deterministic preparation of a family of spin eigenfunctions with ${N \choose N/2}$ Slater determinants with depth $\mathcal{O}(N)$ and $\mathcal{O}(N^2)$ local gates. Their use as highly entangled initial states in quantum algorithms reduces the total runtime of quantum phase estimation and related fault-tolerant methods by orders of magnitude. Furthermore, we assess the application of spin-coupled wavefunctions as initial states for a range of heuristic quantum algorithms, namely the variational quantum eigensolver, adiabatic state preparation, and different versions of quantum subspace diagonalization (QSD) including QSD based on real-time-evolved states. We also propose a novel QSD algorithm that exploits states obtained through adaptive quantum eigensolvers. For all algorithms, we demonstrate that using spin-coupled initial states drastically reduces the quantum resources required to simulate strongly correlated ground and excited states. Our work paves the way towards scalable quantum simulation of electronic structure for classically challenging systems.
Nonstabilizerness, or `magic', is a critical quantum resource that, together with entanglement, characterizes the non-classical complexity of quantum states. Here, we address the problem of quantifying the average nonstabilizerness of random Matrix Product States (RMPS). RMPS represent a generalization of random product states featuring bounded entanglement that scales logarithmically with the bond dimension $\chi$. We demonstrate that the $2$-Stabilizer Rényi Entropy converges to that of Haar random states as $N/\chi^2$, where $N$ is the system size. This indicates that MPS with a modest bond dimension are as magical as generic states. Subsequently, we introduce the ensemble of Clifford enhanced Matrix Product States ($\mathcal{C}$MPS), built by the action of Clifford unitaries on RMPS. Leveraging our previous result, we show that $\mathcal{C}$MPS can approximate $4$-spherical designs with arbitrary accuracy. Specifically, for a constant $N$, $\mathcal{C}$MPS become close to $4$-designs with a scaling as $\chi^{-2}$. Our findings indicate that combining Clifford unitaries with polynomially complex tensor network states can generate highly non-trivial quantum states.
Optimization is one of the keystones of modern science and engineering. Its applications in quantum technology and machine learning helped nurture variational quantum algorithms and generative AI respectively. We propose a general approach to design variational optimization algorithms based on generative models: the Variational Generative Optimization Network (VGON). To demonstrate its broad applicability, we apply VGON to three quantum tasks: finding the best state in an entanglement-detection protocol, finding the ground state of a 1D quantum spin model with variational quantum circuits, and generating degenerate ground states of many-body quantum Hamiltonians. For the first task, VGON greatly reduces the optimization time compared to stochastic gradient descent while generating nearly optimal quantum states. For the second task, VGON alleviates the barren plateau problem in variational quantum circuits. For the final task, VGON can identify the degenerate ground state spaces after a single stage of training and generate a variety of states therein.
Giovanni Rodari, Leonardo Novo, Riccardo Albiero, Alessia Suprano, Carlos T. Tavares, Eugenio Caruccio, Francesco Hoch, Taira Giordani, Gonzalo Carvacho, Marco Gardina, Niki Di Giano, Serena Di Giorgio, Giacomo Corrielli, Francesco Ceccarelli, Roberto Osellame, Nicolò Spagnolo, Ernesto F. Galvão, Fabio Sciarrino Multiphoton indistinguishability is a central resource for quantum enhancement in sensing and computation. Developing and certifying large scale photonic devices requires reliable and accurate characterization of this resource, preferably using methods that are robust against experimental errors. Here, we propose a set of methods for the characterization of multiphoton indistinguishability, based on measurements of bunching and photon number variance. Our methods are robust in a semi-device independent way, in the sense of being effective even when the interferometers are incorrectly dialled. We demonstrate the effectiveness of this approach using an advanced photonic platform comprising a quantum-dot single-photon source and a universal fully-programmable integrated photonic processor. Our results show the practical usefulness of our methods, providing robust certification tools that can be scaled up to larger systems.
Quantum subsystem codes have been shown to improve error-correction performance, ease the implementation of logical operations on codes, and make stabilizer measurements easier by decomposing stabilizers into smaller-weight gauge operators. In this paper, we present two algorithms that produce new subsystem codes from a "seed" CSS code. They replace some stabilizers of a given CSS code with smaller-weight gauge operators that split the remaining stabilizers, while being compatible with the logical Pauli operators of the code. The algorithms recover the well-known Bacon-Shor code computationally as well as produce a new $\left[\left[ 9,1,2,2 \right]\right]$ rotated surface subsystem code with weight-$3$ gauges and weight-$4$ stabilizers. We illustrate using a $\left[\left[ 100,25,3 \right]\right]$ subsystem hypergraph product (SHP) code that the algorithms can produce more efficient gauge operators than the closed-form expressions of the SHP construction. However, we observe that the stabilizers of the lifted product quantum LDPC codes are more challenging to split into small-weight gauge operators. Hence, we introduce the subsystem lifted product (SLP) code construction and develop a new $\left[\left[ 775, 124, 20 \right]\right]$ code from Tanner's classical quasi-cyclic LDPC code. The code has high-weight stabilizers but all gauge operators that split stabilizers have weight $5$, except one. In contrast, the LP stabilizer code from Tanner's code has parameters $\left[\left[ 1054, 124, 20 \right]\right]$. This serves as a novel example of new subsystem codes that outperform stabilizer versions of them. Finally, based on our experiments, we share some general insights about non-locality's effects on the performance of splitting stabilizers into small-weight gauges.
Nonlinear processes with individual quanta beyond bilinear interactions are essential for quantum technology with bosonic systems. Diverse coherent splitting and merging of quanta in them already manifest in the estimation of their nonlinear coupling from observed statistics. We derive non-trivial, but optimal strategies for sensing the basic and experimentally available trilinear interactions using non-classical particle-like Fock states as a probe and feasible measurement strategies. Remarkably, the optimal probing of nonlinear coupling reaches estimation errors scaled down with $N^{-1/3}$ for overall $N$ of quanta in specific but available high-quality Fock states in all interacting modes. It can reveal unexplored aspects of nonlinear dynamics relevant to using such nonlinear processes in bosonic experiments with trapped ions and superconducting circuits and opens further developments of quantum technology with them.
Atomicity is a ubiquitous assumption in distributed computing, under which actions are indivisible and appear sequential. In classical computing, this assumption has several theoretical and practical guarantees. In quantum computing, although atomicity is still commonly assumed, it has not been seriously studied, and a rigorous basis for it is missing. Classical results on atomicity do not directly carry over to distributed quantum computing, due to new challenges caused by quantum entanglement and the measurement problem from the underlying quantum mechanics. In this paper, we initiate the study of atomicity in distributed quantum computing. A formal model of (non-atomic) distributed quantum system is established. Based on the Dijkstra-Lamport condition, the system dynamics and observable dynamics of a distributed quantum system are defined, which correspond to the quantum state of and classically observable events in the system, respectively. Within this framework, we prove that local actions can be regarded as if they were atomic, up to the observable dynamics of the system.
In quantum thermodynamics, entropy production is usually defined in terms of the quantum relative entropy between two states. We derive a lower bound for the quantum entropy production in terms of the mean and variance of quantum observables, which we will refer to as a thermodynamic uncertainty relation (TUR) for the entropy production. In the absence of coherence between the states, our result reproduces classic TURs in stochastic thermodynamics. For the derivation of the TUR, we introduce a lower bound for a quantum generalization of the $\chi^2$ divergence between two states and discuss its implications for stochastic and quantum thermodynamics, as well as the limiting case where it reproduces the quantum Cramér-Rao inequality.
We propose a quantum information processing platform that utilizes the ultrafast time-bin encoding of photons. This approach offers a pathway to scalability by leveraging the inherent phase stability of collinear temporal interferometric networks at the femtosecond-to-picosecond timescale. The proposed architecture encodes information in ultrafast temporal bins processed using optically induced nonlinearities and birefringent materials while keeping photons in a single spatial mode. We demonstrate the potential for scalable photonic quantum information processing through two independent experiments that showcase the platform's programmability and scalability, respectively. The scheme's programmability is demonstrated in the first experiment, where we successfully program 362 different unitary transformations in up to 8 dimensions in a temporal circuit. In the second experiment, we show the scalability of ultrafast time-bin encoding by building a passive optical network, with increasing circuit depth, of up to 36 optical modes. In each experiment, fidelities exceed 97\%, while the interferometric phase remains passively stable for several days.
In the realm of invertible symmetry, the topological approach based on classifying spaces dominates the classification of 't Hooft anomalies and symmetry protected topological phases. In contrast, except for discrete 0-form symmetry, a systematic algebraic approach based on cochains remains poorly explored. In this work, we investigate the systematic algebraic approach for discrete higher-form symmetry with a trivial higher-group structure. Studying the discrete formulation of invertible field theories in arbitrary dimension, we extract a purely algebraic structure that we call extended group cohomology, which directly characterizes and classifies the lattice lagrangian of invertible field theories and the behavior of anomalous topological operators. Using techniques from simplicial homotopy theory, we prove the isomorphism between extended group cohomology and cohomology of classifying spaces. The proof is based on an explicit construction of Eilenberg-MacLane spaces and their products. Our findings also clarify the discrete formulation of a class of generalized Dijkgraaf-Witten-Yetter models.
Constrained optimization plays a crucial role in the fields of quantum physics and quantum information science and becomes especially challenging for high-dimensional complex structure problems. One specific issue is that of quantum process tomography, in which the goal is to retrieve the underlying quantum process based on a given set of measurement data. In this paper, we introduce a modified version of stochastic gradient descent on a Riemannian manifold that integrates recent advancements in numerical methods for Riemannian optimization. This approach inherently supports the physically driven constraints of a quantum process, takes advantage of state-of-the-art large-scale stochastic objective optimization, and has superior performance to traditional approaches such as maximum likelihood estimation and projected least squares. The data-driven approach enables accurate, order-of-magnitude faster results, and works with incomplete data. We demonstrate our approach on simulations of quantum processes and in hardware by characterizing an engineered process on quantum computers.
Gaussian quantum information processing with continuous-variable (CV) quantum information carriers holds significant promise for applications in quantum communication and quantum internet. However, applying Gaussian state distillation and quantum error correction (QEC) faces limitations imposed by no-go results concerning local Gaussian unitary operations and classical communications. This paper introduces a Gaussian QEC protocol that relies solely on local Gaussian resources. A pivotal component of our approach is CV gate teleportation using entangled Gaussian states, which facilitates the implementation of the partial transpose operation on a quantum channel. Consequently, we can efficiently construct a two-mode noise-polarized channel from two noisy Gaussian channels. Furthermore, this QEC protocol naturally extends to a nonlocal Gaussian state distillation protocol.
Parameterised quantum circuits (PQCs) hold great promise for demonstrating quantum advantages in practical applications of quantum computation. Examples of successful applications include the variational quantum eigensolver, the quantum approximate optimisation algorithm, and quantum machine learning. However, before executing PQCs on real quantum devices, they undergo compilation and optimisation procedures. Given the inherent error-proneness of these processes, it becomes crucial to verify the equivalence between the original PQC and its compiled or optimised version. Unfortunately, most existing quantum circuit verifiers cannot directly handle parameterised quantum circuits; instead, they require parameter substitution to perform verification. In this paper, we address the critical challenge of equivalence checking for PQCs. We propose a novel compact representation for PQCs based on tensor decision diagrams. Leveraging this representation, we present an algorithm for verifying PQC equivalence without the need for instantiation. Our approach ensures both effectiveness and efficiency, as confirmed by experimental evaluations. The decision-diagram representations offer a powerful tool for analysing and verifying parameterised quantum circuits, bridging the gap between theoretical models and practical implementations.
Network coordination is considered in three basic settings, characterizing the generation of separable and classical-quantum correlations among multiple parties. First, we consider the simulation of a classical-quantum state between two nodes with rate-limited common randomness (CR) and communication. Furthermore, we study the preparation of a separable state between multiple nodes with rate-limited CR and no communication. At last, we consider a broadcast setting, where a sender and two receivers simulate a classical-quantum-quantum state using rate-limited CR and communication. We establish the optimal tradeoff between communication and CR rates in each setting.
A matrix can be converted into a doubly stochastic matrix by using two diagonal matrices. And a doubly stochastic matrix can be written as a sum of permutation matrices. In this paper, we describe a method to write a given generic matrix in terms of quantum gates based on the block encoding. In particular, we first show how to convert a matrix into doubly stochastic matrices and by using Birkhoff's algorithm, we express that matrix in terms of a linear combination of permutations which can be mapped to quantum circuits. We then discuss a few optimization techniques that can be applied in a possibly future quantum compiler software based on the method described here.
We give a new algorithm for learning mixtures of $k$ Gaussians (with identity covariance in $\mathbb{R}^n$) to TV error $\varepsilon$, with quasi-polynomial ($O(n^{\text{poly log}\left(\frac{n+k}{\varepsilon}\right)})$) time and sample complexity, under a minimum weight assumption. Unlike previous approaches, most of which are algebraic in nature, our approach is analytic and relies on the framework of diffusion models. Diffusion models are a modern paradigm for generative modeling, which typically rely on learning the score function (gradient log-pdf) along a process transforming a pure noise distribution, in our case a Gaussian, to the data distribution. Despite their dazzling performance in tasks such as image generation, there are few end-to-end theoretical guarantees that they can efficiently learn nontrivial families of distributions; we give some of the first such guarantees. We proceed by deriving higher-order Gaussian noise sensitivity bounds for the score functions for a Gaussian mixture to show that that they can be inductively learned using piecewise polynomial regression (up to poly-logarithmic degree), and combine this with known convergence results for diffusion models. Our results extend to continuous mixtures of Gaussians where the mixing distribution is supported on a union of $k$ balls of constant radius. In particular, this applies to the case of Gaussian convolutions of distributions on low-dimensional manifolds, or more generally sets with small covering number.
Tomographic reconstruction of quantum states plays a fundamental role in benchmarking quantum systems and retrieving information from quantum computers. Among the informationally complete sets of quantum measurements the tight ones provide a linear reconstruction formula and minimize the propagation of statistical errors. However, implementing tight measurements in the lab is challenging due to the high number of required measurement projections, involving a series of experimental setup preparations. In this work, we introduce the notion of cyclic tight measurements, that allow us to perform full quantum state tomography while considering only repeated application of a single unitary-based quantum device during the measurement stage process. This type of measurements significantly simplifies the complexity of the experimental setup required to retrieve the quantum state of a physical system. Additionally, we design feasible setup preparation procedure that produce well-approximated cyclic tight measurements, in every finite dimension.
We introduce Harmonic Robustness, a powerful and intuitive method to test the robustness of any machine-learning model either during training or in black-box real-time inference monitoring without ground-truth labels. It is based on functional deviation from the harmonic mean value property, indicating instability and lack of explainability. We show implementation examples in low-dimensional trees and feedforward NNs, where the method reliably identifies overfitting, as well as in more complex high-dimensional models such as ResNet-50 and Vision Transformer where it efficiently measures adversarial vulnerability across image classes.
In this paper we shall use the abstract bifurcation theorems developed by the author in previous papers to study bifurcations of solutions for Lagrangian systems on manifolds linearly or nonlinearly dependent on parameters under various boundary value conditions. As applications, many bifurcation results for geodesics on Finsler and Riemannian manifolds are derived.
Ming Ni, Rong-Long Ma, Zhen-Zhen Kong, Ning Chu, Sheng-Kai Zhu, Chu Wang, Ao-Ran Li, Wei-Zhu Liao, Gang Cao, Gui-Lei Wang, Guang-Can Guo, Xuedong Hu, Hai-Ou Li, Guo-Ping Guo To realize large-scale quantum information processes, an ideal scheme for two-qubit operations should enable diverse operations with given hardware and physical interaction. However, for spin qubits in semiconductor quantum dots, the common two-qubit operations, including CPhase gates, SWAP gates, and CROT gates, are realized with distinct parameter regions and control waveforms, posing challenges for their simultaneous implementation. Here, taking advantage of the inherent Heisenberg interaction between spin qubits, we propose and verify a fast composite two-qubit gate scheme to extend the available two-qubit gate types as well as reduce the requirements for device properties. Apart from the formerly proposed CPhase (controlled-phase) gates and SWAP gates, theoretical results indicate that the iSWAP-family gate and Fermionic simulation (fSim) gate set are additionally available for spin qubits. Meanwhile, our gate scheme limits the parameter requirements of all essential two-qubit gates to a common J~∆E_Z region, facilitate the simultaneous realization of them. Furthermore, we present the preliminary experimental demonstration of the composite gate scheme, observing excellent match between the measured and simulated results. With this versatile composite gate scheme, broad-spectrum two-qubit operations allow us to efficiently utilize the hardware and the underlying physics resources, helping accelerate and broaden the scope of the upcoming noise intermediate-scale quantum (NISQ) computing.
To make practical quantum algorithms work, large-scale quantum processors protected by error-correcting codes are required to resist noise and ensure reliable computational outcomes. However, a major challenge arises from defects in processor fabrication, as well as occasional losses or cosmic rays during the computing process, all of which can lead to qubit malfunctions and disrupt error-correcting codes' normal operations. In this context, we introduce an automatic adapter to implement the surface code on defective lattices. Unlike previous approaches, this adapter leverages newly proposed bandage-like super-stabilizers to save more qubits when defects are clustered, thus enhancing the code distance and reducing super-stabilizer weight. For instance, in comparison with earlier methods, with a code size of 27 and a random defect rate of 2\%, the disabled qubits decrease by $1/3$, and the average preserved code distance increases by 63\%. This demonstrates a significant reduction in overhead when handling defects using our approach, and this advantage amplifies with increasing processor size and defect rates. Our work presents a low-overhead, automated solution to the challenge of adapting the surface code to defects, an essential step towards scaling up the construction of large-scale quantum computers for practical applications.
To realize a global quantum Internet, there is a need for communication between quantum subnetworks. To accomplish this task, there have been multiple design proposals for a quantum backbone network and quantum subnetworks. In this work, we elaborate on the design that uses entanglement and quantum teleportation to build the quantum backbone between packetized quantum networks. We design a network interface to interconnect packetized quantum networks with entanglement-based quantum backbone networks and, moreover, design a scheme to accomplish data transmission over this hybrid quantum network model. We analyze the use of various implementations of the backbone network, focusing our study on backbone networks that use satellite links to continuously distribute entanglement resources. For feasibility, we analyze various system parameters via simulation to benchmark the performance of the overall network.
The emergence of quantum sensor networks has presented opportunities for enhancing complex sensing tasks, while simultaneously introducing significant challenges in designing and analyzing quantum sensing protocols due to the intricate nature of entanglement and physical processes. Supervised learning assisted by an entangled sensor network (SLAEN) [Phys. Rev. X 9, 041023 (2019)] represents a promising paradigm for automating sensor-network design through variational quantum machine learning. However, the original SLAEN, constrained by the Gaussian nature of quantum circuits, is limited to learning linearly separable data. Leveraging the universal quantum control available in cavity-QED experiments, we propose a generalized SLAEN capable of handling nonlinear data classification tasks. We establish a theoretical framework for physical-layer data classification to underpin our approach. Through training quantum probes and measurements, we uncover a threshold phenomenon in classification error across various tasks -- when the energy of probes exceeds a certain threshold, the error drastically diminishes to zero, providing a significant improvement over the Gaussian SLAEN. Despite the non-Gaussian nature of the problem, we offer analytical insights into determining the threshold and residual error in the presence of noise. Our findings carry implications for radio-frequency photonic sensors and microwave dark matter haloscopes.
In the current landscape of noisy intermediate-scale quantum (NISQ) computing, the inherent noise presents significant challenges to achieving high-fidelity long-range entanglement. Furthermore, this challenge is amplified by the limited connectivity of current superconducting devices, necessitating state permutations to establish long-distance entanglement. Traditionally, graph methods are used to satisfy the coupling constraints of a given architecture by routing states along the shortest undirected path between qubits. In this work, we introduce a gradient boosting machine learning model to predict the fidelity of alternative--potentially longer--routing paths to improve fidelity. This model was trained on 4050 random CNOT gates ranging in length from 2 to 100+ qubits. The experiments were all executed on ibm_quebec, a 127-qubit IBM Quantum System One. Through more than 200+ tests run on actual hardware, our model successfully identified higher fidelity paths in approximately 23% of cases.
Richen Xiong, Samuel L. Brantly, Kaixiang Su, Jacob H. Nie, Zihan Zhang, Rounak Banerjee, Hayley Ruddick, Kenji Watanabe, Takashi Taniguchi, Sefaattin Tongay, Cenke Xu, Chenhao Jin Spin and charge are the two most important degrees of freedom of electrons. Their interplay lies at the heart of numerous strongly correlated phenomena including Hubbard model physics and high temperature superconductivity. Such interplay for bosons, on the other hand, is largely unexplored in condensed matter systems. Here we demonstrate a unique realization of the spin-1/2 Bose-Hubbard model through excitons in a semiconducting moiré superlattice. We find evidence of a transient in-plane ferromagnetic (FM-$xy$) order of exciton spin - here valley pseudospin - around exciton filling $\nu_{ex}$ = 1, which transitions into a FM-$z$ order both with increasing exciton filling and a small magnetic field of 10 mT. The phase diagram is different from the fermion case and is qualitatively captured by a simple phenomenological model, highlighting the unique consequence of Bose-Einstein statistics. Our study paves the way for engineering exotic phases of matter from spinor bosons, as well as for unconventional devices in optics and quantum information science.
Apr 30 2024
cs.CV arXiv:2404.18930v1
This survey presents a comprehensive analysis of the phenomenon of hallucination in multimodal large language models (MLLMs), also known as Large Vision-Language Models (LVLMs), which have demonstrated significant advancements and remarkable abilities in multimodal tasks. Despite these promising developments, MLLMs often generate outputs that are inconsistent with the visual content, a challenge known as hallucination, which poses substantial obstacles to their practical deployment and raises concerns regarding their reliability in real-world applications. This problem has attracted increasing attention, prompting efforts to detect and mitigate such inaccuracies. We review recent advances in identifying, evaluating, and mitigating these hallucinations, offering a detailed overview of the underlying causes, evaluation benchmarks, metrics, and strategies developed to address this issue. Additionally, we analyze the current challenges and limitations, formulating open questions that delineate potential pathways for future research. By drawing the granular classification and landscapes of hallucination causes, evaluation benchmarks, and mitigation methods, this survey aims to deepen the understanding of hallucinations in MLLMs and inspire further advancements in the field. Through our thorough and in-depth review, we contribute to the ongoing dialogue on enhancing the robustness and reliability of MLLMs, providing valuable insights and resources for researchers and practitioners alike. Resources are available at: https://github.com/showlab/Awesome-MLLM-Hallucination.
Apr 30 2024
cs.CV arXiv:2404.18929v1
We consider the problem of editing 3D objects and scenes based on open-ended language instructions. The established paradigm to solve this problem is to use a 2D image generator or editor to guide the 3D editing process. However, this is often slow as it requires do update a computationally expensive 3D representations such as a neural radiance field, and to do so by using contradictory guidance from a 2D model which is inherently not multi-view consistent. We thus introduce the Direct Gaussian Editor (DGE), a method that addresses these issues in two ways. First, we modify a given high-quality image editor like InstructPix2Pix to be multi-view consistent. We do so by utilizing a training-free approach which integrates cues from the underlying 3D geometry of the scene. Second, given a multi-view consistent edited sequence of images of the object, we directly and efficiently optimize the 3D object representation, which is based on 3D Gaussian Splatting. Because it does not require to apply edits incrementally and iteratively, DGE is significantly more efficient than existing approaches, and comes with other perks such as allowing selective editing of parts of the scene.
Let $X, Y \subset \mathbb{C}^{2n-1}$ be $n$-dimensional strong complete intersections in a general position. In this note, we consider the set of midpoints of chords connecting a point $x \in X$ to a point $y \in Y$. This set is defined as the image of the map $\Phi(x,y)=\frac{x+y}{2}.$ Under geometric conditions on $X$ and $Y$, we prove that the symmetry defect of $X$ and $Y$, which is the bifurcation set $B(X,Y)$ of the mapping $\Phi$, is an algebraic variety, characterized by a topological invariant. We introduce a hypersurface that approximates the set $B(X,Y)$ and we present an estimate for its degree. Moreover, for any two $n$-dimensional strong complete intersections $X,Y\subset \mathbb{C}^{2n-1}$ (including the case $X=Y$) we introduce a generic symmetry defect set $\tilde{B}(X,Y)$ of $X$ and $Y$, which is defined up to homeomorphism.
Beyond scaling base models with more data or parameters, fine-tuned adapters provide an alternative way to generate high fidelity, custom images at reduced costs. As such, adapters have been widely adopted by open-source communities, accumulating a database of over 100K adapters-most of which are highly customized with insufficient descriptions. This paper explores the problem of matching the prompt to a set of relevant adapters, built on recent work that highlight the performance gains of composing adapters. We introduce Stylus, which efficiently selects and automatically composes task-specific adapters based on a prompt's keywords. Stylus outlines a three-stage approach that first summarizes adapters with improved descriptions and embeddings, retrieves relevant adapters, and then further assembles adapters based on prompts' keywords by checking how well they fit the prompt. To evaluate Stylus, we developed StylusDocs, a curated dataset featuring 75K adapters with pre-computed adapter embeddings. In our evaluation on popular Stable Diffusion checkpoints, Stylus achieves greater CLIP-FID Pareto efficiency and is twice as preferred, with humans and multimodal models as evaluators, over the base model. See stylus-diffusion.github.io for more.
Visual control policies can encounter significant performance degradation when visual conditions like lighting or camera position differ from those seen during training -- often exhibiting sharp declines in capability even for minor differences. In this work, we examine robustness to a suite of these types of visual changes for RGB-D and point cloud based visual control policies. To perform these experiments on both model-free and model-based reinforcement learners, we introduce a novel Point Cloud World Model (PCWM) and point cloud based control policies. Our experiments show that policies that explicitly encode point clouds are significantly more robust than their RGB-D counterparts. Further, we find our proposed PCWM significantly outperforms prior works in terms of sample efficiency during training. Taken together, these results suggest reasoning about the 3D scene through point clouds can improve performance, reduce learning time, and increase robustness for robotic learners. Project Webpage: https://pvskand.github.io/projects/PCWM
ALMA (Atacama Large Millimetre/submillimetre Array) observations of the thermal emission from protoplanetary disc dust have revealed a wealth of substructures that could evidence embedded planets, but planet-driven spirals, one of the more compelling lines of evidence, remain relatively rare. Existing works have focused on detecting these spirals using methods that operate in image space. Here, we explore the planet detection capabilities of fitting planet-driven spirals to disc observations directly in visibility space. We test our method on synthetic ALMA observations of planet-containing model discs for a range of disc/observational parameters, finding it significantly outperforms image residuals in identifying spirals in these observations and is able to identify spirals in regions of the parameter space in which no gaps are detected. These tests suggest that a visibility-space fitting approach warrants further investigation and may be able to find planet-driven spirals in observations that have not yet been found with existing approaches. We also test our method on six discs in the Taurus molecular cloud observed with ALMA at 1.33 mm, but find no evidence for planet-driven spirals. We find that the minimum planet masses necessary to drive detectable spirals range from $\approx$ 0.03 to 0.5 $M_{\text{Jup}}$ over orbital radii of 10 to 100 au, with planet masses below these thresholds potentially hiding in such disc observations. Conversely, we suggest that planets $\gtrsim$ 0.5 to 1 $M_{\text{Jup}}$ can likely be ruled out over orbital radii of $\approx$ 20 to 60 au on the grounds that we would have detected them if they were present.
Due to the limitations of current optical and sensor technologies and the high cost of updating them, the spectral and spatial resolution of satellites may not always meet desired requirements. For these reasons, Remote-Sensing Single-Image Super-Resolution (RS-SISR) techniques have gained significant interest. In this paper, we propose Swin2-MoSE model, an enhanced version of Swin2SR. Our model introduces MoE-SM, an enhanced Mixture-of-Experts (MoE) to replace the Feed-Forward inside all Transformer block. MoE-SM is designed with Smart-Merger, and new layer for merging the output of individual experts, and with a new way to split the work between experts, defining a new per-example strategy instead of the commonly used per-token one. Furthermore, we analyze how positional encodings interact with each other, demonstrating that per-channel bias and per-head bias can positively cooperate. Finally, we propose to use a combination of Normalized-Cross-Correlation (NCC) and Structural Similarity Index Measure (SSIM) losses, to avoid typical MSE loss limitations. Experimental results demonstrate that Swin2-MoSE outperforms SOTA by up to 0.377 ~ 0.958 dB (PSNR) on task of 2x, 3x and 4x resolution-upscaling (Sen2Venus and OLI2MSI datasets). We show the efficacy of Swin2-MoSE, applying it to a semantic segmentation task (SeasoNet dataset). Code and pretrained are available on https://github.com/IMPLabUniPr/swin2-mose/tree/official_code
Apr 30 2024
cs.CL arXiv:2404.18923v1
We introduce Holmes, a benchmark to assess the linguistic competence of language models (LMs) - their ability to grasp linguistic phenomena. Unlike prior prompting-based evaluations, Holmes assesses the linguistic competence of LMs via their internal representations using classifier-based probing. In doing so, we disentangle specific phenomena (e.g., part-of-speech of words) from other cognitive abilities, like following textual instructions, and meet recent calls to assess LMs' linguistic competence in isolation. Composing Holmes, we review over 250 probing studies and feature more than 200 datasets to assess syntax, morphology, semantics, reasoning, and discourse phenomena. Analyzing over 50 LMs reveals that, aligned with known trends, their linguistic competence correlates with model size. However, surprisingly, model architecture and instruction tuning also significantly influence performance, particularly in morphology and syntax. Finally, we propose FlashHolmes, a streamlined version of Holmes designed to lower the high computation load while maintaining high-ranking precision.
In the classical Reinforcement Learning from Human Feedback (RLHF) framework, Proximal Policy Optimization (PPO) is employed to learn from sparse, sentence-level rewards -- a challenging scenario in traditional deep reinforcement learning. Despite the great successes of PPO in the alignment of state-of-the-art closed-source large language models (LLMs), its open-source implementation is still largely sub-optimal, as widely reported by numerous research studies. To address these issues, we introduce a framework that models RLHF problems as a Markov decision process (MDP), enabling the capture of fine-grained token-wise information. Furthermore, we provide theoretical insights that demonstrate the superiority of our MDP framework over the previous sentence-level bandit formulation. Under this framework, we introduce an algorithm, dubbed as Reinforced Token Optimization (\textttRTO), which learns the token-wise reward function from preference data and performs policy optimization based on this learned token-wise reward signal. Theoretically, \textttRTO is proven to have the capability of finding the near-optimal policy sample-efficiently. For its practical implementation, \textttRTO innovatively integrates Direct Preference Optimization (DPO) and PPO. DPO, originally derived from sparse sentence rewards, surprisingly provides us with a token-wise characterization of response quality, which is seamlessly incorporated into our subsequent PPO training stage. Extensive real-world alignment experiments verify the effectiveness of the proposed approach.
Apr 30 2024
math.PR arXiv:2404.18920v1
In [HHL+17] the authors showed existence and uniqueness of solutions to the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise that is white in time and rougher than white in space (in particular, its covariance is not a measure). Here we present a simple alternative to derive such results by considering the equations in the analytically weak sense, using either the variational approach or Krylov's $L^p$-theory. Various improvements are obtained as corollaries.
Junhao Cheng, Baiqiao Yin, Kaixin Cai, Minbin Huang, Hanhui Li, Yuxin He, Xi Lu, Yue Li, Yifei Li, Yuhao Cheng, Yiqiang Yan, Xiaodan Liang Apr 30 2024
cs.CV arXiv:2404.18919v1
Recent advances in diffusion models can generate high-quality and stunning images from text. However, multi-turn image generation, which is of high demand in real-world scenarios, still faces challenges in maintaining semantic consistency between images and texts, as well as contextual consistency of the same subject across multiple interactive turns. To address this issue, we introduce TheaterGen, a training-free framework that integrates large language models (LLMs) and text-to-image (T2I) models to provide the capability of multi-turn image generation. Within this framework, LLMs, acting as a "Screenwriter", engage in multi-turn interaction, generating and managing a standardized prompt book that encompasses prompts and layout designs for each character in the target image. Based on these, Theatergen generate a list of character images and extract guidance information, akin to the "Rehearsal". Subsequently, through incorporating the prompt book and guidance information into the reverse denoising process of T2I diffusion models, Theatergen generate the final image, as conducting the "Final Performance". With the effective management of prompt books and character images, TheaterGen significantly improves semantic and contextual consistency in synthesized images. Furthermore, we introduce a dedicated benchmark, CMIGBench (Consistent Multi-turn Image Generation Benchmark) with 8000 multi-turn instructions. Different from previous multi-turn benchmarks, CMIGBench does not define characters in advance. Both the tasks of story generation and multi-turn editing are included on CMIGBench for comprehensive evaluation. Extensive experimental results show that TheaterGen outperforms state-of-the-art methods significantly. It raises the performance bar of the cutting-edge Mini DALLE 3 model by 21% in average character-character similarity and 19% in average text-image similarity.
While the nondegenerate case is well-known, there are only few results on the existence of strong solutions to McKean-Vlasov SDEs with coefficients of Nemytskii-type in the degenerate case. We consider a broad class of degenerate nonlinear Fokker-Planck(-Kolmogorov) equations with coefficients of Nemytskii-type. This includes, in particular, the classical porous medium equation perturbed by a first-order term with initial datum in a subset of probability densities, which is dense with respect to the topology inherited from $L^1$, and, in the one-dimensional setting, the classical porous medium equation with initial datum in an arbitrary point $x\in\mathbb{R}$. For these kind of equations the existence of a Schwartz-distributional solution $u$ is well-known. We show that there exists a unique strong solution to the associated degenerate McKean-Vlasov SDE with time marginal law densities $u$. In particular, every weak solution to this equation with time marginal law densities $u$ can be written as a functional of the driving Brownian motion. Moreover, plugging any Brownian motion into this very functional yields a weak solution with time marginal law densities $u$.
In magnetic topological insulators, the surface states can exhibit a gap due to the breaking of time-reversal symmetry. Various experiments, while suggesting the existence of the surface gap, have raised questions about its underlying mechanism in the presence of different magnetic orderings. Here, we demonstrate that magnon-mediated electron-electron interactions, whose effects are not limited to the surfaces perpendicular to the magnetic ordering, can significantly influence surface states and their effective gaps. On the surfaces perpendicular to the spin quantization axis, many-body interactions can enhance the band gap to a degree that surpasses the non-interacting scenario. Then, on surfaces parallel to the magnetic ordering, we find that strong magnon-induced fermionic interactions can lead to features resembling a massless-like gap. These remarkable results largely stem from the fact that magnon-mediated interactions exhibit considerable long-range behavior compared to direct Coulomb interactions among electrons, thereby dominating the many-body properties at the surface of magnetic topological insulators.
Annette N. Carroll, Henrik Hirzler, Calder Miller, David Wellnitz, Sean R. Muleady, Junyu Lin, Krzysztof P. Zamarski, Reuben R. W. Wang, John L. Bohn, Ana Maria Rey, Jun Ye Long-range and anisotropic dipolar interactions profoundly modify the dynamics of particles hopping in a periodic lattice potential. Here, we report the realization of a generalized t-J model with dipolar interactions using a system of ultracold fermionic molecules with spin encoded in the two lowest rotational states. We systematically explore the role of dipolar Ising and spin-exchange couplings and the effect of motion on spin dynamics. The model parameters can be controlled independently, with dipolar couplings tuned by electric fields and motion regulated by optical lattices. Using Ramsey spectroscopy, we observed interaction-driven contrast decay that depends strongly both on the strength of the anisotropy between Ising and spin-exchange couplings and on motion. These observations are supported by theory models established in different motional regimes that provide intuitive pictures of the underlying physics. This study paves the way for future exploration of kinetic spin dynamics and quantum magnetism with highly tunable molecular platforms in regimes challenging for existing numerical and analytical methods, and it could shed light on the complex behaviors observed in real materials.
Electrostatically stabilized nanocrystals (NCs) and, in particular, quantum dots (QDs) hold promise for forming strongly coupled superlattices due to their compact and electronically conductive surface ligands. However, studies on the colloidal dispersion and interparticle interactions of electrostatically stabilized sub-10 nm NCs have been limited, hindering the optimization of colloidal stability and self-assembly. In this study, we employed small-angle X ray scattering (SAXS) experiments to investigate the interparticle interactions and arrangement of PbS QDs with thiostannate ligands (PbS-Sn2S64-) in polar solvents. The study reveals significant deviations from ideal solution behavior in electrostatically stabilized QD dispersions. Our results demonstrate that PbS-Sn2S64- QDs exhibit long-range interactions within the solvent, in contrast to the short-range steric repulsion characteristic of PbS QDs with oleate ligands (PbS-OA). Introducing highly charged multivalent electrolytes screens electrostatic interactions between charged QDs, reducing the length scale of the repulsive interactions. Furthermore, we calculate the second virial (B2) coefficients from SAXS data, providing insights into how surface chemistry, solvent, and size influence pair potentials. Finally, we explore the influence of long-range interparticle interactions of PbS-Sn2S64- QDs on the morphology of films produced by drying or spin-coating colloidal solutions. The long-range repulsive term of PbS-Sn2S64- QDs promotes the formation of amorphous films, and screening the electrostatic repulsion by addition of an electrolyte enables the formation of a crystalline film. These findings highlight the critical role of NC-NC interactions in tailoring the properties of functional nanomaterials.
In our recent works, we proposed a theory of turbulence via the mean field effect of an intermolecular potential, which in part relies on an empirically observed "equilibrated" behavior of the pressure variable in a low Mach number flow -- that is, while other variables may exhibit considerable variations at low Mach numbers, the pressure is (nearly) constant. At the same time, conventional kinetic theory does not offer a satisfactory explanation for such a behavior of the pressure variable, instead leading to an isentropic flow in the form of the usual compressible Euler equations. In the current work, we introduce a novel correction term into the pair correlation function of the BBGKY closure for the collision integral, which adjusts the density of incident or recedent pairs of particles depending on the macroscopic compression or expansion rate of the gas. Remarkably, this term does not affect the density and momentum transport equations, and manifests solely in the pressure transport equation. We also find that the effect of the novel term on the pressure dynamics matches the observed behavior -- that is, it tends to attenuate the acoustic waves and smooth out the pressure solution. It appears that the missing piece of the low Mach number puzzle has finally been identified.
Polar molecules confined in an optical lattice are a versatile platform to explore spin-motion dynamics based on strong, long-range dipolar interactions. The precise tunability of Ising and spin-exchange interactions with both microwave and dc electric fields makes the molecular system particularly suitable for engineering complex many-body dynamics. Here, we used Floquet engineering to realize interesting quantum many-body systems of polar molecules. Using a spin encoded in the two lowest rotational states of ultracold KRb molecules, we mutually validated XXZ spin models tuned by a Floquet microwave pulse sequence against those tuned by a dc electric field through observations of Ramsey contrast dynamics, setting the stage for the realization of Hamiltonians inaccessible with static fields. In particular, we observed two-axis twisting mean-field dynamics, generated by a Floquet-engineered XYZ model using itinerant molecules in 2D layers. In the future, Floquet-engineered Hamiltonians could generate entangled states for molecule-based precision measurement or could take advantage of the rich molecular structure for quantum simulation of multi-level systems.
We investigate the topological properties of hardcore bosons possessing nearest-neighbor repulsive interactions on a two-leg ladder. We show that by allowing dimerized interactions instead of hopping dimerization, the system exhibits topological phases and phase transitions under proper conditions. First, by assuming uniform hopping throughout the ladder, we show that when interaction along the legs are dimerized and the dimerization pattern is different in the legs, a trivial rung-Mott insulator to a topological bond order phase transition occurs as a function of the dimerization strength. However, for a fixed dimerization strength, the system exhibits a topological to trivial phase transition with increase in the rung hopping. A completely different scenario appears when the rung interaction is turned on. We obtain that for a ladder with uniform hopping, the repulsive interaction either turns the topological phase into a trivial rung-Mott insulator or a charge density wave phase. Such feature is absent when the dimerization pattern in the nearest neighbour interaction is considered to be identical in both the legs of the ladder. We numerically obtain the ground state properties and show the signatures of topological phase transition through Thouless charge pumping.
Speculative decoding has demonstrated its effectiveness in accelerating the inference of large language models while maintaining a consistent sampling distribution. However, the conventional approach of training a separate draft model to achieve a satisfactory token acceptance rate can be costly. Drawing inspiration from early exiting, we propose a novel self-speculative decoding framework \emphKangaroo, which uses a fixed shallow sub-network as a self-draft model, with the remaining layers serving as the larger target model. We train a lightweight and efficient adapter module on top of the sub-network to bridge the gap between the sub-network and the full model's representation ability. It is noteworthy that the inference latency of the self-draft model may no longer be negligible compared to the large model, necessitating strategies to increase the token acceptance rate while minimizing the drafting steps of the small model. To address this challenge, we introduce an additional early exiting mechanism for generating draft tokens. Specifically, we halt the small model's subsequent prediction during the drafting phase once the confidence level for the current token falls below a certain threshold. Extensive experiments on the Spec-Bench demonstrate the effectiveness of Kangaroo. Under single-sequence verification, Kangaroo achieves speedups up to $1.68\times$ on Spec-Bench, outperforming Medusa-1 with 88.7\% fewer additional parameters (67M compared to 591M). The code for Kangaroo is available at https://github.com/Equationliu/Kangaroo.
Braneshop, and
the US National Science Foundation.
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