Papers

We present a modular atom-array quantum computing architecture with space-time hybrid multiplexing (MAQCY), a dynamic optical tweezer-based protocol for fully connected and scalable universal quantum computation. By extending the concept of globally controlled static dual-species Rydberg atom wires [1], we develop an entirely new approach using Q-Pairs, which consist of globally controlled and temporally multiplexed dual-species Rydberg blockaded atom and superatom pairs. Space-time hybrid multiplexing of Q-Pairs achieves O(N) linear scaling in the number of required physical qubits, while preserving coherence and mitigating circuit-depth limitations through in-situ atom replacement. To demonstrate MAQCY's versatility, we implement a three-qubit quantum Fourier transform using only global operations and atom transport. We also propose a concrete implementation using ytterbium isotopes, paving the way toward large-scale, fault-tolerant quantum computing.

Quantum Annealing (QA) and QAOA are promising quantum optimisation algorithms used for finding approximate solutions to combinatorial problems on near-term NISQ systems. Many NP-hard problems can be reformulated as Quadratic Unconstrained Binary Optimisation (QUBO), which maps naturally onto quantum Hamiltonians. However, the limited qubit counts of current NISQ devices restrict practical deployment of such algorithms. In this study, we present the Hamiltonian Auto-Decomposition Optimisation Framework (HADOF), which leverages an iterative strategy to automatically divide the Quadratic Unconstrained Binary Optimisation (QUBO) Hamiltonian into sub-Hamiltonians which can be optimised separately using Hamiltonian based optimisers such as QAOA, QA or Simulated Annealing (SA) and aggregated into a global solution. We compare HADOF with Simulated Annealing (SA) and the CPLEX exact solver, showing scalability to problem sizes far exceeding available qubits while maintaining competitive accuracy and runtime. Furthermore, we realise HADOF for a toy problem on an IBM quantum computer, showing promise for practical applications of quantum optimisation.

Quadratic Wasserstein distances are obtained between dynamical systems (with states as special case), on $\mathbb{Z}_2$-graded von Neumann algebras. This is achieved through a systematic translation from non-graded to $\mathbb{Z}_2$-graded transport plans, on usual and fermionic (or $\mathbb{Z}_2$-graded) tensor products respectively. The metric properties of these fermionic Wasserstein distances are shown, and their symmetries relevant to deviation of a system from quantum detailed balance are investigated. The latter is done in conjunction with the development of a complete mathematical framework for detailed balance in systems involving indistinguishable fermions.

We address the problem of constructing fully universal private channel coding protocols for classical-quantum (c-q) channels. Previous work constructed universal decoding strategies, but the encoder relied on random coding, which prevents fully universal code construction. In this work, we resolve this gap by identifying an explicit structural property of codebooks – namely, the spectral expansion of an associated Schreier graph – that guarantees universal channel resolvability. Our analysis reveals how this property can be related to channel resolvability through the theory of induced representation. Our main technical result shows that when the transition matrix of a graph associated with a codebook has a large spectral gap, the channel output induced by uniformly sampled codewords is asymptotically indistinguishable from the target output distribution, independently of the channel. This establishes the first deterministic, channel-independent construction of resolvability codebooks. Building on this, we construct a fully universal private channel coding protocol by combining it with universal c-q channel coding based on the Schur-Weyl duality. With appropriate modifications to the requirements on codebooks of universal c-q channel coding, we show that our fully universal private channel coding achieves the known optimal rate. This work thus sheds new light on the expander property of a graph in the context of secure communication.

The combinatorial problem Max-Cut has become a benchmark in the evaluation of local search heuristics for both quantum and classical optimisers. In contrast to local search, which only provides average-case performance guarantees, the convex semidefinite relaxation of Max-Cut by Goemans and Williamson, provides worst-case guarantees and is therefore suited to both the construction of benchmarks and in applications to performance-critic scenarios. We show how extended floating point precision can be incorporated in algebraic subroutines in convex optimisation, namely in indirect matrix inversion methods like Conjugate Gradient, which are used in Interior Point Methods in the case of very large problem sizes. Also, an estimate is provided of the expected acceleration of the time to solution for a hardware architecture that runs natively on extended precision. Specifically, when using indirect matrix inversion methods like Conjugate Gradient, which have lower complexity than direct methods and are therefore used in very large problems, we see that increasing the internal working precision reduces the time to solution by a factor that increases with the system size.

Quantum phase transitions have been shown to be highly beneficial for quantum sensing, owing to diverging quantum Fisher information close to criticality. In this work we consider a periodically modulated Lipkin-Meshkov-Glick model to show that discrete time crystal (DTC) phase transition in this setup can enable us to achieve quantum-enhanced high-precision sensing of field strength. We employ a detailed finite-size scaling analysis, a time-averaged Inverse Participation Ratio analysis, and mean-field analysis in the thermodynamic limit, to determine the critical properties of this second-order phase transition. Our studies provide a comprehensive understanding of how quantum criticality in DTCs involving long-range interactions can be harnessed for advanced quantum sensing applications.

The rising interest in quantum-level communication has resulted in proposals for coexistence schemes with classical signals within the same fiber optic channel, where the most recent proposals leverage novel fibers designed for space-division multiplexing (SDM) transmission. In all cases the large power difference between classical and quantum channels presents challenges for such schemes, as the classical signals generate interfering noise that corrupts the quantum signal. In this work, we discuss the main interference mechanisms in coexistence scenarios and provide a model to quantify their impact on the quantum signal quality. Analytical approximations in the model allow accurate and fast numerical solutions in the millisecond time-scale. The model accounts for out-of-band non-linear interference effects, namely spontaneous Raman scattering (SpRS) and four-wave-mixing (FWM) in both cases of single-mode and SDM fibers with weakly-coupled degenerate mode groups. Rayleigh and SpRS backscattering are considered in counter-propagating scenarios. Since broadband classical transmission is targeted, the model also accounts for the effect of stimulated Raman scattering (SRS)-induced power tilt. Use of the model in sample scenarios indicates that the interference noise power is minimized at the high end of the transmission band in both cases were the quantum is co- and counter-propagating with respect to the classical signals, with a preference of one or the other scheme depending on the link length and quantum signal center frequency. Our model reveals that FWM has negligible impact in counter-propagating schemes, but can be relevant in co-propagating schemes under certain scenarios. Nevertheless, the FWM interference can be mitigated by deallocating the classical signals adjacent to the quantum channel.

Spectroscopy is the most important method for probing the structure of molecules. However, predicting molecular spectra on classical computers is computationally expensive, with the most accurate methods having a cost that grows exponentially with molecule size. Quantum computers have been shown to simulate simple types of optical spectroscopy efficiently – with a cost polynomial in molecule size – using methods such as time-dependent simulations of photoinduced wavepackets. Here, we show that any type of spectroscopy can be efficiently simulated on a quantum computer using a time-domain approach, including spectroscopies of any order, any frequency range, and involving both electric and magnetic transitions. Our method works by computing any spectroscopic correlation function based on the corresponding double-sided Feynman diagram, the canonical description of spectroscopic interactions. The approach can be used to simulate spectroscopy of both closed and open molecular systems using both digital and analog quantum computers.

Quantum entanglement is a fundamental phenomenon in quantum information science and a crucial resource for quantum technologies such as precision sensing, secure communication, and computation. In hybrid cavity magno-optomechanical systems, entanglement among cavity photons, magnons, and phonons enables manipulation of quantum states across different modes via radiation pressure-based light-matter interaction. We propose a hybrid optomechanical cavity-magnonic setup with Yttrium iron garnet (YIG) sphere allowing magnons to couple with photons via magnetic-dipole interaction. The system also uses optomechanical and electrostatic interactions to entangle cavity photons and mechanical resonators. We focus on how the magnon nonlinear Kerr effect and varying coupling strengths influence entanglement dynamics. By analysing nonlinear effects alongside other coupling parameters, we identify optimal conditions for initiating and sustaining robust entanglement between the motional modes (phonons) of two Coulomb-coupled mechanical resonators. Our model predicts that adding Coulomb interaction and magnon coupling enhances the degree and tunability of entanglement, making it more resilient to thermal baths at 3 K. This study addresses how to optimize and sustain phonon-phonon entanglement in complex hybrid quantum systems. These findings offer insights relevant to developing quantum memories for continuous variable quantum information processing and other quantum technologies.

Embedding the vertices of arbitrary graphs into trees while minimizing some measure of overlap is an important problem with applications in computer science and physics. In this work, we consider the problem of bijectively embedding the vertices of an $n$-vertex graph $G$ into the leaves of an $n$-leaf rooted binary tree $\mathcal{T}$. The congestion of such an embedding is given by the largest size of the cut induced by the two components obtained by deleting any vertex of $\mathcal{T}$. We show that for any embedding, the congestion lies between $\lambda_2(G)\cdot 2n/9$ and $\lambda_n(G)\cdot n/4$, letting $0=\lambda_1(G)\le \cdots \le \lambda_n(G)$ be the Laplacian eigenvalues of $G$, and there is an embedding for which the congestion is at most $\lambda_n(G)\cdot 2n/9$. Beyond these general bounds, we determine the congestion exactly for hypercubes and lattice graphs, and obtain asymptotically tight bounds for random regular graphs and Erdős-Rényi graphs. We further introduce an efficient contraction procedure based on spectral ordering and dynamic programming, which produces low-congestion embeddings in practice. Numerical experiments on structured graphs, random graphs, and tensor network representations of quantum circuits validate our theoretical bounds and demonstrate the effectiveness of the proposed method. These results yield new spectral bounds on the memory and time complexity of exact tensor network contraction in terms of the underlying graph structure.

We investigate entanglement sharing in a two-qubit sequential measurement scenario using three complementary classical correlation metrics: mutual information (I), sum of conditional probabilities (S), and the Pearson correlation coefficient (C). By investigating both weak measurement and probabilistic projective measurement (PPM) strategies in unilateral and bilateral scenarios, the phenomenon of entanglement sharing is conclusively certified when multiple pairs of classical correlation metrics simultaneously exceed their thresholds. Our investigation reveals that weak measurement strategies are more favorable than PPM for exhibiting entanglement sharing, regardless of the scenario. Furthermore, the mutual information criterion fails to characterize entanglement sharing in the bilateral scenario. While, the Pearson correlation criterion (C) is proven to be the most robust across all strategies and scenarios. These findings unveil a critical trade-off between measurement disturbance and complementary correlation recovery, which is essential for quantum resource reuse problems.

In this study, we first use a three-qubit system as an example to demonstrate the construction of quantum circuits for the eight maximally entangled basis vectors, subsequently extending the approach to N-qubit systems. We employ a random-number approach to generate maximally entangled basis vectors and their corresponding circuits, while also detailing the required number of single-qubit and CNOT gates. This approach not only provides a solid theoretical foundation but also establishes a practical technique for technological applications, bypassing the difficulty of storing large-scale encoding data.

Simulations of optical quantum systems are essential for the development of quantum technologies. However, these simulations are often computationally intensive, especially when repeated evaluations are required for data fitting, parameter estimation, or real-time feedback. To address this challenge, we develop a Long Short-Term Memory neural network capable of replicating the output of these simulations with high accuracy and significantly reduced computational cost. Once trained, the surrogate model produces spectra in milliseconds, providing a speed-up of 5000x relative to traditional numerical solvers. We focus on applying this technique to Doppler-broadened Electromagnetically Induced Transparency in a ladder-type scheme for Rydberg-based sensing, achieving near-unity agreement with the physics solver for resonant and off-resonant regimes. We demonstrate the effectiveness of the LSTM model on this representative optical quantum system, establishing it as a surrogate tool capable of supporting real-time signal processing and feedback-based optimisation.

Quantum coherence in curved spacetime offers a fresh window into the interplay between gravity, thermality, and quantum resources. While previous work has shown that Markovian evolution can generate entanglement and other nonclassical correlations in de Sitter backgrounds, the basis-dependent nature of coherence has so far limited its unambiguous interpretation. Here, we introduce a basis-independent framework to quantify not only the total coherence of two comoving detectors, but also its collective and localized contributions, and we trace how each of these decomposed measures varies with the inverse of Gibbons-Hawking temperature. By treating the detectors as open quantum systems interacting with a massless scalar field in the Bunch-Davies and squeezed alpha-vacua, we find that non-thermal squeezing substantially enhances extractable coherence, even under strong thermal effects. Our results demonstrate how basis-independent coherence in de Sitter spacetime can serve as a robust resource for relativistic quantum information protocols.

Carbon capture is vital for decarbonizing heavy industries such as steel and chemicals. Metal-organic frameworks (MOFs), with their high surface area and structural tunability, are promising materials for CO2 capture. This study focuses on Fe-MOF-74, a magnetic Mott insulator with exposed metal sites that enhance CO2 adsorption. Its strongly correlated electronic structure challenges standard DFT methods, which often yield inconsistent predictions. We initially benchmark adsorption energies using various DFT functionals, revealing substantial variability and underscoring the need for more accurate approaches, such as those provided by quantum computing. However, practical quantum algorithms are far less established for simulations of periodic materials, particularly when the plane-wave basis set, often comprising tens of thousands of basis vectors, is used. To address this, we employ an active space reduction strategy based on Wannier functions and natural orbital selection. Localized orbitals around the adsorption site are identified, and MP2 natural orbitals are used to improve convergence of correlation energies. Adsorption energies are then computed using a quantum number-preserving ansatz within the variational quantum eigensolver framework. In addition to classical simulations, we conduct quantum experiments using the sample-based quantum diagonalization method. Although current hardware limits the size of feasible simulations, our approach offers a more efficient and scalable path forward. These results advance the applicability of quantum algorithms to realistic models of carbon capture and periodic materials more broadly.

Non-Hermitian quantum systems, governed by nonunitary evolution, offer powerful tools for manipulating quantum states through engineered loss. A prime example is coherent absorption, where quantum states undergo phase-dependent partial or complete absorption in a lossy medium. Here, we demonstrate a fully programmable implementation of nonunitary transformations that emulate coherent absorption of quantum light using a programmable integrated linear photonic circuit, with loss introduced via coupling to an ancilla mode [Phys. Rev. X 8, 021017; 2018]. Probing the circuit with a single-photon dual-rail state reveals phase-controlled coherent tunability between perfect transmission and perfect absorption. A two-photon NOON state input, by contrast, exhibits switching between deterministic single-photon and probabilistic two-photon absorption. Across a range of input phases and circuit configurations, we observe nonclassical effects such as anti-coalescence and bunching, along with continuous and coherent tuning of output Fock state probability amplitudes. Classical Fisher information analysis reveals phase sensitivity peaks of 1 for single-photon states and 3.4 for NOON states, the latter exceeding the shot-noise limit of 2 and approaching the Heisenberg limit of 4 for two-photon states. The experiment integrates quantum state generation, programmable photonic circuitry, and photon-number-resolving detection, establishing ancilla-assisted circuits as powerful tools for programmable quantum state engineering, filtering, multiplexed sensing, and nonunitary quantum simulation.

Recent accounts of probability in the many worlds interpretation of quantum mechanics are vulnerable due to their dependence on probability theory per se. For this reason, the many worlds interpretation continues to suffer from the incoherence and quantitative problems. After discussing various theories of probability, I discuss the incoherence problem and argue that self-locating probabilities centered in time-extended worlds can solve it. I then discuss and refute various solutions to the quantitative problem. I argue that the only tenable way to ground these self-locating probabilities is to identify the mathematical form of the Born rule as a generic pattern in a time-extended wavefunction, and to distribute degrees of belief over the region of wavefunction occupied by this pattern. I then outline a time-symmetric version of quantum mechanics - the Fixed Point Formulation - which, interpreted within a time-symmetric Everettian framework, can provide the foundation for a theory of quantum probability.

Quantum machine learning (QML) algorithms have demonstrated early promise across hardware platforms, but remain difficult to interpret due to the inherent opacity of quantum state evolution. Widely used classical interpretability methods, such as integrated gradients and surrogate-based sensitivity analysis, are not directly compatible with quantum circuits due to measurement collapse and the exponential complexity of simulating state evolution. In this work, we introduce HattriQ, a general-purpose framework for computing amplitude-based input-attribution scores in circuit-based QML models. HattriQ supports the widely-used input amplitude embedding feature encoding scheme and uses a Hadamard test-based construction to compute input gradients directly on quantum hardware to compute integrated gradient attributions. We validate HattriQ on classification tasks across several datasets (Bars and Stripes, MNIST, FashionMNIST, and TFIM quantum data).

We study a class of time-dependent (TD) non-Hermitian Hamiltonians $H(t)$ that can be transformed into a time-independent pseudo-Hermitian Hamiltonian $\mathcal{H}_{0}^{PH}$ using a suitable TD unitary transformation $F(t)$. The latter can in turn be related to a Hermitian Hamiltonian $h$ by a similarity transformation, $h=\rho \mathcal{H}_{0}^{PH} \rho^{-1}$ where $\rho$ is the Dyson map. Accordingly, once the Schrödinger equation for the Hermitian Hamiltonian $h$ is solved, the general solution of the initial system can be deduced. This allows to define the appropriate $\tilde{\eta}(t)$-inner product for the Hilbert space associated with $H(t)$, where $\tilde{\eta}(t)=F^{\dagger}(t)\eta F(t)$ and $\eta=\rho^{\dagger}\rho$ is the metric operator. This greatly simplifies the computation of the relevant uncertainty relations for these systems. As an example, we consider a model of a particle with a TD mass subjected to a specific TD complex linear potential. We thus obtain two Hermitian Hamiltonians, namely that of the standard harmonic oscillator and that of the inverted oscillator. For both cases, the auxiliary equation admits a solution, and the exact analytical solutions are squeezed states given in terms of the Hermite polynomials with complex coefficients. Moreover, when the Hermitian Hamiltonian is that of the harmonic oscillator, the position-momentum uncertainty relation is real and greater than or equal to $\hbar/2$, thereby confirming its consistency.

Quantum mutual information is an important tool for characterizing correlations in quantum many-body systems, but its numerical evaluation is often prohibitively expensive. While some variants of Rényi Mutual Information (RMI) are computationally more tractable, it is not clear whether they correctly capture the long-wavelength physics or are dominated by UV effects, which is of key importance in lattice simulations. We analyze the relevance of lattice effects on the family of $\alpha$-$z$ Rényi mutual informations for ground states of models with conformal field theory descriptions. On the example of massless free fermions we identify distinct regions in the $\alpha$-$z$ plane, where RMI corrections due to the lattice are relevant or irrelevant. We further support these findings with MPS calculations on the transverse field Ising model (TFIM). Our results, accompanied by the open-source Julia package QMICalc$.$jl, provide guidance to using RMI in quantum-many body physics numerical computations.

Efficient characterization of noise during quantum gate operations is an essential step to building and scaling up a quantum computer. One such protocol is averaged circuit eigenvalue sampling (ACES) which efficiently characterizes a noisy gate set by reconstructing a Pauli noise model for a each gate. Here we utilize the ACES protocol to characterize two coupled superconducting qubits. For accurate reconstruction, we tailor the noise via Pauli twirling and account for measurement errors. We verify the accuracy of the protocol by comparing the predicted gate fidelities to that extracted from conventional benchmarking approaches, such as interleaved randomized benchmarking. Furthermore, we demonstrate the efficacy of ACES in accurately identifying specific noise sources by reconstructing injected phase errors in the two-qubit gates.

Integrability is a cornerstone of classical mechanics, where it has a precise meaning. Extending this notion to quantum systems, however, remains subtle and unresolved. In particular, deciding whether a quantum Hamiltonian - viewed simply as a matrix - defines an integrable system is far from obvious, yet crucial for understanding non-equilibrium dynamics, spectral correlations, and correlation functions in many-body physics. We develop a statistical framework that approaches quantum integrability from a probabilistic standpoint. A key observation is that integrability requires a finite probability of vanishing energy gaps. Building on this, we propose a two-step protocol to distinguish integrable from non-integrable Hamiltonians. First, we apply a systematic Monte Carlo decimation of the spectrum, which exponentially compresses the Hilbert space and reveals whether level spacings approach Poisson statistics or remain mixed. The termination point of this decimation indicates the statistical character of the spectrum. Second, we analyze $k$-step gap distributions, which sharpen the distinction between Poisson and mixed statistics. Our procedure applies to Hamiltonians of any finite size, independent of whether their structure involves a few blocks or an exponentially fragmented Hilbert space. As a benchmark, we implement the protocol on quantum Hamiltonians built from the permutation group $\mathcal{S}_N$, demonstrating both its effectiveness and generality.

We prove that variational quantum algorithms using discrete variable boson samplers suffer from barren plateaus and that by changing to fermionic statistics, which is classically efficient to simulate, the barren plateau scaling is less severe. Moreover, when using fermionic statistics the cost landscape boils down to one unit frequency Fourier mode per variational parameter, irrespective of circuit design, ansatz or variational problem, allowing for more efficient parameter shift rules. This simplified cost landscape allows for the gradient-free Rotosolve algorithm to be used to gain a considerable speed-up over the original bosonic algorithm. Motivated by this, we propose a non-linear parametrised phase shifter, the dual-valued phase shifter, that generates these single-harmonic cost landscapes for bosonic statistics. We propose three ways to achieve this by using either non-linear optics, measurement-induced non-linearities, or entangled resource states simulating fermionic statistics. The latter two require linear optics only, allowing for implementation with widely-available technology today. Despite this, the classical simulability of free fermions and the fact the fermionic algorithm can defeat the bosonic algorithm casts doubt on whether the quantum advantage of boson sampling results in any practical advantage in this setting.

The family of nickelate superconductors have long been explored as analogs of the high temperature cuprates. Nonetheless, the recent discovery that certain stoichiometric nickelates superconduct up to high $T_c$ under pressure came as a surprise. The mechanisms underlying the superconducting state remain experimentally unclear. In addition to the practical challenges posed by working in a high pressure environment, typical samples exhibit anomalously weak diamagnetic responses, which have been conjectured to reflect inhomogeneous `filamentary' superconducting states. We perform wide-field, high-pressure, optically detected magnetic resonance spectroscopy to image the local diamagnetic responses of as grown La$_3$Ni$_2$O$_7$ samples in situ, using nitrogen vacancy quantum sensors embedded in the diamond anvil cell. These maps confirm significant inhomogeneity of the functional superconducting responses at the few micron scale. By spatially correlating the diamagnetic Meissner response with both the local tensorial stress environment, also imaged in situ, and stoichiometric composition, we unravel the dominant mechanisms suppressing and enhancing superconductivity. Our wide-field technique simultaneously provides a broad view of sample behavior and excellent local sensitivity, enabling the rapid construction of multi-parameter phase diagrams from the local structure-function correlations observed at the sub-micron pixel scale.

We use Pauli Path simulation to variationally obtain parametrized circuits for preparing ground states of various quantum many-body Hamiltonians. These include the quantum Ising model in one dimension, in two dimensions on square and heavy-hex lattices, and the Kitaev honeycomb model, all at system sizes of one hundred qubits or more – sizes at which generic quantum circuits are beyond the reach of exact state-vector simulation – thereby reaching utility scale. We benchmark the Pauli Path simulation results against exact ground-state energies when available, and against density-matrix renormalization group calculations otherwise, finding strong agreement. To further assess the quality of the variational states, we evaluate the magnetization in the x and z directions for the quantum Ising models and compute the topological entanglement entropy for the Kitaev honeycomb model. Finally, we prepare approximate ground states of the Kitaev honeycomb model with 48 qubits, in both the gapped and gapless regimes, on Quantinuum's System Model H2 quantum computer using parametrized circuits obtained from Pauli Path simulation. We achieve a relative energy error of approximately $5\%$ without error mitigation and demonstrate the braiding of Abelian anyons on the quantum device beyond fixed-point models.

Czachor's model of hierarchical arithmetics begins with a valid formal premise but fixes the key probability mapping g by importing the Born rule and Fubini-Study metric from standard quantum mechanics, where Born probabilities are Kolmogorov within a fixed measurement context. This g is then applied in a non-Newtonian hidden-variable setting, producing a hybrid framework whose agreement with quantum correlations is built in by design, not derived from new physics, and thus does not constitute a genuine counterexample to Bell's theorem

Tensor network contraction on arbitrary graphs is a fundamental computational challenge with applications ranging from quantum simulation to error correction. While belief propagation (BP) provides a powerful approximation algorithm for this task, its accuracy limitations are poorly understood and systematic improvements remain elusive. Here, we develop a rigorous theoretical framework for BP in tensor networks, leveraging insights from statistical mechanics to devise a cluster expansion that systematically improves the BP approximation. We prove that the cluster expansion converges exponentially fast if an object called the loop contribution decays sufficiently fast with the loop size, giving a rigorous error bound on BP. We also provide a simple and efficient algorithm to compute the cluster expansion to arbitrary order. We demonstrate the efficacy of our method on the two-dimensional Ising model, where we find that our method significantly improves upon BP and existing corrective algorithms such as loop series expansion. Our work opens the door to a systematic theory of BP for tensor networks and its applications in decoding classical and quantum error-correcting codes and simulating quantum systems.

We establish a relationship between the correlations in a many-qubit mixed state and the minimum circuit depth needed for its preparation. If the mutual information between two subsystems exceeds the mutual information between one of those subsystems and the environment, which purifies the mixed state of the system, then the past lightcones of the subsystems must intersect one another. This results in a lower bound on the circuit depth of any ensemble of geometrically local unitaries that prepares the state to some specified degree of approximation. As an application, we derive lower bounds on the circuit depth needed to prepare thermal states of one-dimensional quantum critical systems described by conformal field theory, showing that the depth diverges as temperature is decreased up to a cutoff set by the preparation error.

We studied the dynamics of a pair of single-electron double quantum dots (DQD) under longitudinal and transverse static magnetic fields and time-dependent harmonic modulation of their interaction couplings. We propose to modulate the tunnel coupling between the QDs to produce one-qubit gates and the exchange coupling between DQDs to generate entangling gates, the set of operations required for quantum computing. We developed analytical approximations to set the conditions to control the qubits and applied them to numerical calculations to test the accuracy and robustness of the analytical model. The results shows that the unitary evolution of the two-electron state performs the designed operations even under conditions shifted from the ideal ones.

Reproducible builds are a set of software development practices that establish an independently verifiable path from source code to binary artifacts, helping to detect and mitigate certain classes of supply chain attacks. Although quantum computing is a rapidly evolving field of research, it can already benefit from adopting reproducible builds. This paper aims to bridge the gap between the quantum computing and reproducible builds communities. We propose a generalization of the definition of reproducible builds in the quantum setting, motivated by two threat models: one targeting the confidentiality of end users' data during circuit preparation and submission to a quantum computer, and another compromising the integrity of quantum computation results. This work presents three examples that show how classical information can be hidden in transpiled quantum circuits, and two cases illustrating how even minimal modifications to these circuits can lead to incorrect quantum computation results. Our work provides initial steps towards a framework for reproducibility in quantum software toolchains.