The one-dimensional hard-rod model describes impenetrable bosons with finite diameter, extending the Lieb-Liniger model to systems with excluded volume interactions. Here, we investigate the thermodynamics of quantum hard rods using Yang-Yang theory, path integral quantum Monte Carlo calculations, and Tomonaga-Luttinger liquid theory. We first discuss the behavior of characteristic thermodynamic quantities, exhibiting deviations to the Lieb-Liniger model for sufficiently high densities, with excellent agreement between analytical and numerical results. We then show that the hard-rod model exhibits Tomonaga-Luttinger liquid behavior across a wide range of parameters, at zero and finite temperature, as unveiled by correlation functions. The Luttinger parameter and thermal length can be extracted by fitting correlation functions to Tomonaga-Luttinger liquid theory, hence demonstrating a robust method for thermometry. This work provides a comprehensive study of strongly correlated hard-rod systems at finite temperatures, with applications to quantum wires, spin chains, and ultracold atoms.

Recently, it was shown that quantum interference in a system containing a polarized and an unpolarized emitter can allow directional emission of photons into a circulating cavity. Here we ask whether high directionality of photon emission in this system implies a high degree of quantum correlation between the two emitters. We show that the answer is a qualified “yes,” with photon emission directionality and emitter-emitter entanglement showing a monotonic relationship over a broad parameter range. The relationship breaks down only in the limit of perfect directionality. Furthermore, under reasonable assumptions for experimental parameters and stability, we show that the statistics of measured directionality allow a reliable estimate of the concurrence. This result implies that directionality of photon emission in the state preparation stage can be used to determine the entanglement between the emitters, with potential applications to more generic cases including quantum networks.

Considering the emerging applications of quantum technologies, studying energy storage and usage at the quantum level is of great interest. In this context, there is a significant contemporary interest in studying ergotropy, the maximum amount of work that can be extracted unitarily from an energy-storing quantum device. Here, we propose a feedback-based quantum algorithm for ergotropy estimation using Lyapunov control techniques. By iteratively adjusting the strengths of applied drive fields, our algorithm achieves both unitary energy extraction and passive state preparation efficiently. Unlike previous approaches, this algorithm does not require any classical optimization, is resilient to cumulative errors, and eliminates the need for any time-consuming quantum state tomography. We validate these advantages via numerical simulations demonstrating robustness even under noisy conditions. Additionally, we experimentally implement the algorithm on up to three-qubit NMR registers, establishing its practical viability.

Herein, we present a polylogarithmic decomposition method to load the matrix from the linearized one-dimensional Burgers' equation onto a quantum computer. First, we use the Carleman linearization method to map the nonlinear Burgers' equation into an infinite linear system of equations, which is subsequently truncated to order $\alpha$. This new finite linear system is then embedded into a larger system of equations with the key property that its matrix can be decomposed into a linear combination of $\mathcal{O}({log}_2{n}_t+{\alpha }^2{log}_2{n}_x)$ terms for $n_t$ time steps and $n_x$ spatial grid points. While the terms in this linear combination are not unitary, each can be implemented using a simple block-encoding procedure. A numerical simulation is performed by combining our approach with the variational quantuam linear solver, demonstrating that accurate solutions are possible. Finally, a resource estimate shows that the upper bound of the Clifford- and $T$-gate counts scale like $\mathcal{O}\left[\alpha {\left({log}_2{n}_x\right)}^2\right]$ and $\mathcal{O}\left[{\left({log}_2{n}_x\right)}^2\right]$, respectively. This is therefore the first explicit polylogarithmic data loading method with respect to $n_x$ and $n_t$ for a Carleman linearized system.

Quantum multiparameter estimation has important applications in quantum imaging and distributed sensor networks. In this work, we propose a displacement-enhanced interferometric scheme for the simultaneous estimation of two independent phases, based on a conventional three-mode linear interferometer supplemented with three displacement operations (DOs). We show that the per-photon quantum Cramér-Rao bound (QCRB) can be minimized by optimizing the amplitudes and arguments of the DOs and by enhancing the entanglement of the input signal states. Squeezed probe states yield improved phase-estimation precision due to their reduced noise, and this advantage can be further amplified by the DOs, especially for the input two-mode squeezed vacuum state. In the ideal case, optimal per-photon QCRB can be achieved by stabilizing the DO parameters for most signal states, except for single-mode squeezed inputs. When photon loss is included, the optimal DO settings for two coherent-state inputs remain insensitive to loss, whereas for other signal states, the DO parameters must be tuned within a finite range, increasing the experimental complexity. Our results provide useful guidance for practical quantum-enhanced multiparameter estimation.

We study interaction-induced bound states in a system of ultracold bosons loaded into the states with orbital angular momentum in a one-dimensional staggered lattice of rings. We consider the hard-core limit and strong nearest-neighbor interactions such that two particles in next-neighboring sites are bound. Focusing on the manifold of such bound states, we derive the corresponding effective model for doublons. With orbital angular momentum $l=1$, the original physical system is described as a Creutz ladder by using the circulations as a synthetic dimension and the effective model obtained consists of two Su-Schrieffer-Heeger (SSH) chains and two Bose-Hubbard chains. Therefore, the system can exhibit topologically protected edge states. In a structure that alternates $l=1$ and $l=0$ states, the original system can be mapped to a diamond chain. In this case, the effective doublon model corresponds to a Creutz ladder with extra vertical hoppings between legs and can be mapped to two SSH chains if all the couplings in the original system are equal. Spatially tuning the amplitude of the couplings destroys the inversion symmetry of these SSH chains, but enables the appearance of multiple flat bands.

We propose a stochastic Schrödinger equation (SSE) approach to investigate the dynamics of giant atoms coupled to a waveguide, addressing two critical gaps in existing research, namely, insufficient exploration of continuous coupling and multiple excitations. A key finding is that continuous coupling, unlike discrete coupling at finite points, breaks the constant phase difference condition, thereby weakening the interference effects in giant-atom–waveguide systems. In addition, a key technical advantage of the SSE approach is that auto- and cross-correlation functions can directly reflect the complex photon emission-absorption processes and time-delay effects in giant-atom–waveguide systems. Moreover, the SSE approach also naturally handles multiple excitations, without increasing equation complexity as the number of excitations grows. This feature enables the investigation of multiexcitation initial states of the waveguide, such as thermal and squeezed initial states. Overall, our approach provides a powerful tool for studying the dynamics of giant atoms coupled to a waveguide, particularly for continuous coupling and multiexcitation systems.

Finding the solution to linear systems is at the heart of many applications in science and technology. Over the years, a number of algorithms have been proposed to solve this problem on a digital quantum device, yet most of these are too demanding to be applied to the current noisy hardware. In this work, an original algorithmic procedure to solve the quantum linear system problem (QLSP) is presented, which combines ideas from variational quantum algorithms and the framework of classical shadows. The result is the shadow quantum linear solver (SQLS), a quantum algorithm solving the QLSP while avoiding the need for large controlled unitaries and requiring a number of qubits that is logarithmic in the system size. In particular, our heuristics show an exponential advantage of the SQLS in circuit execution per cost function evaluation when compared with other notorious variational approaches to solving linear systems of equations. We test the convergence of the SQLS on a number of linear systems, and the results highlight how the theoretical bounds on the number of resources used by the SQLS are conservative. Finally, we apply this algorithm to a physical problem of practical relevance by leveraging decomposition theorems from linear algebra to solve the discretized Laplace equation in a two-dimensional grid.

While variational quantum algorithms (VQAs) have demonstrated considerable success in unconstrained optimization, their application to constrained combinatorial problems face a trade-off. Penalty-based methods, despite their circuit simplicity, suffer from a fundamental limitation: inefficient sampling in vast infeasible regions. This often results in suboptimal solutions that violate constraints and impede convergence to high-quality results. In contrast, ansatz-based approaches enforce solution feasibility by design but require complex problem-specific circuits that are challenging to implement on current noisy intermediate-scale quantum devices. To overcome these limitations, we introduce an alternative VQA whose core innovation lies in a strategically designed loss function. This function offers a dual advantage. First, it is provably guaranteed that its global minimum corresponds uniquely to the optimal feasible solution, as this is achieved by ensuring universally higher loss values for all infeasible solutions. Second, it furnishes distinct computational pathways for feasible versus infeasible regions, thus creating clear and noncompeting guidance for the optimizer. As a result of these combined features, the algorithm's overall performance is significantly enhanced. Regarding hardware overhead, our design requires adding only an efficient validation oracle module to the penalty-based circuit, resulting in a circuit complexity significantly lower than that of ansatz-based approaches with their custom mixers. To validate the practical efficiency of our method, we empirically demonstrate its effectiveness by solving minimum vertex cover and maximum-independent-set problems on random graphs of varying small-scale sizes.

A pronounced geometric-phase (GP) effect is observed in the integral cross sections (ICSs) of the $\mu +{\mathrm{H}}_2{}^{+}$ reaction and is analyzed using the interaction-asymptotic region decomposition method within the thermal-collision-energy range of 0.17 to 0.4 eV. Based on topological analysis, two distinct reaction pathways are identified, with a significant GP effect arising from strong interference between these pathways. Wave-function analysis indicates that the GP effect originates from an increased nodal structure around the conical-intersection (CI) region. Further investigation reveals that the time delay of the reactive resonance state is closely correlated with the amplitude of the wave function near the CI region. These results enable sensitive probing of the GP effect using the $\mu$ atom from the perspective of the ICS.

Ideal quantum measurement requires divergent thermodynamic resources. This is a consequence of the third law of thermodynamics, which prohibits the preparation of the measurement pointer in a fully erased, pure state required for the acquisition of perfect, noiseless measurement information. In this work, we investigate the consequences of finite resources in the emergence of intersubjectivity as a model for measurement processes with multiple observers. Here, intersubjectivity refers to a condition in which observers agree on the observed outcome (agreement), and their local random variables exactly reproduce the original random variable for the system observable (probability reproducibility). While agreement and reproducibility are mutually implied in the case of ideal measurement, finite thermodynamic resources constrain each of them. Starting from the third law of thermodynamics, we derive how the achievability of ideal intersubjectivity is affected by restricted thermodynamic resources. Specifically, we establish a no-go theorem concerning perfect intersubjectivity and present a deviation metric to account for the influence of limited resources. We further present attainable bounds for the agreement and bias that are exclusively dependent on the initial state of the environment. In addition, we show that either by cooling or coarse graining, we can approximate ideal intersubjectivity even with finite resources. This work bridges quantum thermodynamics and the emergence of classicality in the form of intersubjectivity.

We demonstrate that non-Markovian effects inherent in a central-spin quantum battery model (CSQB) can be efficiently exploited to significantly improve the key performance metrics of QB. Based on the exact analytical derivation of the CSQB, we show that by tuning the effective spin-bath coupling strength or the size of the spin bath, one can enhance the charging dynamics and steady-state performance of QB, including its charging power and extractable work. These results establish non-Markovianity as a critical resource for optimizing the performance of quantum thermodynamic devices and advance the understanding of quantum thermodynamics in spin-bath models.

As quantum chips scale up for large-scale computation, hardware defects become inevitable and must be carefully addressed. In this work we introduce Halma, a defect mitigation technique empowered by an expanded native gate set that incorporates the $\mathrm{i}\mathrm{SWAP}$ gate alongside the conventional $\mathrm{CNOT}$ gate. Halma emerges as a supplementary technique within the defect mitigation toolbox, offering effective mitigation of ancilla qubit defects encountered during surface code stabilizer measurements while maintaining compatibility with existing superstabilizer-based methodologies. Halma introduces zero reduction in the spacelike distance of the code without further sacrifice to the timelike distance. Numerical simulation suggests that in comparison to previous methods, Halma could provide an order of magnitude improvement in the average logical error rate under realistic experimental settings, leading to a $\sim 3\times$ reduction in the footprint of a teraquop. These results clearly demonstrate the capability of Halma in easing the near-term realization of fault-tolerant quantum computing on hardware with fabrication defects and exemplifies how leveraging intrinsic hardware capabilities can enhance quantum hardware performance.

We demonstrate that charge teleportation serves as a superior observable for quantum energy teleportation–based cryptographic primitives. While following the local operations and classical communication (LOCC) protocol structure of earlier proposals [S. Dolev, K. Ikeda, and Y. Oz, arXiv:2506.02054], we show that decoding key bits via local charge rather than energy provides exact bit symmetry and enhanced robustness: By LOCC on an entangled many-body ground state, Alice's one-bit choice steers the sign of a local charge shift at Bob, which directly encodes the key bit. Relative to energy teleportation schemes, the charge signal is bit symmetric, measured in a single basis, and markedly more robust to realistic noise and model imperfections. We instantiate the protocol on transverse-field Ising models, star-coupled, and one-dimensional chain, obtain closed-form results for two qubits, and for larger systems confirm performance via exact diagonalization, circuit-level simulations, and a proof-of-principle hardware run. We quantify resilience to classical bit flips and local quantum noise, identifying regimes where sign integrity, and hence key correctness, is preserved. These results position charge teleportation as a practical, low-rate quantum key distribution primitive compatible with near-term platforms.

High-dimensional quantum systems leverage an expanded Hilbert space to enhance resilience against decoherence and noise. However, standard quantum teleportation is fundamentally limited by the quadratic growth of measurement complexity and high classical communication overhead, requiring the resolution of $d^2$ Bell states and $2{log}_{2}d$ classical bits. In this study, we propose a resource-efficient high-dimensional coherence teleportation (REHDCT) protocol. By designing $d$ sets of specialized positive operator-valued measure (POVM) bases, our protocol achieves a 50% reduction in classical communication by utilizing one of the $d$ designed POVM sets, which effectively scales the measurement complexity from $O\left(d^2\right)$ to $O\left(d\right)$. Furthermore, we demonstrate that by utilizing initial phase engineering to align the target qudit with the measurement basis, theoretically perfect teleportation of quantum coherence can be achieved for arbitrary qudit states. A quantitative robustness analysis reveals that the protocol remains highly resilient to operational errors, maintaining an efficiency above 99.6% even under a 0.1-rad phase deviation for $d=16$. Our analysis under various noise models (amplitude damping, phase flip, depolarizing, and dit-flip) confirms that high-dimensional systems exhibit an expanding quantum advantage window as dimensionality increases. Notably, under dit-flip noise, perfect coherence teleportation can be restored through the optimal selection of the POVM basis. These findings establish REHDCT as a practical, hardware-friendly framework for resource-efficient quantum communication in future high-dimensional networks.

As quantum computers scale toward millions of physical qubits, it becomes essential to robustly encode individual logical qubits to ensure fault tolerance under realistic noise. A high-quality foundational encoding allows future compilation techniques and heuristics to build on optimal or near-optimal layouts, improving scalability and error resilience. In this work, we synthesize a one-dimensional shuttling-bus architecture for the rotated surface code, leveraging coherent spin-qubit shuttling, following a methodology we name quantum reverse mapping. We formulate a mixed-integer optimization model that yields optimal solutions with relatively low execution time for small code distances, and propose a scalable heuristic that matches optimal results while maintaining linear computational complexity. We evaluate the synthesized architecture using architectural metrics, such as shuttling distance and cycle time, and full quantum simulations under realistic noise models, showing that the proposed design can sustain logical error rates as low as $2\times {10}^{-10}$ per round at code distance 21, showcasing its feasibility for scalable quantum error correction in spin-based quantum processors.

The partition search algorithm (PSA) and iterative quantum optimization with an adaptive problem (IQOAP) are leading variational quantum algorithms for solving the shortest vector problem (SVP). However, each has limitations that restrict its practical impact. IQOAP suffers from ineffective iterations that fail to update the lattice basis, whereas PSA's static partitioning leads to oversized search spaces. In this work, we propose the iterative partition search algorithm (IPSA), which systematically addresses these drawbacks by integrating a “1-tailed search spaces” with a dynamic, stack-managed iterative process. Specifically, the “1-tailed” strategy ensures that every successful execution yields an effective lattice basis update, thereby eliminating the ineffective iterations associated with IQOAP. Concurrently, the dynamic iterative process reduces the required a qubit count, thereby avoiding the limitation of an oversized search space inherent to PSA. We validate IPSA on the Baihua superconducting quantum processor via the quafu platform. Small-scale real hardware experiments demonstrate that, compared to PSA, IPSA achieves a 14-fold increase in success rate at a cost of less than two times the total circuit depth. Conversely, compared to IQOAP, IPSA reduces the total circuit depth by 82.7% while achieving approximately 2.5 times its success rate. Furthermore, we also conduct numerical simulations whose results are in good agreement with the experimental findings and extend our analysis.