Papers

We introduce a generalized mass-horizon relation applicable to cosmological horizons. This formulation provides a unified framework for deriving a broad class of Bekenstein entropy extensions motivated by statistical mechanics, quantum gravity, and phenomenological considerations, through the application of the Clausius relation together with the Hawking temperature. We further introduce this notion as a foundational framework for constructing generalized entropy forms that remain consistent with thermodynamic laws and the holographic principle.

In quantum systems with infinitely many degrees of freedom, states can be infinitely entangled across a pair of subsystems, but are there different forms of infinite entanglement? To understand entanglement in such systems, we use a framework in which subsystems are described by von Neumann algebras on the full system's Hilbert space. Although this approach has been known for over 50 years, an operational justification has been missing so far. We resolve this by deriving the von Neumann algebraic description of subsystems from operational axioms. This raises the question of how physical properties of the subsystem relate to algebraic properties. Our main result shows a surprisingly strong connection: The type classification of von Neumann algebras (types I, II, III, and their respective subtypes) is in one-to-one correspondence with a family of operational entanglement properties. For instance, Connes' classification of type III factors can be formulated in terms of the smallest achievable error when "embezzling" entanglement from the system. Our findings promote the type classification from algebraic bookkeeping to a classification of infinite quantum systems based on the kind of infinite entanglement that they support.

We introduce a general model of stochastically generated matrix product states (MPS) in which the local tensors share a common distribution and form a strictly stationary sequence, without requiring spatial independence. Under natural conditions on the associated transfer operators, we prove the existence of thermodynamic limits of expectations of local observables and establish almost-sure exponential decay of two-point correlations. In the homogeneous (random translation-invariant) case, for any error tolerance in probability, the two-point function decays exponentially in the distance between the two sites, with a deterministic rate. In the i.i.d. case, the exponential decay still holds with a deterministic rate, with the probability approaching one exponentially fast in the distance. For strictly stationary ensembles with decaying spatial dependence, the correlation decay quantitatively reflects the mixing profile: ($\rho$)-mixing yields polynomial bounds with high probability, while stretched-exponential (resp. exponential) decay in ($\rho$) (resp. ($\beta$)) yields stretched-exponential (resp. exponential) decay of the two-point function, again with correspondingly strong high-probability guarantees. Altogether, the framework unifies and extends recent progress on stationary ergodic and Gaussian translation-invariant ensembles, providing a transfer-operator route to typical correlation decay in random MPS.

We present explicit quantum channels with strictly sub-additive minimum output Rényi entropy for all $p>1$, improving upon prior constructions which handled $p>2$. Our example is provided by explicit constructions of linear subspaces with high geometric measure of entanglement. This construction applies in both the bipartite and multipartite settings. As further applications, we use our construction to find entanglement witnesses with many highly negative eigenvalues, and to construct entangled mixed states that remain entangled after perturbation.

Quantum advantage in computation refers to the existence of computational tasks that can be performed efficiently on a quantum computer but cannot be efficiently simulated on any classical computer. Identifying the precise boundary of efficient classical simulability is a central challenge and motivates the development of new simulation paradigms. In this paper, we introduce polyhedral classical simulators, a framework for classical simulation grounded in polyhedral geometry. This framework encompasses well-known methods such as the Gottesman-Knill algorithm, while also extending naturally to more recent models of quantum computation, including those based on magic states and measurement-based quantum computation. We show how this framework unifies and extends existing simulation methods while at the same time providing a geometric roadmap for pushing the boundary of efficient classical simulation further.

Certain types of quantum computing platforms, such as those realized using Rydberg atoms or Kerr-cat qubits, are natively more susceptible to Pauli-Z noise than Pauli-X noise, or vice versa. On such hardware, it is useful to ensure that computations use only gates that maintain the Z-bias (or X-bias) in the noise. This is so that quantum error-correcting codes tailored for biased-noise models can be used to provide fault-tolerance on these platforms. In this paper, we follow up on the recent work of Fellous-Asiani et al. (npj Quantum Inf., 2025) in studying the structure and properties of bias-preserving gates. Our main contributions are threefold: (1) We give a novel characterization of Z-bias-preserving gates based on their decomposition as a linear combination of Pauli operators. (2) We show that any Z-bias-preserving gate can be approximated arbitrarily well using only gates from the set {X,R_z(\theta),CNOT,CCNOT}, where \theta is any irrational multiple of 2\pi. (3) We prove, by drawing a connection with coherence resource theory, that any Z-bias-preserving logical operator acting on the logical qubits of a Calderbank-Shor-Steane (CSS) code can be realized by applying Z-bias-preserving gates on the physical qubits. Along the way, we also demonstrate that Z-bias-preserving gates are far from being universal for quantum computation.

In 2021, Chen, Liu, and Zhandry presented an efficient quantum algorithm for the average-case $\ell_\infty$-Short Integer Solution ($\mathrm{SIS}^\infty$) problem, in a parameter range outside the normal range of cryptographic interest, but still with no known efficient classical algorithm. This was particularly exciting since $\mathrm{SIS}^\infty$ is a simple problem without structure, and their algorithmic techniques were different from those used in prior exponential quantum speedups. We present efficient classical algorithms for all of the $\mathrm{SIS}^\infty$ and (more general) Constrained Integer Solution problems studied in their paper, showing there is no exponential quantum speedup anymore.

In this work, we study the task of encoding logical information via a noisy quantum circuit. It is known that at superlogarithmic depth, the output of any noisy circuit without reset gates or intermediate measurements becomes indistinguishable from the maximally mixed state, implying that all input information is destroyed. This raises the question of whether there is a low-depth regime where information is preserved as it is encoded into an error-correcting codespace by the circuit. When considering noisy random encoding circuits, our numerical simulations show that there is a sharp phase transition at a critical depth of order $p^{-1}$, where $p$ is the noise rate, such that below this depth threshold quantum information is preserved, whereas after this threshold it is lost. Furthermore, we rigorously prove that this is the best achievable trade-off between depth and noise rate for any noisy circuit encoding a constant rate of information. Thus, random circuits are optimal noisy encoders in this sense.

Optically-active spin qubits have emerged as powerful quantum sensors capable of nanoscale magnetometry, yet conventional coherent sensing approaches are ultimately limited by the coherence time of the sensor, typically precluding detection in the sub-MHz regime. We present a broadly applicable fluorescence-encoding method that circumvents coherence-time constraints by transducing time-varying magnetic fields directly into modulated fluorescence signals. Using nitrogen-vacancy centers in diamond as a model system, we demonstrate shot-noise-limited sensitivity for AC magnetic fields spanning near-DC to MHz frequencies, with detection bandwidth tunable via optical excitation power. The technique captures complete spectral information in a single measurement, eliminating the need for point-by-point frequency scanning, and allows phase-sensitive multi-frequency detection with Hz-level resolution. This approach transforms quantum sensors into atomic-scale spectrum analyzers, with immediate applications for low-frequency RF communication, zero-field NMR, and bioelectronic sensing. Our approach is broadly applicable to the expanding class of optically-active spin qubits, including molecular systems and fluorescent proteins, opening new sensing regimes previously inaccessible to coherent techniques

In the framework of quantum mechanics over a quadratic extension of the ultrametric field of p-adic numbers, we introduce a notion of tensor product of p-adic Hilbert spaces. To this end, following a standard approach, we first consider the algebraic tensor product of p-adic Hilbert spaces. We next define a suitable norm on this linear space. It turns out that, in the p-adic framework, this norm is the analogue of the projective norm associated with the tensor product of real or complex normed spaces. Eventually, by metrically completing the resulting p-adic normed space, and equipping it with a suitable inner product, we obtain the tensor product of p-adic Hilbert spaces. That this is indeed the correct p-adic counterpart of the tensor product of complex Hilbert spaces is also certified by establishing a natural isomorphism between this p-adic Hilbert space and the corresponding Hilbert-Schmidt class. Since the notion of subspace of a p-adic Hilbert space is highly nontrivial, we finally study the tensor product of subspaces, stressing both the analogies and the significant differences with respect to the standard complex case. These findings should provide us with the mathematical foundations necessary to explore quantum entanglement in the p-adic setting, with potential applications in the emerging field of p-adic quantum information theory.

We investigate the mechanisms necessary for the stabilization of complex quantum correlations by exploring dissipative couplings to nonreciprocal reservoirs. We analyze the role of locality in the coupling between the environment and the quantum system of interest, as we consider either local couplings throughout the system, or a single global coupling. We contrast the results obtained for the two scenarios in which a chain of strongly interacting hardcore bosonic atoms is coupled directly to Markovian kinetic dissipative processes, or experiences effective dissipation through the mediation of the field of a lossy optical cavity. To investigate the dissipative dynamics of the many-body quantum systems considered we perform numerical simulations employing matrix product states methods. We show that by coupling atomic tunneling terms to the global field of a dissipative cavity we can stabilize at long times both finite currents and current-current correlations throughout the atomic chain. This is in contrast to the setup in which dissipation acts directly via local tunneling processes, where currents arise in a narrow region of the system and the current-current correlations are rapidly decaying.

We investigate the computational complexity of the Local Hamiltonian (LH) problem and the approximation of the Quantum Partition Function (QPF), two central problems in quantum many-body physics and quantum complexity theory. Both problems are known to be QMA-hard, and under the widely believed assumption that $\mathsf{BQP} \neq \mathsf{QMA}$, no efficient quantum algorithm exits. The best known quantum algorithm for LH runs in $O\bigl(2^{\frac{n}{2}(1 - o(1))}\bigr)$ time, while for QPF, the state-of-the-art algorithm achieves relative error $\delta$ in $O^\ast\bigl(\frac{1}{\delta}\sqrt{\frac{2^n}{Z}}\bigr)$ time, where $Z$ denotes the value of the partition function. A nature open question is whether more efficient algorithms exist for both problems. In this work, we establish tight conditional lower bounds showing that these algorithms are nearly optimal. Under the plausible Quantum Strong Exponential Time Hypothesis (QSETH), we prove that no quantum algorithm can solve either LH or approximate QPF significantly faster than $O(2^{n/2})$, even for 3-local Hamiltonians. In particular, we show: 1) 3-local LH cannot be solved in time $O(2^{\frac{n}{2}(1-\varepsilon)})$ for any $\varepsilon > 0$ under QSETH; 2) 3-local QPF cannot be approximated up to any constant relative error in $O(2^{\frac{n}{2}(1-\varepsilon)})$ time for any $\varepsilon > 0$ under QSETH; and 3) we present a quantum algorithm that approximates QPF up to relative error $1/2 + 1/\mathrm{poly}(n)$ in $O^\ast(2^{n/2})$ time, matching our conditional lower bound. Notably, our results provide the first fine-grained lower bounds for both LH and QPF with fixed locality. This stands in sharp contrast to QSETH and the trivial fine-grained lower bounds for LH, where the locality of the SAT instance and the Hamiltonian depends on the parameter $\varepsilon$ in the $O(2^{\frac{n}{2}(1-\varepsilon)})$ running time.

Quantum state transfer is a fundamental requirement for scalable quantum computation, where fast and reliable communication between distant subsystems is essential. In this work, we present a protocol for quantum state transfer in linear Ising chains. Starting from a perfect state transfer scheme via a Heisenberg Hamiltonian with inhomogeneous couplings, we adapt it for architectures implementing the transverse-field Ising model by encoding the information in domain walls. The resulting linear Ising chain makes quantum transport experiments accessible to many platforms for analog quantum simulation. We test the protocol for 1-, 2-, and 3- spin states, obtaining high transfer fidelities of up to 0.99 and study the accuracy dependence on the domain wall approximation. These results are the first step in paving the way for an experimental implementation of the protocol.

Long-distance quantum communication requires reliable entanglement distribution, but direct generation with protocols such as Barrett–Kok suffers from exponentially decreasing success probability with distance, making it impractical over hundreds of kilometers. Quantum repeaters address this by segmenting the channel and combining entanglement generation, swapping, and purification. In this work, we present a simulation framework for chain-based repeaters under continuous-time depolarizing noise. Our model implements heralded entanglement generation, Bell-state swapping, and multi-round purification, with configurable chain length, noise levels, and purification depth. Numerical results highlight how memory decoherence constrains performance, how purification mitigates fidelity loss, and how time and entanglement costs scale with distance. While simplified, the framework offers a flexible tool for exploring trade-offs in repeater design and provides a basis for extensions toward more complex network scenarios.

Driven by the growing demand in the energy, medical, and industrial sectors, we investigate a hydrogen isotope separation technique that offers both a high separation factor and economic feasibility. Our findings reveal that filtering isotopes through two-dimensional graphene layers provides an exceptionally efficient quantum-mechanical method for isotope separation. Using a recently developed analytical pairwise potential between hydrogen isotopes and carbon atoms in graphene, we examine the classical trajectories of isotopes near the graphene layer, as well as the quantum-mechanical tunneling properties of isotopes through the graphene layer. Using various quantum-mechanical methods, we calculate both the isotope tunneling probabilities and the quantum-mechanical isotope sticking probabilities. Our study shows that quantum filtering through graphene layers can be an effective technique for enriching deuterium by separating it from protium.

A simple way to calculate Rabi frequencies is outlined for interactions of atomic or nuclear multipole moments with laser fields that focuses on their relative geometry. The resulting expression takes the form of a dot product between the laser polarization and a vector spherical harmonic, thereby naturally connecting to the multipole's far-field spontaneous-emission pattern and providing a way to visualize the interaction. Since the vector spherical harmonics are not yet a standard tool in quantum science, their relevant properties are reviewed. This approach is illustrated in the calculation of a variety of beam effects, yielding both perturbative corrections and some nontrivial cases with non-vanishing coupling.

Fine-grained spectral properties of quantum Hamiltonians, including both eigenvalues and their multiplicities, provide useful information for characterizing many-body quantum systems as well as for understanding phenomena such as topological order. Extracting such information with small additive error is $\#\textsf{BQP}$-complete in the worst case. In this work, we introduce QFAMES (Quantum Filtering and Analysis of Multiplicities in Eigenvalue Spectra), a quantum algorithm that efficiently identifies clusters of closely spaced dominant eigenvalues and determines their multiplicities under physically motivated assumptions, which allows us to bypass worst-case complexity barriers. QFAMES also enables the estimation of observable expectation values within targeted energy clusters, providing a powerful tool for studying quantum phase transitions and other physical properties. We validate the effectiveness of QFAMES through numerical demonstrations, including its applications to characterizing quantum phases in the transverse-field Ising model and estimating the ground-state degeneracy of a topologically ordered phase in the two-dimensional toric code model. We also generalize QFAMES to the setting of mixed initial states. Our approach offers rigorous theoretical guarantees and significant advantages over existing subspace-based quantum spectral analysis methods, particularly in terms of the sample complexity and the ability to resolve degeneracies.

State merging is a fundamental protocol in quantum information theory that generalizes quantum teleportation. Traditionally, it is achieved by local operations on shared entanglement and classical communication. In this work, we study state merging done with alpha-bits, a versatile quantum communication resource weaker than qubits. We study alpha-bit state merging with and without catalytic entanglement, and we find a potential gap between the rates of alpha-bits consumed. In light of our result, we discuss how to interpret entanglement wedge reconstruction in AdS/CFT in terms of alpha-bit state merging

To overcome the bottleneck of classical path planning schemes in solving NP problems and address the predicament faced by current mainstream quantum path planning frameworks in the Noisy Intermediate-Scale Quantum (NISQ) era, this study attempts to construct a quantum path planning solution based on parallel Quantum Approximate Optimization Algorithm (QAOA) architecture. Specifically, the grid path planning problem is mapped to the problem of finding the minimum quantum energy state. Two parallel QAOA circuits are built to simultaneously execute two solution processes, namely connectivity energy calculation and path energy calculation. A classical algorithm is employed to filter out unreasonable solutions of connectivity energy, and finally, the approximate optimal solution to the path planning problem is obtained by merging the calculation results of the two parallel circuits. The research findings indicate that by setting appropriate filter parameters, quantum states corresponding to position points with extremely low occurrence probabilities can be effectively filtered out, thereby increasing the probability of obtaining the target quantum state. Even when the circuit layer number p is only 1, the theoretical solution of the optimal path coding combination can still be found by leveraging the critical role of the filter. Compared with serial circuits, parallel circuits exhibit a significant advantage, as they can find the optimal feasible path coding combination with the highest probability.

The dynamics of hybrid systems – i.e. ones in which classical and quantum degrees of freedom co-exist and interact – feature both diffusion in the classical sector and decoherence in the quantum state. In this article, we will consider the simple setup of a classical damped oscillator interacting with its quantum counterpart and show that, for any initial state, the dynamics flows to a unique (non-equilibrium) steady state, which we compute explicitly. To do so, we make use of a useful mapping between hybrid and classical diffusive dynamics, which we characterise in detail in the master equation formalism.

A quantum error-correcting code with a nonzero error threshold undergoes a mixed-state phase transition when the error rate reaches that threshold. We explore this phase transition for Haar-random quantum codes, in which the logical information is encoded in a random subspace of the physical Hilbert space. We focus on the spectrum of the encoded system density matrix as a function of the rate of uncorrelated, single-qudit errors. For low error rates, this spectrum consists of well-separated bands, representing errors of different weights. As the error rate increases, the bands for high-weight errors merge. The evolution of these bands with increasing error rate is well described by a simple analytic ansatz. Using this ansatz, as well as an explicit calculation, we show that the threshold for Haar-random quantum codes saturates the hashing bound, and thus coincides with that for random $\textit{stabilizer}$ codes. For error rates that exceed the hashing bound, typical errors are uncorrectable, but postselected error correction remains possible until a much higher $\textit{detection}$ threshold. Postselection can in principle be implemented by projecting onto subspaces corresponding to low-weight errors, which remain correctable past the hashing bound.

Lattice gauge theories (LGTs) represent one of the most ambitious goals of quantum simulation. From a practical implementation perspective, non-Abelian theories present significantly tougher challenges than Abelian LGTs. However, it is unknown whether this is also reflected in increased values of quantum resources relating to the complexity of simulating quantum many-body models. Here, we compare three paradigmatic measures of quantum resources – stabilizer Rényi entropy, generalized geometric measure of entanglement, and fermionic antiflatness – for pure-gauge theories on a ladder with Abelian $\mathbb{Z}_N$ as well as non-Abelian $D_3$ and SU(2) gauge symmetries. We find that non-Abelian symmetries are not necessarily inherently harder to simulate than Abelian ones, but rather the required quantum resources depend nontrivially on the interplay between the group structure, superselection sector, and encoding of the gauge constraints. Our findings help indicate where quantum advantage could emerge in simulations of LGTs, both in NISQ and fault-tolerant eras.

Here we describe an approach for simulating electronic structure on quantum computers with significantly lower asymptotic complexity than prior work. The approach uses a real-space first-quantised representation of the molecular Hamiltonian which we propagate using high-order product formulae. Essential for this low complexity is the use of a technique similar to the fast multipole method for computing the Coulomb operator with $\widetilde{\cal O}(\eta)$ complexity for a simulation with $\eta$ particles. We show how to modify this algorithm so that it can be implemented on a quantum computer. We ultimately demonstrate an approach with $t(\eta^{4/3}N^{1/3} + \eta^{1/3} N^{2/3} ) (\eta Nt/\epsilon)^{o(1)}$ gate complexity, where $N$ is the number of grid points, $\epsilon$ is target precision, and $t$ is the duration of time evolution. This is roughly a speedup by ${\cal O}(\eta)$ over most prior algorithms. We provide lower complexity than all prior work for $N<\eta^7$ (the regime of practical interest), with only first-quantised interaction-picture simulations providing better performance for $N>\eta^7$. As with the classical fast multipole method, large particle numbers $\eta\gtrsim 10^3$ would be needed to realise this advantage.

Autonomous quantum machines (AQMs) execute tasks without requiring time-dependent external control. Motivations for AQMs include the restrictions imposed by classical control on quantum machines' coherence times and geometries. Most AQM work is theoretical and abstract; yet an experiment recently demonstrated AQMs' usefulness in qubit reset, crucial to quantum computing. To further reduce quantum computing's classical control, we propose realizations of quantum-autonomous gates on three platforms: Rydberg atoms, trapped ions, and superconducting qubits. First, we show that a Rydberg-blockade interaction or an ultrafast transition can quantum-autonomously effect entangling gates on Rydberg atoms. Passive lasers control these gates quantum-autonomously. One can perform $Z$ or entangling gates on trapped ions quantum-autonomously, by sculpting a linear Paul trap or leveraging a ring trap. Finally, circuit quantum electrodynamics can enable quantum-autonomous $Z$ and $XY$ gates on superconducting qubits. The gates can serve as building blocks for (fully or partially) quantum-autonomous circuits, which may reduce classical-control burdens.

We present a novel quantum storage algorithm for k binary vectors of dimension m into a superposition of a m qubit quantum state based on a permutation technique. We compare this algorithm to the storage algorithm proposed by Ventura and Martinez. The permutation technique is simpler and can lead to an additional reduction through the reduce algorithm. To retrieve a binary vector from the superposition of k vectors represented by a m qubit quantum state, we must use a modified version of Grover algorithm, as Grover algorithm does not function correctly for non uniform distributions. We introduce the permutation trick that enables an exhaustive search by Grover algorithm in square root of k steps for k patterns, independent of n equal two power m. We compare this trick to the Ventura and Martinez trick, which requires square root of n steps for k patterns.

The Mølmer-Sørensen gate, a cornerstone entangling operation in trapped-ion systems, represents a promising alternative to standard entangling gates in superconducting quantum architectures. However, its performance on superconducting hardware has remained unverified. In this work, we present a hardware-efficient implementation of the Mølmer-Sørensen gate and characterize its performance using quantum process tomography (QPT) on IBM Quantum's superconducting processors. Our implementation achieves a process fidelity of 92.47% on the real quantum hardware, a performance competitive with the 93.02% fidelity of the device's native controlled-NOT (CX) gate. Furthermore, for the $|00\rangle$ input state, the gate prepares the target Bell state with $94.2\%$ success probability, confirming its correct logical operation. These results demonstrate that non-native entangling gates can be optimized to perform on par with hardware-native operations. This work expands the effective gate set for algorithm design on fixed-architecture processors and provides a critical benchmark for cross-platform gate evaluation, underscoring the role of hardware-aware compilation in advancing noisy intermediate-scale quantum (NISQ) computing.

Gaussian states are widely regarded as one of the most relevant classes of continuous-variable (CV) quantum states, as they naturally arise in physical systems and play a key role in quantum technologies. This motivates a fundamental question: given copies of an unknown CV state, how can we efficiently test whether it is Gaussian? We address this problem from the perspective of representation theory and quantum learning theory, characterizing the sample complexity of Gaussianity testing as a function of the number of modes. For pure states, we prove that just a constant number of copies is sufficient to decide whether the state is exactly Gaussian. We then extend this to the tolerant setting, showing that a polynomial number of copies suffices to distinguish states that are close to Gaussian from those that are far. In contrast, we establish that testing Gaussianity of general mixed states necessarily requires exponentially many copies, thereby identifying a fundamental limitation in testing CV systems. Our approach relies on rotation-invariant symmetries of Gaussian states together with the recently introduced toolbox of CV trace-distance bounds.

Unambiguous measurements play an important role in quantum information, with applications ranging from quantum key distribution to quantum state reconstruction. Recently, such measurements have also been used in quantum algorithms based on Regev's reduction. The key problem for these algorithms is the S-$|LWE>$ problem in the lattice setting and the Quantum Decoding Problem in the code setting. A key idea for addressing this problem is to use unambiguous measurements to recover $k$ coordinates of a code (or lattice) element $x$ from a quantum state $|\psi_x\rangle$, which corresponds to a noisy word $x$ with errors in quantum superposition. However, a general theoretical framework to analyze this approach has been lacking. In this work, we introduce the notion of fine-grained unambiguous measurements. Given a family of states $\{\,|\psi_x\rangle\,\}_{x\in\{0,1\}^n}$, we ask whether there exist measurements that can return, with certainty, $k$ bits of information about $x$. We study this question in the setting of symmetric states, which naturally arises in the Quantum Decoding Problem. We show that determining the maximal number of parities that a measurement can output can be formulated as a linear program, and we use its dual formulation to derive several upper bounds. In particular, we establish necessary and sufficient conditions for the existence of fine-grained unambiguous measurements and prove impossibility results showing, in particular, that such measurements cannot improve upon the approach of arXiv:2310.20651. Finally, we discuss the implications of these findings for the Quantum Decoding Problem.

The presence of energy barriers in the state space of a physical system can lead to exponentially slow convergence for sampling algorithms like Markov chain Monte Carlo (MCMC). In the classical setting, replica exchange (or parallel tempering) is a powerful heuristic to accelerate mixing in these scenarios. In the quantum realm, preparing Gibbs states of Hamiltonians faces a similar challenge, where bottlenecks can dramatically increase the mixing time of quantum dynamical semigroups. In this work, we introduce a quantum analogue of the replica exchange method. We define a Lindbladian on a joint system of two replicas and prove that it can accelerate mixing for a class of Hamiltonians with local energy barriers. We provide a rigorous lower bound on the spectral gap of the combined system's Lindbladian, which leads to an exponential improvement in spectral gap with respect to the barrier height. We showcase the applicability of our method with several proof-of-concept examples that satisfy a commuting-cut assumption, including the defected 1D Ising model at arbitrary constant temperature, and defected non-commuting local Hamiltonians at high temperature.

Topology optimization is a key methodology in engineering design for finding efficient and robust structures. Due to the enormous size of the design space, evaluating all possible configurations is typically infeasible. In this work, we present an end-to-end, fault-tolerant quantum algorithm for topology optimization that operates on the exponential Hilbert space representing the design space. We demonstrate the algorithm on the two-dimensional Messerschmitt-Bölkow-Blohm (MBB) beam problem. By restricting design variables to binary values, we reformulate the compliance minimization task as a combinatorial satisfiability problem solved using Grover's algorithm. Within Grover's oracle, the compliance is computed through the finite-element method (FEM) using established quantum algorithms, including block-encoding of the stiffness matrix, Quantum Singular Value Transformation (QSVT) for matrix inversion, Hadamard test, and Quantum Amplitude Estimation (QAE). The complete algorithm is implemented and validated using classical quantum-circuit simulations. A detailed complexity analysis shows that the method evaluates the compliance of exponentially many structures in quantum superposition in polynomial time. In the global search, our approach maintains Grover's quadratic speedup compared to classical unstructured search. Overall, the proposed quantum workflow demonstrates how quantum algorithms can advance the field of computational science and engineering.