Papers

Morohoshi, Nakayama, Manabe, and Mitarai proposed a physically motivated quantum machine learning problem in which the goal is to predict quantities of the form $\operatorname{Tr}[f(H)\rho]$ from classical descriptions of a Hamiltonian $H$ and a quantum state $\rho$, where $f$ is an unknown function. We call this problem Hamiltonian function learning in this paper. They constructed an efficient quantum learning algorithm under suitable conditions, while leaving a rigorous proof of average-case classical hardness open. In this paper, we rigorously prove the average-case classical hardness for two distribution-specific Hamiltonian function learning problems for $f_{\cos,\pi}(\lambda)=\cos(\pi\lambda)$ and $f_{\exp,\beta}(\lambda)=e^{-\beta\lambda}$ discussed in the paper of Morohoshi et al. under the assumption of the average-case hardness of factoring random RSA moduli. More specifically, we show that an efficient classical randomized learner under squared loss whose output hypotheses are evaluable in classical polynomial time for either problem would yield a classical randomized polynomial-time algorithm for factoring random RSA moduli.

We develop Multivariate Quantum Signal Processing for designing matrix-valued transformations of multiple noncommuting nonnormal block-encoded matrices. Our framework equips quantum transducers with the analytic structure of multiport Infinite-Impulse-Response (IIR) filters and establishes a transfer-function methodology for designing quantum query algorithms. Efficiently computable analytic bounds that hold uniformly across the oracle promise yield efficient quantum circuits with logarithmic error dependence and near-unity success probability, paralleling the approximation-theoretic guarantees of univariate QSP/QSVT. We provide a complete characterization of achievable transfer functions and a principled library of analytic IIR components. Our modular designs greatly improve or resolve the per-oracle query complexity of open multi-oracle problems: (1) Hamiltonian simulation under $H=\sum_j H_j$ with weighted quasinorm cost $\approx t\langle\vec\lambda,\vec C\rangle_{1/2}+\mathcal{O}(\|\vec C\|_1\log(1/\epsilon))$ for block-encoding normalizations $\vec\lambda$ and costs $\vec C$; (2) sparse simulation with optimal time–norm $\Theta(\sqrt{d}\|H\|_{\rm 1\to2}t)$ and additive error dependence; (3) solving linear systems and (4) differential equations under minimal matrix assumptions with optimal weighted state-preparation and multi-term cost; (5) ground-state preparation and energy estimation; (6) generalized eigenvalue problems. We apply these to exactly simulate downfolded Hamiltonians with leading cost $t\langle\vec\lambda_{\rm eff},\vec C_{\rm eff}\rangle_{1/2}$ further reduced by fractional dynamic correlation energy contributions from coarse-grained Hamiltonians, and show similar classical-data-input-reduction results for multiscale graph classification via Kron reduction. We also show the online generalization with anisotropic Kalman filtering of streaming quantum data.

We discover a universal trade-off between the dissipation required to maintain a quantum state more sensitive than a thermal one and the sensitivity gain for a driven single-mode bosonic system under a thermal environment. Specifically, for Gaussian states, we rigorously derive a lower bound on the entropy production rate in the steady state in terms of the quantum Fisher information gain relative to a thermal reference state. Numerical investigations of Kerr nonlinearities further support that these bounds can hold beyond the Gaussian regime. Our results establish a new connection between steady-state thermodynamics and quantum metrological performance.

Distributed quantum processors could scale variational algorithms beyond single devices, but circuit depth, communication overhead, and noise limit their performance. We compare ladder, mixed-canonical, and brick-wall realizations of matrix-product-state (MPS) pretraining with matched per-layer two-qubit-block resources. Despite comparable ideal variational quantum eigensolver performance and gradient scales, the shallower brick-wall architecture reduces circuit duration, idle-time decoherence, and zero-noise-extrapolation (ZNE) overhead, yielding superior noisy and ZNE-assisted performance. We then extend MPS-pretrained circuits to modular processors with one communication qubit per quantum processing unit (QPU); a nearest-neighbor QPU-path schedule keeps the per-layer depth constant as QPUs are added. Distributed circuits whose inter-QPU links realize long-range interactions of the target Hamiltonian match or outperform the single-processor brick-wall under noise when communication idle time is short compared with the coherence time. These results establish hardware-aware co-design of tensor-network pretraining, circuit scheduling, and communication topology as a principle for variational quantum computation on noisy modular hardware.

We consider a cavity quantum electrodynamics (CQED) setup where an ensemble of spin-1 atoms driven by a classical field interacts with two driven cavity field modes. We show that the two sub-systems - the atoms and the two-mode cavity field, exhibit limit-cycle or quantum synchronization depending on the cavity drive strengths and other system parameters. In order to visualize the limit cycle and synchronization in the field, we introduce generalized two-mode field Husimi-Q function using SU(2) coherent states. For atomic spin states, we make use of spin-1 Husimi-Q function to visualize the same. We further corroborate the occurrence of field synchronization and limit cycle by analyzing $U(1)$ symmetry breaking, Wigner quasi-probability distribution, coherence properties of reduced field density matrix. Our results reveal intriguing interplay between the limit-cycle and quantum synchronization behavior, highlighting emergent quantum phenomena in driven dissipative interacting quantum systems. Additionally, we calculate Wehrl mutual information between the two modes and find that the field synchronization and Wehrl mutual information are mutually exclusive. Our study would be important to extract quantum advantages in quantum metrology using coupled atom-cavity systems.

The task of learning the Hamiltonian interactions governing a quantum system, given samples of its thermal (or 'Gibbs') states, is a foundational question at the intersection of quantum learning theory and many-body physics. In this paper, we draw connections to the quantum Gibbs sampling literature to introduce a natural learning algorithm we call the stationarity test: which simply "guesses" the Hamiltonian, and measures the rate-of-change of local observables, under the associated detailed-balanced quantum Markov chain [CKG23]. We leverage the stationarity test to address the following applications: 1. To give the first learning algorithm for the underlying interaction graph, i.e. structure learning, of lattice Hamiltonians at all temperatures, given copies of their Gibbs states. 2. To give the first learning algorithm for the coefficients of a lattice Hamiltonian, given only copies of its thermal metastable states, modeled as the "local minima" of the free energy. 3. In addition, we present a refinement to the recent area law for thermal metastable states [BCV25], which holds in the thermodynamic limit. Our learning algorithms are rigorous, time-efficient, and nearly sample-optimal in system size and accuracy. At a technical level, our arguments are based on new approximate locality and convexity properties for the quantum Fisher information of these Gibbs sampling algorithms.

Quantum low-density parity-check (QLDPC) codes are promising candidates for low-overhead fault-tolerant quantum computation, but their practical use requires fast, low-complexity, and reliable decoders. Belief propagation (BP) is attractive because of its local message-passing structure, yet standard flooding BP often suffers from convergence failures on QLDPC codes due to short cycles, degeneracy, and symmetric decoding trajectories. Learned sequential BP improves convergence by using a reinforcement-learning policy to choose variable-node update orders, but a single learned trajectory can still be sensitive to unfavorable local Pauli decisions. We propose a learned parallel bit-flipping sequential BP decoder with a new quaternary score combining syndrome gain, a quantized Pauli log-likelihood penalty, and Q-table lookahead at hypothetical post-flip states. Our decoder first runs learned sequential BP for a fixed number of iterations. If the syndrome is not satisfied, it constructs quaternary bit-flipping candidates, each corresponding to changing the current Pauli decision of one qubit. The selected candidates initialize independent learned sequential BP continuations from the same decoder state. Since these continuations are independent, they can be executed in parallel, so testing several candidates mainly increases parallel hardware resources rather than sequential decoding latency. Simulations on representative QLDPC codes over the depolarizing channel show that the proposed decoder improves the reliability of learned sequential BP while having a parallel low-latency structure.

Haar-random unitaries provide a canonical model of generic random quantum evolution, but they typically have exponential description and circuit complexity. Although pseudorandom unitaries efficiently emulate a single Haar-random unitary, many tasks require an entire reusable family of independently random-looking operations. We introduce pseudorandom function-like unitaries (PRFU), which generate such a family indexed by public labels using only a single short key. We distinguish classical- and coherent-label access and establish security under adaptive quantum queries. For classical labels, we provide a generic construction from a post-quantum pseudorandom function and a pseudorandom unitary. For coherent labels, we use an indexed path-recording framework to analyze interference across labels and prove security of a construction based on quantum-secure function and permutation primitives. We further show that PRFUs generate pseudorandom channels and quantum combs with private memory, which are secure against adaptive interventions and concurrent sessions. Combining PRFUs with unitary gluing yields a one-key family of pseudorandom unitaries whose supported register widths can be chosen after key generation. Further applications include nonce-resolved quantum authentication, coherently masked QRAM queries, and efficient emulation of random multi-time dynamics. Our results extend quantum pseudorandomness from individual operations to efficiently generated families of random-looking quantum dynamics.

Device-independent conference key agreement (DI-CKA) lets a group of parties establish a shared secret key from untrusted quantum devices, with security certified by non-locality. Existing DI-CKA protocols are each built around a single Bell inequality, typically a multiparty variant of the CHSH game. DI-QKD protocols, in contrast, have been built from a much richer landscape of non-local games, and it has remained unclear how to carry this landscape over to the conference setting. We introduce $\textit{Parity-$G$ games}$, which extend any two-player game $G$ to $N$ players, for every $N$, provided $G$ has an optimal strategy in which one player measures Pauli observables. The extension preserves the quantum and classical values of $G$, and the security of the resulting $N$-party protocol follows from an analysis of the two-player game alone. Our framework recovers the Parity-CHSH game of Ribeiro, Murta and Wehner (Phys. Rev. A, 2018) as a special case. Applied to the Mermin–Peres Magic Square Game, it yields a new $N$-player pseudo-telepathy game, the $\textit{Parity Magic Square Game}$, which ideal devices win in every round. We use it to construct the $\textit{first}$ DI-CKA protocol based on a pseudo-telepathy game. We prove the protocol secure against coherent attacks. It produces up to two key bits per round, and at low noise its key rate exceeds that of the DI-CKA protocol based on the Parity-CHSH game.

The $T$-count is a dominant cost of fault-tolerant Clifford$+T$ computation. We prove that a layer of $m$ disjoint CCZ gates, the diagonal core of a parallel Toffoli layer, needs exactly $6m+1$ $T$ gates in every Hadamard-free Clifford$+T$ circuit with clean ancillas. Campbell and Howard gave the matching construction, and to our knowledge this is the first proof that it is optimal for general $m$. The proof rests on a novel isotropy bound. When a gate's phase polynomial has only cubic terms, the vectors recording which $T$ gates touch each qubit span a self-orthogonal subspace over $\mathbb{F}_2$, and this forces the $T$-count to be at least twice its dimension. This argument gives a lower bound, computable by Gaussian elimination, on the $T$-count of every diagonal gate in the third level of the Clifford hierarchy. It is never below the stabilizer nullity $\nu$ and reaches $2\nu+1$ on non-Clifford cubic gates. No bound that also holds for circuits with measurement and feedforward can do this, since such circuits implement CCZ ($\nu=3$) with four $T$ gates, while the floor gives seven. It also recovers Campbell and Howard's count $4m+3$ for a fan-out of Toffolis. On the output of PyZX's TODD-based optimizer, relative to its Hadamard placement, it certifies $193$ of $311$ phase-polynomial blocks $T$-optimal, against $113$ for nullity, including $37$ of the $72$ blocks too large for exhaustive search.

Discretizing electronic degrees of freedom into atomic orbitals is the default choice to accurately model electrons in molecules in a compact and flexible way. We consider the task of simulating such electronic structure models on a quantum computer for $N$ orbitals, keeping the number of orbitals per atom constant. Atomic orbitals give rise to Hamiltonians with potentially up to $\mathcal{O}(N^4)$ terms and little structure, which made it challenging to match the complexity of methods based on plane waves and real-space grids. In this work, we show that a Trotter step for atomic orbitals can be implemented in depth $\mathcal{O}(\mathrm{polylog}(N))$ without ancillas by combining a rigorous treatment of orbital localization, a hierarchical Hamiltonian decomposition based on the Fast Multipole Method, and shallow quantum Fourier arithmetic circuits. By bounding the Trotter error, we obtain sublinear simulation depth, and our total gate count $N^{5/3 + o(1)}$ matches the best scaling known for any basis.

One of the most important initial steps in quantum computing is high-fidelity quantum state preparation, because errors in it can affect the final computational result. Therefore, one of the major challenges is to design a quantum circuit that can achieve the desired target state accurately with a smaller number of gates. Traditionally, circuits are designed using predefined rules and mathematical decompositions, but this makes it difficult to design circuits for different and complex target states. This paper presents TATVA, a reinforcement learning (RL) system for synthesizing quantum circuits. TATVA views circuit synthesis as a sequential decision problem in which the agents select one gate at a time and calculate the fidelity after each applied gate, with the gate producing the highest fidelity selected for the circuit. The system introduces a parallel architecture that uses two RL agents, Deep Q-Network (DQN) and Proximal Policy Optimization (PPO), along with Qiskit's statevector simulator. The system can synthesize up to 5 qubits while achieving a fidelity of 0.999999 and producing compact circuits. After achieving the desired fidelity, it performs a post-hoc optimization step that reduces the circuit depth while preserving the achieved fidelity. The circuit is finalized using fidelity, success rate, gate count, and circuit depth. Target states that are not used during training are used to test whether the system has learned effectively and can generalize beyond the training states. This approach aims to enable automatic quantum circuit synthesis with high fidelity using reinforcement learning.

Rare-earth (RE) atoms, such as erbium (Er), have inner-shell optical transitions in the near-infrared, some of which are in the telecom bands. These transitions are largely insensitive to the host environment due to effective shielding by the filled outer shells. Cryogenic rare-gas (RG) solids, such as solid neon (Ne) and argon (Ar), combine high chemical purity with a nearly nuclear-spin-free environment, making them attractive solid hosts for preserving optical and spin coherence. In this work, we isolate neutral Er atoms in solid Ne and Ar at 6 K and characterize their emission by steady-state and time-resolved photoluminescence (PL) spectroscopy. In both hosts, we observe several near-infrared transitions between 1000–1500 nm, including inner-shell emission in the telecom O and E bands. The $4f \rightarrow 5d$ transition near 1299 nm forms a multiplet of narrow components, consistent with crystal-field splitting, and decays on a microsecond timescale. The $4f \rightarrow 4f$ transition near 1437 nm shows a matrix shift below 1 cm$^{-1}$ in both hosts. In solid Ne, its inhomogeneous linewidth is bounded by the spectrometer resolution to < 22 GHz, and its PL lifetime reaches up to 78.9 ms, close to the estimated radiative limit. Thermal annealing extends the 1437 nm lifetime in Ne and suppresses the phonon sidebands relative to the zero-phonon lines in Ar. These results identify RG solids as promising hosts for long-lived telecom-band Er emission and provide a foundation for future spin-photon interfaces and hybrid quantum architectures.

Codon optimization is a challenging combinatorial optimization problem with important applications in synthetic biology, protein expression, and biotechnology. While quantum annealing has previously been explored for this problem, the application of gate-based quantum algorithms remains largely unexplored. In this work, we present a gate-based quantum computing framework for codon optimization by formulating the optimization objective as an Ising Hamiltonian and expressing it in terms of Pauli operators suitable for gate-based quantum processors. The proposed framework is investigated using the Variational Quantum Eigensolver (VQE), Sampling Variational Quantum Eigensolver (SVQE), and the Quantum Approximate Optimization Algorithm (QAOA), with benchmarking against exact diagonalization, classical optimization, and quantum annealing. Using a three-amino-acid benchmark, the proposed implementations successfully reproduce the exact ground-state solutions while identifying optimized ansatz selections, optimization strategies, initialization schemes, and hardware execution settings that provide reproducible performance on current noisy quantum hardware. Hardware demonstrations are performed on IBM Quantum processors to evaluate the practical implementation of the proposed workflow. As a work in progress, this study establishes a reproducible computational framework for gate-based quantum codon optimization and provides the foundation for future investigations of larger protein sequences as quantum hardware and algorithms continue to advance.

A 35 input/single output quantum phase neural network (QPNN) is proposed to recognize the English letters' A 'and' B 'composed 7*5 of pixels. Each node of the proposed QPNN has the input with 0 or 1. Through normalization and quantum phase encoding, each set of 35 with 0 or 1 digital inputs is encoded into a quantum superposition state described by 35 quantum phases. Then, a quantum rotation gate is used to introduce adjustable phase, and a controlled NOT gate is used to entangle the relative phase between the two inputs. The relationship between the input and output of the network is derived. This paper also derived the phase weight learning training algorithm with adaptive learning rate. The solutions with the recognition probability of 1 is designed, and the analytical expressions for all adjustable phase solutions with zero errors are not unique. The experimental performance is verified on the Qiskit platform. This paper uses phase drive to convert the probability calculation into an analytical polynomial function with adjustable rotation angles in the network, avoiding the bottleneck of generating all 2^35 complex exponential amplitudes and providing an effective way to solve the "exponential wall" problem, which provides a new implementation solution for the practical application of multi-input recognition problems.

We construct a two-parameter family of single-error-correcting seven-ququart codes with transversal $\tilde{A_7}$ symmetry, realizing the finite component of a two-qubit super-golden gate set. These $((7,4,3))_4$ codes encode two logical qubits and support non-Clifford operations by applying the same gate to each physical ququart. Our method constructs invariant parent states rather than searching directly for a codespace. For $n$ systems of local dimension $q$, suppose the local symmetry is a unitary $t$-group and the permutation symmetry is $t$-transitive. Maximal mixing of all marginals on at most $t$ sites is then equivalent to linear equations in Schur–Weyl sector weights. Every feasible solution yields parents of pure distance at least $t+1$; puncturing one site produces a $q$-dimensional code of distance at least $t$ with the prescribed local symmetry acting transversally. Steane and the nonstabilizer Fake Steane code reveal why the construction leaves continuous freedom. They share the same prescribed transversal Clifford and permutation symmetries, and their eight-qubit purifications lie on a circle: error correction fixes two invariant-sector norms but leaves the relative phase free. Keeping the same permutation group and replacing Clifford symmetry by $\tilde{A_7}$ $\leq SU(4)$ gives three fixed sector norms and two free relative phases, producing the new ququart family.

The equalities IP = PSPACE and QIP = PSPACE, the latter achievable with three messages, raise a basic question: how much of an interactive proof's power comes from the underlying physical theory? We study interactive proofs in general probabilistic theories, which include classical and quantum theory. The answer depends on what the prover and verifier exchange and how the theory specifies efficient operations. When they exchange only classical messages, protocols in every theory satisfying our standard assumptions decide exactly PSPACE. For protocols with a quantum verifier and quantum messages, allowing a prover to use any theory containing quantum theory does not increase the maximum acceptance probability. Thus, the three-message PSPACE result remains valid against such provers. When messages may be arbitrary systems, the interactive-proof class can strictly exceed PSPACE.

The Wigner function, in general, takes on negative values, and the amount of negativity in the Wigner function gives an operationally meaningful measure of the complexity of simulating the quantum state on a classical computer. In this paper, we study the growth of Wigner negativity of the Hartle-Hawking state of Jackiw-Teitelboim gravity under time evolution. We work in the gravitational length basis, at genus zero, and at high temperature, $\beta \ll 1$. Our main analytic result is simple: to leading order in $\beta$ the state is a Gaussian wavepacket of minimum uncertainty, sitting at rest at the turning point of the Liouville wall. Its Wigner function is therefore positive, and the negativity is $1+\delta(\beta,t)$, where the correction $\delta$ is smaller than any power of $\beta$. We show that $\delta$ is an even function of time, so there is no linear growth at $t=0$, and that once the packet has reflected off the wall its leading-order evolution is a Clifford shear, which cannot change the negativity. We also numerically study the time evolution of the Wigner function and its negativity. We observe that $\delta$ stays below $10^{-11}$ at $t=0$ and through the reflection, then rises slowly over a few tens of $\beta/\pi$, and then approaches a late-time value consistent with $\delta_\infty(\beta) \simeq 0.08\, e^{-4.4/\beta}$ for $0.25 \le \beta \le 1$: the lower the temperature, the larger the late-time negativity. The exact survival amplitude $Z(\beta+it)/Z(\beta)$ fixes the spread complexity to order $t^4$, and it also fixes the seed-normalised Wigner diagnostic of our earlier work (arXiv:2607.04065, arXiv:2607.17346). We take this as evidence that the length basis is ideally suited for a dual, semi-classical description of the dynamics at genus zero. Beyond genus zero the length basis is overcomplete, and we make no statement about finite $e^{S_0}$.

We revisit an established Quantum Control objective, characterize its exact local metric geometry, and reposition it as a rigorous benchmark for Search and Optimization. The trap-free topology of the landscape, established two decades ago, guarantees unhindered optimal pathways, but global topology alone does not govern convergence speed. Although the so-called Quantum Sphere is defined by the fourth power of the control field, we show that its yield gap admits an exact representation as a nonnegative linear combination of $\sin^2$ terms. From this single identity, we derive a two-sided quadratic sandwich with ratio $4/\pi^2$ on a certified, worst-case quarter-wave region, proving the optimal peak nondegenerate modulo its affine gauge and well-conditioned. For white-box optimization, on a halved (eighth-wave) region, the objective satisfies a Polyak-Łojasiewicz inequality with an explicit constant, granting Gradient Descent a linear rate of $1 - 16/(\pi^4\kappa_r)$, where $\kappa_r$ is the condition number of the relevant Hessian block. For black-box optimization, we prove that the elitist single-parent Evolution Strategy converges linearly, almost surely and in expected hitting time, from a certified sublevel set, despite the landscape's continuous gauge symmetry and its lattice of periodic optima; the certified level is explicit whenever the landscape is trap-free, and near the optimum the strategy provably sees only the quadratic tangent of the peak. Systematic numerical simulations corroborate the theory. Finally, we show that additive input (actuator) noise reweights each term of the representation by a Debye-Waller factor without disrupting the landscape's structure, and outline open challenges: output (signal) noise, far-field plateau escape, angular-synchronization certificates, and another physically scalable benchmark (SHG with Glass).

For quantum machine learning, the exact boundary between classical and quantum advantage is still poorly understood. Direct comparison between quantum neural networks (QNNs) and existing classical models, which encompass fundamentally different function classes, often fails to provide broader insight into the difference between the two. Inspired by the techniques of Neural Quantum States and Random Fourier Features, this work introduces Neural Fourier Surrogates (NFS), a stochastic classical neural network architecture for efficiently learning coefficients over the same finite Fourier series support as quantum neural networks. Testing on a selection of tabular benchmark datasets, we find that NFS is an effective classifier architecture broadly competitive with established classical baselines, including a comparable Random Fourier Features model, and possessing comparable performance to data-reuploading QNNs; combined with additional analysis comparing the learned Fourier spectra of QNNs and NFS on synthetic data, these results establish NFS as a natural classical baseline for evaluating QNN performance.

Remote state preparation is a fundamental quantum-information protocol that exploits prior knowledge of a target state to reduce the communication resources required for quantum-state distribution. Here, we propose a remote-state-preparation protocol for a stationary electron-spin qubit using hybrid entanglement between the electron spin and a coherent-state light pulse, generated by spin-dependent reflection from a spin-cavity system. Unlike single-photon encodings, the coherent-state encoding is naturally tolerant of photon loss: a loss channel attenuates the coherent-state amplitude, leading to a gradual reduction in preparation fidelity rather than probabilistic protocol failure. The central difficulty—implementing the projection onto superpositions of nonorthogonal coherent states required in the conventional protocol—is circumvented by coupling the transmitted pulse to an auxiliary spin, followed by homodyne detection and a spin projective measurement. The protocol therefore avoids direct coherent-state-superposition measurements and photon-number-resolving detection. In the ideal limit, deterministic preparation of a particular class of target states can be achieved using only one bit of classical communication. We analytically quantify the effects of coherent-state nonorthogonality, fiber loss, and spin dephasing on the preparation fidelity. Increasing the coherent-state amplitude improves state distinguishability and hence the preparation fidelity, but also enhances which-branch information leakage caused by photon loss, resulting in an optimal amplitude at each transmission distance. For experimentally relevant parameters, the optimized average fidelity remains well above the classical benchmark over distances of tens of kilometers. We also discuss a possible implementation using diamond nitrogen-vacancy centers.

We study mixed-state entanglement in Gibbs states with strong $\mathrm{SU}(2)$ symmetry, focusing on locally interacting spin systems with ferromagnetic interactions. Our main result is to show that finite-temperature ordering transitions are associated with entanglement transitions, and therefore the steady state of strongly symmetric Lindbladians can exhibit entanglement transitions. While in the paramagnetic phase it is known that the distillable entanglement and logarithmic entanglement negativity between two halves of a large system grow logarithmically with the square root of the number of spins, we show that in ferromagnetic phases these quantities grow parametrically faster with system size. To arrive at this result we first establish relations between these mixed-state entanglement measures and spin correlations in states that are singlets under global $\rm{SU}(2)$ symmetry transformations. We then introduce a semiclassical theory for $\rm{SU}(2)$ singlet thermal states. While the global singlet constraint generally enters this theory as a complicated function of the full semiclassical spin configuration, we show that in large $S$ limit it simplifies drastically to a Gaussian suppression of total magnetization in disordered phases as well as in ordered phases in the vicinity of continuous thermal phase transitions. This leads us to a field theory describing spin correlations in the singlet sector. Using this we determine the behavior of various probes of mixed-state entanglement at low and at high temperatures, supporting our analytical results using numerical Monte Carlo simulations of a three-dimensional lattice realization of our semiclassical theory. We also use exact numerics in one-dimensional spin-$1/2$ systems to confirm our predictions for the scaling of mixed-state entanglement with correlation length and system size in the paramagnetic phase.

Control and readout systems for superconducting quantum computing support real-time control and high-fidelity qubit-state discrimination. We examine when additional digital processing improves readout fidelity. A common baseline for dispersive readout uses a boxcar averager to compute a uniformly weighted average over a fixed window, followed by threshold-based state assignment. In this paper, we evaluated an adaptive finite-impulse-response (FIR) filter trained in real time using the least-mean-squares (LMS) algorithm on a field-programmable gate array (FPGA) quantum controller. We also analyzed measured readout shots offline to compare the frozen filter with boxcar averaging and to evaluate per-sample weighting and sequential detection. For the fixed FIR filters tested, we show summing the filtered samples gives the boxcar sum multiplied by one complex number, apart from a small edge correction. We call this the kernel collapse. The multiplication scales the state separation and noise equally without improving state discrimination, and we call this the boxcar limit. The frozen LMS filter reduces trace noise, but same-shot offline comparisons show no resolved improvement in readout fidelity at the tested operating points. On a 2D transmon, tuning the integration window accounts for much of the observed improvement over full-window integration, highlighting the importance of an optimized boxcar baseline when evaluating per-sample weighting. We then examine how changing the decision method can reduce calibration effort and decision time. On a higher-fidelity 3D ancilla readout, model-based template estimation reaches the same fidelity target as direct averaging with about 30 rather than 300 labeled shots per state. Offline sequential replay assigns most shots before the acquisition window ends, with contrast fidelity within an absolute +/-0.5% tolerance of the boxcar on the primary...

We establish duality relations for conditional entropies relative to subalgebras of arbitrary von Neumann algebras, including the Umegaki relative entropy as well as the sandwiched- and Petz-Rényi divergences. Even in finite dimensions, these results extend the familiar dualities for conditional entropies from tensor-product subsystems to general subalgebras, while also lifting the framework to the fully infinite-dimensional setting. As an application, we establish an infinite-dimensional extension of quantum Stein's lemma when the alternative hypothesis is the state space of a finite-index subalgebra, which gives an operational interpretation of the relative entropy to a subalgebra as the optimal asymptotic error exponent in composite quantum hypothesis testing-the first beyond finite dimensions.

Uncovering new phenomena in nature requires experiments. For centuries, their design has been exclusively a human endeavor. Today, a new paradigm is emerging in which artificial intelligence and computational methods can design experiments themselves. Realizing this form of automated scientific discovery requires simulators that are sufficiently expressive to represent the diverse physical processes and couplings from which new experiments can be constructed. In this direction, we introduce esQueranto, a differentiable software that brings photon-number quantum optics and structured-light propagation into a common description, allowing the spatial evolution of light to directly influence non-classical quantum states and their interference. esQueranto is implemented in JAX, providing automatic differentiation and hardware-accelerated evaluation for optimization and automated search. We demonstrate the framework across a broad range of quantum-optical applications that exercise complementary aspects of its physical description. By combining quantum and structured-light physics within a single differentiable simulator, esQueranto takes an important step towards the dream of a foundational simulator in physics.

Negative Kirkwood–Dirac quasiprobabilities are credited with the quantum advantage of interaction-free measurement and postselected metrology. We test that claim on the task interaction-free measurement was designed for: learning about a sample letting it absorb as little light as possible. The Kirkwood–Dirac distribution of path and output gives the linear response to a weak sample: its real part responds to absorption, its imaginary part to a phase. For a pure single photon passing once through any interferometer, the Fisher information about transmittance per absorbed photon is the direct-transmission value minus a sum of squared imaginary parts: no interferometer or readout beats direct transmission. Negativity plays no role beyond concentrating information in weakly lit outputs. The imaginary parts of the Kirkwood-Dirac distribution depend on the output basis here, not on the sample, so a basis exists in which every term is real, which is optimal. A single photon gains information per absorbed photon only through a phase response, which for an optical line needs a thick or inhomogeneously broadened sample, or through many passes when absorptions go uncounted, as shown by a critically coupled resonator. For detecting a weak absorber, negativity gives a single-shot advantage that does not accumulate over multiple trials; advantage instead accumulates when there are outputs which are dark without the object, a case which needs no negativity.

Excited organic dyes chemically bound to an icosahedral virus shell can spontaneously synchronize and emit a superradiant burst of light. The mechanism that allows it to occur at room temperature, despite collisional dephasing and inhomogeneous broadening, is not understood. Few other known low-dimensional condensed matter systems exhibit room-temperature superradiance (SR). In the fluctuation-prone environment of molecular-based systems, electron–vibrational coupling has been proposed to play a central role. Here, we addressed experimentally the existence of underdamped virus capsid phonon-like modes and theoretically their involvement in the transition from uncorrelated to cooperative emission. We find that SR-active dye-labeled capsids exhibit underdamped low-frequency oscillations that modulate the dye excited-state response, and modeling shows how such capsid motion can promote the collective polarization required for superradiant emission.

Constraint-preserving mixers keep QAOA within a feasible subspace, but feasibility and global mixer connectivity do not determine which feasible configurations are available to a particular shallow circuit. We study constrained QAOA at the level of the circuit actually executed: a specified feasible initial state, finite depth, and finite schedule of mixer interactions. We define the finite-depth accessible set $R_p(M,x_0)$ and show that the computational-basis support of the ideal QAOA circuit is contained within it. This gives a parameter-independent objective ceiling $f_R^\star=\max_{x\in R_p}f(x)$ and a normalized reachable-quality diagnostic $Q_R$, separating accessible volume from the objective quality contained within it. We evaluate this framework using resource-matched block-local XY mixer schedules for constrained portfolio optimization and synthetic block-constrained quadratic problems. Across 207 favorable-tail CVaR QAOA configurations, $Q_R$ shows the strongest association with realized shallow-QAOA performance among the structural diagnostics considered, with Pearson and Spearman correlations of $0.7003$ and $0.8057$; the relationship remains positive under controlled and dependence-aware analyses. The distinction persists across changes in feasible initialization, portfolio size, and objective family. A compilation-only study further shows that, for the dense portfolio Hamiltonians considered here, phase-separator routing dominates the compiled two-qubit resource scale, while mixer schedules with comparable compiled two-qubit cost can exhibit markedly different finite-depth accessible quality. These results motivate objective-relevant finite-depth accessibility as a complementary diagnostic for resource-bounded constrained QAOA.

We consider multi-dimensional quasiperiodic Schrödinger operators with monotone sawtooth-type potentials in the perturbative localization regime. We prove that a given gap is closed iff a corresponding (via a natural gap labeling) eigenfunction vanishes at the origin. Using this, we show that for a generic choice of the sampling function $f$, the spectrum of such an operator is a Cantor set, with all possible gaps being open. We also provide a class of functions $f$ for which some gaps are closed. Finally, we observe that certain gaps are more difficult to close than the others.

We present a routing-aware pruning strategy for quantum circuits that selectively removes parametric two-qubit gates whose computational contribution is outweighed by the fidelity cost of their execution, and assess it across both Noisy Intermediate-Scale Quantum (NISQ) and fault-tolerant quantum computing (FTQC) architectures. Each two-qubit gate of a circuit is evaluated by comparing an architecture-independent lower bound on the fidelity cost of omitting the gate against a hardware-specific model for the routing execution cost in each setting. We additionally provide an analytical characterization of the pruning boundary as a function of rotation angle, qubit distance, and hardware noise. Simulations on benchmark circuits demonstrate gate count reductions of up to 48.6% and fidelity improvements of up to 47.7% in the NISQ regime, while a feasibility analysis on FT hardware indicates that pruning is expected to remain relevant across a range of code distances and physical error rates. These results establish routing-aware pruning as a practical and unified compilation strategy across the quantum computing stack.