Papers

Quantum differential privacy provides a rigorous framework for quantifying privacy guarantees in quantum information processing. While classical correlations are typically regarded as adversarial to privacy, the role of their quantum analogue, entanglement, is not well understood. In this work, we investigate how quantum entanglement fundamentally shapes quantum local differential privacy (QLDP). We consider a bipartite quantum system whose input state has a prescribed level of entanglement, characterized by a lower bound on the entanglement entropy. Each subsystem is then processed by a local quantum mechanism and measured using local operations only, ensuring that no additional entanglement is generated during the process. Our main result reveals a sharp phase-transition phenomenon in the relation between entanglement and QLDP: below a mechanism-dependent entropy threshold, the optimal privacy leakage level mirrors that of unentangled inputs; beyond this threshold, the exact privacy leakage is strictly smaller than its unentangled value and admits an explicitly computable upper bound that strictly decreases with the entropy. This bound can also certify that some non-private mechanisms become private under sufficiently strong entanglement constraints. The phase-transition phenomenon gives rise to a nonlinear dependence of the certified privacy-leakage upper bound on the entanglement entropy, even though the underlying quantum mechanisms and measurements are linear. We show that the transition is governed by the intrinsic non-convex geometry of the set of entanglement-constrained quantum states, which we parametrize as a smooth manifold and analyze via Riemannian optimization. Our findings demonstrate that entanglement serves as a genuine privacy-enhancing resource, offering a geometric and operational foundation for designing robust privacy-preserving quantum protocols.

This article is an expository account aimed at viewing entanglement in finite-dimensional quantum many-body systems as a phenomenon of global geometry. While the mathematics of general quantum states has been studied extensively, this article focuses specifically on their entanglement. When a quantum system varies over a classical parameter space, each fiber may look like the same Hilbert space, yet there may be no global identification because of twisting in the gluing data. Describing this situation by an Azumaya algebra, one always obtains the family of pure-state spaces as a Severi-Brauer scheme. The main focus is to characterize the condition under which the subsystem decomposition required to define entanglement exists globally and compatibly, by a reduction to the stabilizer subgroup of the Segre variety, and to explain that the obstruction appears in the Brauer class. As a consequence, quantum states yield a natural filtration dictated by entanglement on the Severi-Brauer scheme. Using a spin system on a torus as an example, we show concretely that the holonomy of the gluing can produce an entangling quantum gate, and can appear as an obstruction class distinct from the usual Berry numbers or Chern numbers. For instance, even for quantum systems that have traditionally been regarded as having no topological band structure, the entanglement of their eigenstates can be related to global geometric universal quantities, reflecting the background geometry.

The discrimination of quantum states is fundamental to quantum information processing. Inverse-squeezing Kennedy (IS-Kennedy) receivers can outperform the coherent-state BPSK Helstrom benchmark at the same energy by converting transmitter-side squeezing into an effective coherent-state separation gain, without violating the Helstrom bound for the squeezed-state alphabet. This work investigates how squeezing mismatch degrades this mechanism. We show that imperfect inverse squeezing transforms the ideally nulled output into a residually squeezed state, thereby altering the photon-number statistics before detection. This residual-squeezing picture reveals a strong physical asymmetry between squeezing-magnitude and squeezing-phase mismatches. Magnitude mismatch produces an energy-independent error floor in the high-signal-energy regime, whereas phase mismatch generates a residual squeezing term that grows with signal energy. In the small-residual-squeezing regime, this leads to a polynomial growth of the leading error contribution and a rapid collapse of the SQL advantage. We also identify a parity-step effect in photon-number-resolving detection: because the nulled residual squeezed vacuum contains only even photon numbers, increasing detector resolution improves the high-energy robustness only when the effective saturation threshold crosses the next even photon number. These results identify phase locking as the dominant bottleneck for IS-Kennedy-type non-Gaussian receivers under unitary squeezing mismatch and provide design guidelines for robust squeezed-state quantum receivers.

Generative models for materials have achieved strong performance on periodic bulk crystals, yet their ability to generalize across scale transitions to finite nanostructures remains largely untested. We introduce Crystal-to-Nanoparticle (C2NP), a systematic benchmark for evaluating generative models when moving between infinite crystalline unit cells and finite nanoparticles, where surface effects and size-dependent distortions dominate. C2NP defines two complementary tasks: (i) generating nanoparticles of specified radii from periodic unit cells, testing whether models capture surface truncation and geometric constraints; and (ii) recovering bulk lattice parameters and space-group symmetry from finite particle configurations, assessing whether models can infer underlying crystallographic order despite surface perturbations. Using diverse materials as a structurally consistent testbed, we construct over 170,000 nanoparticle configurations by carving particles from supercells derived from DFT-relaxed crystal unit cells, and introduce size-based splits that separate interpolation from extrapolation regimes. Experiments with state-of-the-art approaches, including diffusion, flow-matching, and variational models, show that even when losses are low, models often fail geometrically under distribution shift, yielding large lattice-recovery errors and near-zero joint accuracy on structure and symmetry. Overall, our results suggest that current methods rely on template memorization rather than scalable physical generalization. C2NP offers a controlled, reproducible framework for diagnosing these failures, with immediate applications to nanoparticle catalyst design, nanostructured hydrides for hydrogen storage, and materials discovery. Dataset and code are available at https://github.com/KurbanIntelligenceLab/C2NP.

We evaluate the quantum resource requirements for ATP/metaphosphate hydrolysis, one of the most important reactions in all of biology with implications for metabolism, cellular signaling, and cancer therapeutics. In particular, we consider three algorithms for solving the ground state energy estimation problem: the variational quantum eigensolver, quantum Krylov, and quantum phase estimation. By utilizing exact classical simulation, numerical estimation, and analytical bounds, we provide a current and future outlook for using quantum computers to solve impactful biochemical and biological problems. Our results show that variational methods, while being the most heuristic, still require substantially fewer overall resources on quantum hardware, and could feasibly address such problems on current or near-future devices. We include our complete dataset of biomolecular Hamiltonians and code as benchmarks to improve upon with future techniques.

Accurate quantum state readout is crucial for error correction and algorithms, but measurement errors are detrimental. Readout fidelity is typically limited by a poor signal-to-noise ratio (SNR) and energy relaxation ($T_1$ decay), a significant problem for superconducting qubits. While most approaches classify results using clustering algorithms on integrated readout signals, these methods cannot distinguish a qubit that was initially in the ground state from one that decayed to it during measurement. We instead propose using machine learning (ML) on the raw, non-integrated analog signal. We apply time-series classification models, such as a long short-term memory (LSTM) network, to the full data trajectory. We find that our LSTM model, combined with filtering and feature engineering, consistently outperforms clustering. The largest improvements come from reclassifying points in the boundary regions between clusters. These points correspond to atypical measurement records, likely due to transient or noisy features lost during data integration. By retaining temporal information, sequence-aware models like LSTMs can better discriminate these trajectories, whereas clustering methods based on integrated values are more prone to misclassification.

The frequency- and time-resolved second order quantum coherence function (g(2)({\tau})) of single-molecule fluorescence has recently been proposed as a powerful new quantum light spectroscopy that can reveal intrinsic quantum coherence in excitation energy transfer in molecular systems ranging from simple dimers to photosynthetic complexes. Yet, no experiments have been reported to date. Here, we have developed a single-molecule fluorescence g(2)({\tau}) quantum light spectroscopy (SMFg2-QLS) that can simultaneously measure the fluorescence intensity, lifetime, spectra, and g(2)({\tau}) with frequency resolution, for a single molecule in a controlled environment at both room temperature and cryogenic temperature. As a proof of principle, we have studied single molecules of IDTBT (indacenodithiophene-co-benzothiadiazole), a semiconducting donor-acceptor conjugated copolymer with a chain-like structure that shows a high carrier mobility and annihilation-limited long-range exciton transport. We have observed different g(2)({\tau}=0) values with different bands or bandwidths of the single molecule IDTBT fluorescence. The general features are consistent with theoretical predictions and suggest non-trivial excited state quantum dynamics, possibly showing quantum coherence, although further analysis and confirmation will require additional theoretical calculations that take into account the complexity and inhomogeneity of individual IDTBT single molecular chains. Our results demonstrate the feasibility and promise of frequency- and time-resolved SMFg2-QLS to provide new insights into molecular quantum dynamics and to reveal signatures of intrinsic quantum coherence in photosynthetic light harvesting that are independent of the nature of the light excitation.

We propose a scheme for accumulating entanglement between long-lived qudits provided by central nuclear spins of defect centers. Assuming a generic setting, the electron spin of each node acts as the communication qubit and may be entangled with other nodes, e.g., through a spin-photon interface. The generally available Ising component of the hyperfine interaction is shown to facilitate repeated entanglement transfer onto memory qudits of arbitrary dimension $d\le 2I+1$ with $I$ the nuclear spin quantum number. When $d$ is set to an integer power of two, maximal entanglement can be generated deterministically and without intermittent driving of nuclear spins. The scheme is applicable to several candidate systems, including the $^{73}$Ge germanium vacancy in diamond.

Quantum hardware suffers from intrinsic device heterogeneity and environmental drift, forcing practitioners to choose between suboptimal non-adaptive controllers or costly per-device recalibration. We derive a scaling law lower bound for meta-learning showing that the adaptation gain (expected fidelity improvement from task-specific gradient steps) saturates exponentially with gradient steps and scales linearly with task variance, providing a quantitative criterion for when adaptation justifies its overhead. Validation on quantum gate calibration shows negligible benefits for low-variance tasks but >40% fidelity gains on two-qubit gates under extreme out-of-distribution conditions (10$\times$ the training noise), with implications for reducing per-device calibration time on cloud quantum processors. Further validation on classical linear-quadratic control confirms these laws emerge from general optimization geometry rather than quantum-specific physics. We further introduce a few-shot pre-adaptation protocol that estimates the optimal adaptation budget from $N{=}3$-5 probe steps within 3-19% relative error across out-of-distribution regimes.

If a quantum walk starting on a vertex tends to stay at home, then that vertex is said to be sedentary. We prove that almost all planar graphs and almost all trees contain at least two sedentary vertices for any assignment of edge weights — a result that suggests vertex sedentariness is a common phenomenon in trees and planar graphs. For weighted bipartite graphs, we show that a vertex is not sedentary whenever 0 does not belong to its eigenvalue support. Consequently, each vertex in a nonsingular weighted bipartite graph is not sedentary, a stark contrast to weighted trees and weighted planar graphs. A corollary of this result is that every vertex in a bipartite graph with a unique perfect matching is not sedentary for any assignment of edge weights. We also construct new families of weighted bipartite graphs with sedentary vertices using the bipartite double, subdivision operation, and corona product. Finally, we show that unweighted paths and unweighted even cycles contain no sedentary vertices.

Position verification schemes are interactive protocols where entities prove their physical location to others; this enables interactive proofs for statements of the form "I am at a location $L$." Although secure position verification cannot be achieved with classical protocols (even with computational assumptions), they are feasible with quantum protocols. In this paper we introduce the notion of zero-knowledge position verification, which generalizes position verification in two ways: 1. enabling entities to prove more sophisticated statements about their locations at different times (for example, "I was NOT near location $L$ at noon yesterday"). 2. maintaining privacy for any other detail about their true location besides the statement they are proving. We construct zero-knowledge position verification from standard position verification and post-quantum one-way functions. The central tool in our construction is a primitive we call position commitments, which allow entities to privately commit to their physical position in a particular moment, which is then revealed at some later time.

Traditionally, Quantum Information, and Quantum Communication specifically, have been focused on qubit-based architectures. Recent results, however, highlighted that higher dimensional architectures (qudit-based) may present advantages both in terms of communication and computation; a family of channels called Multi-level Amplitude Damping (MAD) channels, which are a possible qudit generalization of the well known Amplitude Damping Channels, is able to model energy decay processes that may happen during signal transmission. In this work, the Quantum Capacity of 4-dimensional MAD's is studied, relying on a technique for computing it even outside of degradable and antidegradable conditions. We also characterized the complete region of antidegradability and degradability in the parameter space for a generic d-dimensional MAD using both analytical and semi-numerical methods.

Many challenges arising in Quantum Technology can be successfully addressed using a set of machine learning algorithms collectively known as reinforcement learning (RL), based on adaptive decision-making through interaction with the quantum device. After a concise and intuitive introduction to RL aimed at a broad physics readership, we discuss the key ideas and core concepts in reinforcement learning with a particular focus on quantum systems. We then survey recent progress in RL in all relevant areas. We discuss state preparation in few- and many-body quantum systems, the design and optimization of high-fidelity quantum gates, and the automated construction of quantum circuits, including applications to variational quantum eigensolvers and architecture search. We further highlight the interactive capabilities of RL agents, emphasizing recent progress in quantum feedback control and quantum error correction, and briefly discuss quantum reinforcement learning as well as applications to quantum metrology. The review concludes with a discussion of open challenges – such as scalability, interpretability, and integration with experimental platforms – and outlines promising directions for future research. Throughout, we highlight experimental implementations that exemplify the increasing role of reinforcement learning in shaping the development of quantum technologies.

We compare Krylov's state complexity with an information-geometric (IG) measure of complexity for the quantum evolution of two-level systems. Focusing on qubit dynamics on the Bloch sphere, we analyze evolutions generated by stationary and nonstationary Hamiltonians, corresponding to geodesic and nongeodesic trajectories. We formulate Krylov complexity in geometric terms, both instantaneously and in a time-averaged sense, and contrast it with an IG complexity of quantum evolutions characterized in terms of efficiency and curvature. We show that the two measures reflect fundamentally different aspects of quantum dynamics: Krylov's state complexity quantifies the directional spread of the evolving state relative to the initial state, whereas the IG complexity captures the effective volume explored along the trajectory on the Bloch sphere. This geometric distinction explains their inequivalent behavior and highlights the complementary nature of state-based and information-geometric notions of complexity in quantum systems.

The phenomena of induced transparency, with the typical examples of electromagnetically induced transparency (EIT) in atomic media and those based on coupled optical resonators, have attracted tremendous interest since their discoveries. Owing to the limitations of the involved physical elements, however, near-100% transmissions were reported under highly demanding experimental conditions. With a structure of three linearly coupled optical resonators, an active one carrying optical gain and two passive ones simply with dissipation, we demonstrate that a transmitted light field can become completely transparent through the structure, which displays all properties similar to those of EIT. It is due to a destructive interference mechanism that totally eliminates the intracavity field in the dissipative resonator directly coupled to the transmitted field of any feasible power, when the coupling strength of two other resonators is tuned across a point determined by their associated gain and loss rates. This mechanism works for all possible coupling strengths of the dark resonator with the input field and its neighboring resonator, as well as for any available quality factor from its fabrication. The transparency window size and output field intensity can be freely adjusted by tuning two inter-cavity couplings of wide ranges, without modifying the built-in optical gain which can be just slightly stronger than the dissipation of the active resonator.

We analyze the quantum states of an isolated composite system consisting of two stacked quantum Ising (SQI) subsystems, coupled by a local Hamiltonian term that preserves the $Z_2$ symmetry of each subsystem. The coupling strength is controlled by an intercoupling parameter $w$, with $w=0$ corresponding to decoupled quantum Ising systems. We focus on the quantum correlations of one of the two SQI subsystems, $S$, in the ground state of the global system, and study their dependence on both the state of the weakly-coupled complementary part $E$ and the intercoupling strength. We concentrate on regimes in which $S$ develops critical long-range correlations. The most interesting physical scenario arises when both SQI subsystems are critical. In particular, for identical SQI subsystems, the global system is equivalent to the quantum Ashkin-Teller model, characterized by an additional $Z_2$ interchange symmetry between the two subsystem operators. In this limit, one-dimensional SQI systems exhibit a peculiar critical line along which the length-scale critical exponent $\nu$ varies continuously with $w$, while two-dimensional systems develop quantum multicritical behaviors characterized by an effective enlargement of the symmetry of the critical modes, from the actual $Z_2\oplus Z_2$ symmetry to a continuous O(2) symmetry.

Relativistic spin effects drive subtle molecular phenomena ranging from intersystem crossing in photodynamic therapy to spin-mediated catalysis and high-resolution spectroscopy. These effects are described by the Pauli-Breit Hamiltonian, which extends the nonrelativistic electronic Hamiltonian by including one- and two-electron spin-orbit and spin-spin interactions. First-principles simulations of the full Pauli-Breit Hamiltonian rapidly become intractable on classical computers due to the exponential growth of the Hilbert space and the complexity of two-body spin-dependent terms. We propose a fault-tolerant quantum algorithm for computing molecular energy levels and properties governed by the Pauli-Breit Hamiltonian. Our approach block-encodes the relativistic Hamiltonian in a second-quantized, doubly factorized representation. By reformulating the Hamiltonian in a symmetry-adapted Majorana basis, we construct efficient linear-combination-of-unitaries circuits that encode spin-orbit interactions without effective or mean-field approximations. We introduce spin-controlled Pauli-SWAP networks that decouple spin and orbital control logic, enabling a unified treatment of relativistic spin mixing with only modest overhead relative to spin-free simulations. We analyze quantum resources in terms of logical qubits and T-gate complexity, showing that explicit spin degrees of freedom do not worsen the asymptotic scaling. The prefactor is reduced by a factor of two compared to direct linear-combination-of-unitaries approaches. Finally, we outline a hybrid quantum-classical workflow for designing photodynamic therapy photosensitizers, artificial photosynthesis catalysts, and other systems where accurate relativistic spin effects are essential.

We investigate and compare two particle number-conserving protocols for the preparation of a topologically nontrivial state. The first is derived from thermally coupling the system to a cold bath, while the second is based on engineered dissipation. We numerically study the time required to reach the target state as well as its robustness against physically important perturbations. Crucially, in both protocols, the cooling capability is limited by dissipatively induced diffusion processes. The resulting quadratic scaling of the cooling time with system size is also corroborated analytically using mean-field approximations and a purely classical random-walk model. Furthermore, we find that the engineered protocol admits a unique and stable dark state, which contributes to an ongoing discussion regarding the applicability of dissipative state preparation to many-body systems.

We introduce multivariate multicycle (MM) codes, a new family of quantum error-correcting codes (QECCs) that unifies bivariate bicycle, multivariate bicycle, abelian two-block group algebra, generalized bicycle, trivariate tricycle, and toric codes. MM codes are Calderbank-Shor-Steane (CSS) codes defined from length-$\textit{t+1}$ chain complexes with $\textit{$t \ge 4$}$. The chief advantage of these codes is that they possess metachecks and high confinement that permit complete single-shot decoding. We offer a framework that facilitates the construction of long-length chain complexes through the use of Koszul complex. In particular, obtaining explicit boundary maps (parity check and metacheck matrices) is particularly straightforward in our approach. This simple but very general parameterization of codes permitted us to efficiently perform a numerical search, where we identify several MM code candidates that demonstrate these capabilities at high rates and high code distances. Examples of new codes with parameters $[[n,k,d]]$ include $[[96, 12, 8]]$, $[[144, 12, 12]]$, $[[216, 12, 14]]$, $[[288, 12, 16]]$, $[[324, 12, 20]]$, $[[432, 12, 27]]$, $[[486, 24, 12]]$, $[[630, 70, 9]]$, and $[[648, 18, 23]]$. Notably, our codes achieve confinement profiles that surpass all known single-shot-decodable quantum CSS codes of practical blocksize. Our codes are also the first explicit instances of collapsed 5D through 9D higher dimensional QECCs, with check weights significantly lower than those of recent small instances of quantum Tanner codes.

The state of a quantum system can be represented by listing the outcome probabilities for a tomographically complete set of measurements. Such representations appear throughout physics, for example, in quantum field theory via correlation functions and in quantum foundations within generalized probabilistic frameworks. In this paper, we show a no-go result: To enable useful statements, the probability representation must be topologically robust$\unicode{x2014}$preserving the notion of closeness between states. Yet, a topologically robust probability representation cannot simultaneously retain other essential structure, such as the subsystem structure.

The canonical commutation relation is a cornerstone of quantum theory and underlies the Heisenberg uncertainty principle. Although uncertainty relations have been extensively tested, direct verifications of the underlying commutation relation itself have remained elusive. We report an experimental demonstration of the bosonic commutation relation for optical field operators based on measurements of two distinct intensity correlation functions. From these measurements, we extract the expectation value of the field-operator commutator for both a single-photon state and coherent state. In both cases, the measured values are consistent with unity, in quantitative agreement with quantum theory.

Random quantum states drawn from the Haar ensemble with a constraint on the energy expectation value $E_{\mathrm{av}} = \langle \psi | H | \psi\rangle$ display eigenstate condensation: for $E_{\mathrm{av}}$ below a critical value $E_c$, they develop macroscopic overlap with the ground state. We study eigenstate condensation in systems with finite-dimensional Hilbert spaces. These systems display three phases: a ground-state phase, in which energy-constrained random states have macroscopic overlap with the ground state; a high-temperature phase, in which they have exponentially small overlap with each energy eigenstate; and an anti-ground-state phase, in which they have macroscopic overlap with the most highly excited state. In local spin systems the ground-state and anti-ground-state phases approach the middle of the spectrum as $1/[\text{system size}]$, but – because the condensation phase transitions have exponential, rather than polynomial, finite-size scaling – the crossover becomes exponentially sharp in system size and the high-temperature phase is best understood as an extended phase.

The Jordan-Wigner transformation connects spin operators in one-dimensional spin systems and fermionic operators. In this work, we elucidate the relationship between the finite-size corrections in the spin representation and the fermionic Casimir effect in the corresponding fermion representation. In particular, we focus on the ground-state energy of one-dimensional transverse-field Ising and XY models, and show that all finite-size corrections can be interpreted as lattice fermionic Casimir effects. We further find several types of Casimir phenomena, such as the conventional Casimir energy from massless fields, damping behavior from massive fields, vanishing behavior from flat or nonrelativistic bands, and oscillating behavior from the finite-density effect. Our findings establish a dictionary between finite-size corrections in spin chains and fermionic Casimir effects, and provide experimentally relevant platforms for the fermionic Casimir phenomena.

Effective field theories consistent with quantum gravity obey surprising finiteness constraints, appearing in several distinct but interconnected forms. In this work we develop a framework that unifies these observations by proposing that the defining data of such theories, as well as the landscape of effective field theories that are valid at least up to a fixed cutoff, admit descriptions with a uniform bound on complexity. To make this precise, we use tame geometry and work in sharply o-minimal structures, in which tame sets and functions come with two integer parameters that quantify their information content; we call this pair their tame complexity. Our Finite Complexity Conjectures are supported by controlled examples in which an infinite Wilsonian expansion nevertheless admits an equivalent finite-complexity description, typically through hidden rigidity conditions such as differential or recursion relations. We further assemble evidence from string compactifications, highlighting the constraining role of moduli space geometry and the importance of dualities. This perspective also yields mathematically well-defined notions of counting and volume measures on the space of effective theories, formulated in terms of effective field theory domains and coverings, whose finiteness is naturally enforced by the conjectures.

In this paper, we introduce post-selection games, a generalization of nonlocal games where each round can be not only won or lost by the players, but also discarded by the referee. Such games naturally formalize possibilistic proofs of nonlocality, such as Hardy's paradox. We develop algorithms for computing the local and Tsirelson bounds of post-selection games. Furthermore, we show that they have an unbounded advantage in statistical power over traditional nonlocal games, making them ideally suited for analysing Bell tests with low detection efficiency.

The preferred-basis problem and the definite-outcome aspect of the measurement problem persist even when the detector is modeled unitarily. Experimental data are represented in a Boolean event algebra of mutually exclusive records, while the theoretical description employs a noncommutative operator algebra with continuous unitary symmetry. This change of mathematical structure constitutes the core of the “cut”: a necessary interface from group-based kinematics to set-based counting. In the Operationally Induced Preferred Basis (OIPB) framework, the basis relevant for recorded outcomes is not fixed by the system Hamiltonian but induced by the measurement interface – the detector channel together with its coarse-grained readout. The Born rule follows from Gleason-type uniqueness (Gleason for projections in $d>2$ and Busch's extension for POVMs including $d=2$), as the unique probability measure consistent with additivity over exclusive events and basis-independence of the unitary sector. A compact qubit-pointer model yields an induced unsharp POVM $E_{\pm}=\frac12(\mathbb{1}\pm\eta\sigma_z)$ with sharpness $\eta$ fixed by pointer resolution, explicitly demonstrating detector-induced basis selection. OIPB aligns with decoherence and operational theories while diverging from collapse models (no spontaneous reductions) and the Many-Worlds Interpretation (no ontological branching). Empirical distinctions arise through POVM tomography, Wigner-friend incompatibility tests, and superposition stability bounds. Nested-observer paradoxes are resolved by a non-composability lemma: joint assignment of outcome propositions is possible only if a joint instrument exists. This relocates the origin of randomness to the stochasticity of the interface rules.

We demonstrate direct, non-invasive and non-contact detection of human cardiac magnetic signals using quantum sensors based on nitrogen-vacancy (NV) centers in diamond. Three configurations were employed recording magnetocardiography (MCG) signals in various shielded and unshielded environments. The signals were averaged over a few hundreds up to several thousands of heart beats to detect the MCG traces. The compact room-temperature NV sensors exhibit sensitivities of 6-26 pT/Hz^(1/2) with active sensing volumes below 0.5 mm^3, defining the performance level of the demonstrated MCG measurements. While the present signals are obtained by averaging, this performance already indicates a clear path toward single-shot MCG sensing. To move beyond shielded environments toward practical clinical use, strong noise suppression is required. To this end, we implement NV-based gradiometry and achieve efficient common-mode noise rejection, enabled by the intrinsically small sensing volume of NV sensors. Together, these multi-platform results obtained across diverse magnetic environments provide a solid foundation for translating quantum sensors into human medical diagnostics such as MCG and magnetoencephalography (MEG).

The simulation of strongly correlated fermionic systems remains a significant challenge in computational physics due to the exponential growth of the Hilbert space and the fermionic sign problem. In this work, we report a quantum computing demonstration exploring the unified physics of the Fermi polaron and the Bose-Einstein Condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) crossover. We develop an effective Hamiltonian formalism that bridges pairing superfluidity and impurity physics, mapping the system onto a gate-based quantum processor via the Jordan-Wigner transformation. By utilizing a first-order Trotter-Suzuki decomposition, we implement an ancilla-controlled Ramsey interferometry protocol to resolve the system's spectral response. Our implementation captures the smooth transition from a dressed quasiparticle (polaron) regime to a stable molecular bound state, characterized by a linear energy renormalization in the strong-coupling limit. We benchmark the quantum protocol against exact diagonalization and demonstrate its execution on the Barcelona Supercomputing Center (BSC-CNS) quantum hardware. To ensure reproducibility, we provide comprehensive device calibration metrics, including qubit coherence times and gate fidelities at the time of execution. Despite inherent hardware noise, the hybrid variational approach qualitatively observes the bifurcation of the spectral density.

In this work, we study the Hamiltonian Decoded Quantum Interferometry (HDQI) for the general Hamiltonians $H=\sum_ic_iP_i$ on an $n$-qubit system, where the coefficients $c_i\in \mathbb{R}$ and $P_i$ are Pauli operators. We show that, given access to an appropriate decoding oracle, there exist efficient quantum algorithms for preparing the state $\rho_{\mathcal P}(H) = \frac{\mathcal P^2(H)}{\text{Tr}[\mathcal P^2(H)]}$, where $\mathcal P(H)$ denotes the matrix function induced by a univariate polynomial $\mathcal P(x)$. Such states can be used to approximate the Gibbs states of $H$ for suitable choices of polynomials. We further demonstrate that the proposed algorithms are robust to imperfections in the decoding procedure. Our results substantially extend the scope of HDQI beyond stabilizer-like Hamiltonians, providing a method for Gibbs-state preparation and Hamiltonian optimization in a broad class of physically and computationally relevant quantum systems.

Quantum circuits naturally implement unitary operations on input quantum states. However, non-unitary operations can also be implemented through "block encodings", where additional ancilla qubits are introduced and later measured. While block encoding underlies a host of well-established theoretical applications, its implementation in practice has been prohibitively expensive for current quantum hardware. In this paper, we present practical and explicit block encoding circuits implementing matrix polynomial transformations of a target matrix. With standard approaches, block-encoding a degree-d matrix polynomial requires a circuit depth scaling as d times the depth for block-encoding the original matrix alone. By leveraging the recently introduced Fast One-Qubit Controlled Select Linear Combination of Unitaries (FOQCS-LCU) framework, we show that the additional circuit-depth overhead required for encoding matrix polynomials can be reduced to scale linearly in d with no dependence on system size or the cost of block encoding the original matrix. Moreover, we demonstrate that the FOQCS-LCU circuits and their associated matrix polynomial transformations can be controlled with negligible overhead, enabling efficient applications such as Hadamard tests. Finally, we provide explicit hardware-efficient circuits for representative non-unitary operators, namely quantum spin models, together with detailed non-asymptotic gate counts and circuit depths.