We develop, to our knowledge, the first receiver-centric blockwise sequential-detection framework for covert communication over thermal-loss bosonic channels. In this architecture, each block serves as a binary super-symbol, and the key design problem is to determine the minimum detection-segment length that enables Bob to detect an active block before the block ends while remaining covert to Willie. For any fixed physically realizable general-dyne receiver, Bob's post-change information growth is linear in the small-signal regime, whereas Willie's detectability obeys a quadratic quantum relative entropy law. Exploiting this asymmetry, we show that under a per-block covertness budget the asymptotically optimal signaling strategy is uniform across the detection segment, and we derive an explicit minimum-length condition under which a single-pass cumulative sum (CUSUM) detector crosses threshold within the same block with exponentially high probability. The resulting design law yields a covert blockwise binary codebook over a finite transmission horizon and establishes a concrete link between bosonic covert communication, sequential detection, and blockwise signaling design. More broadly, these results provide design guidance for covert quantum communication systems with physically realizable receivers, and help bridge information-theoretic covertness guarantees with implementable receiver-aware optical communication design.

We present an analytical and numerical Floquet treatment of a driven polar two-level quantum system characterized by both longitudinal and transverse coupling to a periodic field. Analytically, we derive a dressed-frame effective Hamiltonian up to first order in the inverse driving frequency, incorporating the longitudinal coupling nonperturbatively. This yields closed expressions for the effective transverse coupling strength and the effective detuning, both of which are modified by the presence of the longitudinal interaction. In the nonpolar limit, these expressions recover the usual near-resonant Rabi coupling and the Bloch-Siegert shift. As a second main result, we develop a numerical flow-equation framework that yields a time-independent effective Hamiltonian across a broad range of transverse and longitudinal coupling strengths. This dual framework is relevant for a variety of platforms, including driven polar quantum systems, optical lattices, superconducting circuits, and solids subject to surface acoustic waves.

We present numerical simulations supporting the random-matrix state-reduction framework developed in the companion theoretical paper. The simulations test the main derived features of the model: isotropic diffusion generated by Gaussian Unitary Ensemble Hamiltonians in projective state space, the restriction of this diffusion to Brownian motion on the classical submanifold, Born-rule frequencies for detector-defined outcome classes, and stroboscopic Newtonian motion for macroscopic systems under repeated environmental monitoring. We also compare GUE and GOE random Hamiltonians and show that GOE fails to produce the required isotropic complex projective diffusion. Further simulations examine finite-resolution detector records in the double-slit experiment, Zeno stability of recorded equivalence classes, effective irreversibility from high-dimensional state-space dynamics and loss of path information, and tensor-product particle-device dynamics in the device limit. The results show that microscopic state reduction, stable measurement records, effective irreversibility, and macroscopic classicality can be described as different coarse-grained manifestations of the same stochastic unitary mechanism.

We develop a state-space geometric framework for measurement, classicality, and quantum paradoxes, based on one dynamical conjecture. Classical configuration space and classical phase space for a mechanical system arise as distinguished submanifolds of projective quantum state space. On these submanifolds, the Fubini--Study geometry induces Euclidean classical geometry, and the tangent component of Schrödinger evolution reproduces Newtonian dynamics. Within this framework, interactions with measuring devices and environments are described by random-matrix dynamics on projective state space, generated by matrices drawn from the Gaussian Unitary Ensemble. We show that this random-matrix dynamics yields isotropic diffusion, giving Born-rule transition probabilities in microscopic measurements and stabilizing classical behavior in macroscopic systems. We further argue that the random-matrix conjecture is not an independent ad hoc assumption: under natural translation-invariance assumptions on the distribution of state-space steps originating on the classical submanifold, the unitary lift of homogeneous and isotropic Brownian motion on that submanifold is uniquely given by the Gaussian Unitary Ensemble, up to scale and an irrelevant scalar part. The resulting framework provides a unitary account of measurement and the quantum-to-classical transition and, if accepted, offers a dynamical resolution of standard quantum paradoxes.

We introduce algorithmic improvements to quantum-classical auxiliary-field quantum Monte Carlo (QC-AFQMC) that reduce the dominant per-step classical scaling from $\tilde{\mathcal{O}}(N^{5.5})$ to $\tilde{\mathcal{O}}(N^{4.5})$ as a function of the number of molecular spin-orbitals $N$. Central to this improvement is the application of Aitken's block transformation to handle singular Pfaffians arising in the estimation of overlaps between a quantum trial state and classical Slater-determinant walkers. Together with the use of algorithmic differentiation for the computation of the force bias, this yields a $248\times$ estimated runtime improvement for a system of 100 molecular orbitals. Using our workflow, we demonstrate a ground-state energy calculation for $H_8$ from quantum data collected on IQM Emerald and post-processed with a tensor-network-based error-mitigation technique. We further validate the method's scalability through noiseless simulation of hydrogen chains up to $H_{12}$, and on the lithium-air battery related rearrangement pathway of the $Li_2O_4$ lithium superoxide dimer in a (26e, 20o) active space. We estimate both quantum and classical runtimes for a potential fault-tolerant implementation of QC-AFQMC, showing that the method holds promise for the early fault-tolerant era. These results move QC-AFQMC a step closer to treating chemically relevant systems.

Measuring a quantum computation in a basis adapted to a symmetry it carries reduces the repeated measurements, commonly referred to as ``shots'', needed to read a statistical answer. Detecting the symmetry a quantum state carries has many uses: certifying a claimed symmetry, identifying a conserved-charge sector, flagging symmetry-breaking as an error signature, and selecting a compression or readout basis; shot-count reduction is developed here as one exemplary case. Existing methods assume the symmetry is known in advance; we remove that assumption. When it is unknown, the carried symmetry is discovered from the data by a symmetry test that scores candidate groups, and the largest passing group is exploited as the measurement basis. We state the pipeline precisely, prove the selection rule is unbiased, and charge discovery in full. Two conditions are treated, both detected by the same score with a different projection: a weak condition, commutation with the representation, and a strong condition, confinement to a single charge sector, the distinction drawn in the quantum-reference-frame literature. A single circuit, a controlled twirl followed by a SWAP test, discovers both: discarding the group register tests the weak condition, post-selecting it the strong one. The framework is general over finite groups, with cyclic (Fourier), dihedral, and symmetric-group (Schur-Weyl) examples; strong confinement to the symmetric, or Dicke, subspace is an exponential reduction. Seeded demonstrations show the loop wins net of discovery: weak matching on momentum readout reduces shots by a factor widening from ten to several thousand, and strong matching on a two-system target by a further factor of the subsystem size. Blind symmetry matching is a practical primitive for the common case where the matched basis cannot be written down in advance.

The emergence of classical behavior and the origin of thermal equilibrium are two central problems in the foundations of physics. In the standard accounts, both phenomena are typically explained through interactions with an external environment: decoherence suppresses quantum interference, while coupling to a thermal bath drives relaxation toward equilibrium. Over the last decades, however, it has become clear that equilibration and thermalization can arise even in fully isolated quantum systems, in the operational sense that the expectation values of relevant observables remain close to equilibrium values for most of the time. Here, we ask whether the same intrinsic equilibration mechanism can also account for the emergence of classical behavior. Using rigorous bounds on equilibration in closed systems, we derive sufficient conditions under which a time-evolved pure state becomes, for most times, operationally indistinguishable from a classical mixture associated with a chosen physical property. We identify two complementary routes to such operational classicality: either the chosen property almost commutes with the system Hamiltonian or the observables used to probe the system lose access to the remaining coherence after equilibration. Our results show that classical behavior need not be confined to the energy basis and may emerge even when substantial coherence remains present in the equilibrium state. This establishes a direct connection between two foundational questions: the origin of thermalization in isolated quantum systems and the quantum-to-classical transition

We investigate the dynamics of Quantum magic, formally known as non-stabilizerness, quantified by the stabilizer Rényi entropy (SRE), across the stages of the wormhole-inspired teleportation protocol (WITP) in the Sachdev-Ye-Kitaev (SYK) model. By tracking the SRE of the full pure state across scrambling, message insertion, left-right coupling, and right-side extraction, we uncover a regime-dependent relationship between magic accumulation and teleportation fidelity. In the gravitational (low temperature) regime, fidelity rises concurrently with magic from early times, whereas in the peaked-size (high temperature) regime, the magic saturates near the Haar-typical value before teleportation onset. A baseline-subtracted diagnostic comparing coupled and uncoupled protocols reveals that the double-trace coupling first suppresses and then channels non-stabilizer resources toward the teleportation signal, with the channel amplitude decreasing monotonically with inverse temperature. Comparison with a chaotic random two-local model, which generates near-maximal magic yet fails to teleport, demonstrates that structured magic redistribution, rather than raw non-stabilizerness, underlies successful wormhole traversal. Moreover, the magic transiently dips at the fidelity peak, marking the teleportation event in the time domain. Our results are robust across the three system sizes studied ($N_{\mathrm{maj}}=8,10,12$), and the fidelity-magic trajectories exhibit an approximate collapse across system sizes when the SRE is normalized by the Haar-typical prediction.

We investigate quantum pump depletion and non-Gaussian state generation in doubly pumped Kerr microresonators operating in the intraresonance regime. The pump modes are treated quantum mechanically rather than as undepleted classical amplitudes, allowing pump depletion, back-action, entanglement generation, quadrature fluctuations, and Wigner-function negativity to emerge from the same multimode dynamics. Starting from the Kerr four-wave-mixing selection rule, we distinguish an effective resonant photon-conversion model from the full Kerr Hamiltonian containing self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM). The reduced model isolates the photon-conversion network responsible for the discrete $\mathbb{Z}_{n+1}$ phase structure, whereas the full model retains operator-valued nonlinear Kerr phases. For the \(n=2\) intraresonance branch, the four-mode reduced initial-value problem with fixed coherent pump phases has a residual \(\mathbb{Z}_3\) symmetry and generates cat-like Wigner structures near the interaction length at which the generated-mode population \(\langle n_1\rangle\) is maximal and the pump population \(\langle n_0\rangle\) is strongly depleted. The resulting states are not the canonical even or odd coherent states of Dodonov, Malkin, and Man'ko, but multicomponent Schrödinger-cat-like states characterized by Wigner negativity, non-Poissonian statistics, pump-mode quadrature squeezing, and large single-mode Schmidt numbers. Comparison of the reduced and full Kerr dynamics shows that uncompensated SPM/XPM-induced phase shearing suppresses the interference fringes and Wigner negativity responsible for the clearest cat-like signatures. These results identify quantum-depleted intraresonance Kerr dynamics as a route to symmetry-organized non-Gaussian states in Kerr resonators.

We develop a block-encoding compiler that speeds up linear combination of unitaries Hamiltonian simulation programs by treating matrix product operators as compressed, virtual-path LCU programs. In showing how these new conditional PREP and SELECT stages are compiled in terms of a parent matrix product operator, we go beyond typical operator splitting product formulas and illustrate how tensor networks are a natural language and valid intermediate representation for quantum circuits. Our results are numerically verified for two important cases, namely, Heisenberg and perturbed Heisenberg-adjacent chain real-time evolution, and highlight polynomial speedups. Specifically, we highlight a polynomial speedup that avoids the $\mathcal{O}(N^K)$ Pauli-string growth when the compressed MPO bond dimension and path normalization remain mild. We quantify how MPO truncation error and bond-dimension budgets affect the compiled polynomial representation. Our algorithms show how classical pre-processing in terms of tensor network data structures opens new avenues to accelerate quantum algorithms.

We present a method for performing distributed quantum computing with controlled approximations. Exact distributed quantum computing requires exponential classical information to reconstruct the quantum process. However, we show how the classical cost is reduced to polynomial if the quantum procedure can be partitioned between a qubit that is weakly coupled the other qubits. We demonstrate our method for a layered circuit based on the circuits used for the quantum approximate optimization algorithm.

Bell- and contextuality-type inequalities have become practical probes of many-body quantum correlations, often involving only few-body correlators and quantities with a direct Hamiltonian interpretation such as an energy density. Here we show that, in infinite one-dimensional translation-invariant chains, contextuality can acquire a genuinely thermodynamic meaning: within the witness families studied, the maximal quantum violation coincides with spontaneous breaking of one-site translation symmetry, producing strictly $p$-periodic ground states with $p>1$. Along natural continuous interpolations between classical-bound and quantum-optimal Hamiltonians, the classical bound marks a symmetry-breaking point where competing classical periodicities are lifted in favor of a unique quantum-selected period. At the quantum optimum, the studied families admit exact finite-size reductions: a translation-invariant contextuality witness induces a $p$-site periodic-boundary-condition inequality with identical classical and quantum bounds (hence no loss under reduction), and in several cases the resulting finite inequalities are tight. This reduction turns an infinite-chain contextuality certification into a compact, hardware-testable benchmark on a small ring, requiring only local energy measurements. We establish the mechanism analytically in representative two- and three-body witness models and corroborate it more broadly using a translation-invariant adaptation of semidefinite-program hierarchies together with variational matrix-product-state algorithms.

Stochastic resetting has emerged as a versatile protocol to drive quantum many-body systems to non-equilibrium steady states by interspersing unitary dynamics with measurements and resets at random times. In spite of this, a quantum hardware validation of such non-equilibrium steady states is still missing. Here, we achieve this goal by first formulating a noisy discrete-time theory where unitary gates alternate with noisy mid-circuit projective measurements and conditional resets. This noisy conditional resetting theory is then demonstrated on a superconducting quantum processor for up to $N=7$ qubits. We consider, as a paradigmatic case, the unitary dynamics of the interacting Floquet transverse-field Ising model. The stationary state of the noisy conditional resetting agrees quantitatively with the experiments, and it shows crossover behavior related to the equilibrium quantum phase transition of the model. Our results might thus pave the way for the preparation of collective stationary states on noisy quantum devices and for further developments of quantum algorithms involving mid-circuit measurements.

The Dirac operator on a lattice cannot be both local and free of fermion doubling, at least not without breaking fundamental symmetries. Non-local, symmetry-preserving discretizations that avoid doubling have a quantum circuit representation as a linear-combination-of-unitaries (LCU) in which both the number of terms and their norm (the subnormalization factor) grow with the lattice size, compromising the efficiency of a quantum algorithm. We show that the tangent-fermion discretization escapes this obstruction when the Dirac equation is written as a generalized eigenvalue problem with a local operator pencil: Each member of the pencil has an exact LCU, with term count that is independent of lattice size and with subnormalization factor of order unity, on a par with elliptic operators. This provides an efficient block-encoding primitive for Dirac spectra and Green functions without fermion doubling.

Optically addressable shallow donors in ZnO combine efficient spin-selective optical transitions with the potential for long spin coherence in an isotopically purifiable host lattice, making them an attractive platform for spin-photon quantum technologies. A key missing capability, however, has been coherent control beyond the small-angle rotations accessible with ultrafast optical pulses. Here we demonstrate coherent microwave control of implanted $^{115}\mathrm{In}$ donors in ZnO. Resonant optical pumping initializes and reads out the donor electron spin. Pulsed optically-detected magnetic resonance resolves the ten hyperfine transitions associated with the coupled $^{115}\mathrm{In}$ nuclear spin (I = 9/2) and reveals optical-pumping-induced nuclear spin polarization. We observe coherent Rabi oscillations with a maximum Rabi frequency of $Ω/2π= 36.2 \pm 0.7$\;MHz, corresponding to a $π$-pulse time of 13.8$\pm$0.3\;ns, and characterize the spin coherence using Ramsey, Hahn echo and dynamical-decoupling measurements. Unexpectedly, the measured coherence is substantially shorter than reported in previous optical studies of donor spins in ZnO at high magnetic field. Control experiments rule out several simple explanations including microwave heating and instantaneous diffusion from the driven donor ensemble, leaving an open question regarding the origin of decoherence at low magnetic field in microwave-controlled ZnO donors. These results establish microwave control of ZnO donor qubits with resonant optical access to specific donor species. More broadly, they demonstrate that coherent microwave control can be achieved in optically addressable spin systems with nanosecond-scale inhomogeneous dephasing, enabling field-, temperature-, and materials-dependent studies of coherence-limiting mechanisms and the development of optically interfaced electron-nuclear spin registers.

We introduce a quantum reservoir computing online protocol that realizes amplitude encoding on quantum hardware. Our scheme combines mid-circuit measurement and reset operations to implement the partial-trace dynamics underlying amplitude encoding, while an indirect measurement scheme provides access to reservoir observables without interrupting temporal processing. In contrast to other approaches, our method preserves online operation, avoids input buffering, and keeps the runtime linear in the number of time steps. We present the theoretical formulation of the protocol and a proof-of-principle implementation on quantum hardware, and we evaluate its performance on two standard benchmark tasks. Our results show that the reservoir dynamics can be monitored through both direct measurements of the input qubits and indirect measurements of the memory qubits, enabling observation of the full system while isolating the internal evolution of the reservoir. This work provides a practical route toward scalable hardware implementations of amplitude-encoded quantum reservoir computing and opens the door to systematic experimental studies of complex quantum reservoirs.

We introduce the Biorthogonal Variational Quantum Eigensolver (B-VQE), a quantum algorithm for simulating non-Hermitian many-body systems on noisy intermediate-scale quantum (NISQ) hardware. Non-Hermitian quantum matter exhibits exceptional points, parity-time symmetry breaking, and non-Hermitian skin effects, yet existing quantum algorithms often rely on costly post-selection procedures and are not designed to capture biorthogonal eigenstates. B-VQE employs independent variational circuits to represent the left and right eigenstates of a non-Hermitian Hamiltonian and optimizes a biorthogonal objective function that directly tracks non-Hermitian phase transitions. The framework incorporates an Exceptional-Point Detector (EPD) that identifies exceptional points through a hardware-native coalescence metric and a Non-Hermitian Quantum Geometric Tensor (NH-QGT) readout that distinguishes state-topological and band-topological signatures in interacting many-body systems. To overcome the exponential overhead associated with conventional non-Hermitian simulation, we develop an importance-sampling mitigation strategy that removes the need for ancilla-based post-selection while retaining polynomial computational scaling. We validate the approach on three representative models: a non-Hermitian Hubbard chain, a non-Hermitian XXZ spin chain, and a two-dimensional non-Hermitian (t)-(J) model. B-VQE achieves relative energy errors below (5\times10^{-3}) and locates exceptional points with high accuracy on noise-free simulations while resolving phase boundaries associated with localization, quantum scars, and skin-effect physics. These results establish B-VQE as a scalable NISQ methodology for constructing non-Hermitian many-body phase diagrams and exploring topological and critical phenomena in open quantum systems.

The continuous progress of quantum technologies has spurred the exploration of their potential applications across diverse fields, particularly in combinatorial optimisation. In this work, we study a quantum-classical optimisation framework based on Pauli Correlation Encoding, an encoding scheme that can represent m binary variables using a polynomial number of qubits. To evaluate the performance of the method, we use four classical optimisation problems against the instances of the QOPTLib benchmark. The study includes an analysis of the impact of the compression order of the encoding scheme, the problem structure, and hyperparameter selection on solution quality, as well as the role of post-processing in improving performance. Additionally, we study the effect of shot-based execution and hardware noise, showing how these factors influence both the accuracy of expected value estimation and the overall dynamics of the optimisation process. The results indicate that the proposed PCE-based framework achieves competitive performance against the benchmark and, in several cases, obtains equivalent or even superior solutions, highlighting its potential as an efficient encoding strategy for quantum optimisation in the NISQ and near fault-tolerant era.

Realizing scalable Quantum-to-the-Home (QTTH) faces a bottleneck: link asymmetry in broadcast continuous-variable quantum access networks (CV-QANs) hinders the selection of a globally optimal modulation variance. We demonstrate a downstream broadcast CV-QAN connecting a Quantum Line Terminal (QLT) to multiple Quantum Network Units (QNUs) over commercial fiber. Operating within a trusted local network domain, we establish a multi-user utility model to select the optimal shared variance, balancing network efficiency and user fairness. Supported by robust digital signal processing, our 1:16 field trial achieves Mbit/s-level asymptotic secure key rates, bridging theoretical protocols with Fiber-to-the-Home reality and guiding future scalable access architectures.

End-to-end entanglement distribution is a key capability of upcoming quantum networks, enabling applications like distributed quantum computing, quantum sensor networks, and secure communications. Hence, its realistic and efficient simulation is crucial for quantum network design and for assessing the ability of a network to run certain applications. This work provides tools to scale-up and improve the realism of entanglement generation simulations in quantum networks. This is achieved by deriving analytical results that directly return the success probability, the output state and corresponding fidelity of a selected entanglement generation protocol, while accounting for a variety of noise sources affecting the protocol. These results are then integrated and streamlined in an upgraded version of SeQUeNCe, one of the most popular quantum network simulators. The resulting simulator features increased scalability by reducing computation time by more than 60%, while allowing for a variety of realistic noise sources, including imperfect mode matching, dark counts, and imperfect memory initialization. The simulator is also benchmarked with real experimental data and is capable of replicating the average entanglement generation time and the final state fidelity of a selected experiment. Altogether, the results can enhance current quantum network simulation capabilities towards large-scale networks, paving the way for the future quantum internet.

The photon blockade (PB) effect is a hallmark non-classical phenomenon in quantum optics and finds important applications for building quantum sources, while the control of PB by the non-Hermitian exceptional points remains largely unexplored. In this work, we theoretically investigate universal photon blockade in a microcavity harboring chiral exceptional points (CEPs) for building multiplexing quantum sources with nonreciprocal photon statistics. The results reveal that the presence of the CEPs leads to a stark contrast in the photon statistics of two whispering-gallery modes with opposite propagating directions. That is, one mode exhibits a strong PB effect while the other displays either sub-Poissonian or super-Poissonian distribution. Our findings thus may pave the way for advanced applications of photon blockade, and provide a theoretical foundation for the selective generation of single-photon and two-photon emission

Complex quantum networks can support a diverse set of long-range entanglement distribution schemes ranging from linear repeater protocols to multipath entanglement purification strategies. As a result, a network's resourcefulness, that is its ability to facilitate quantum communication, depends on the deployed distribution scheme. In this work, we analyse and compare the resourcefulness of quantum networks across a broad range of network topologies, including both regular and random networks, under two distinct entanglement distribution schemes. The first relies on entanglement swapping along a single path connecting a source-target pair, while the second exploits entanglement purification using multiple paths between the same source and target nodes. The resourcefulness of the network is quantified using a recently described metric [1] that averages over the maximum teleportation fidelity between arbitrary source-target pairs in the network. We present algorithms for estimating this metric under constraints of edge-usage and ordering of paths. Our results not only demonstrate the sensitivity of the average maximum teleportation fidelity metric to the choice of entanglement distribution protocol, but also highlight the significant improvements enabled by network purification schemes. In particular, purification-based approaches can substantially enhance average teleportation fidelity, thereby improving the overall teleportation capability of quantum networks.

We analyze how memory in disorder facilitates quantum communication in many-body scar systems. We consider three distinct types of disorder, viz., memoryful, and memoryless uniform and Gaussian, and compare their respective performances in facilitating quantum state transfer. Using the maximum transfer fidelity and fidelity area as figures of merit, we find that memoryful disorder yields a better performance than the memoryless disordered channels. Furthermore, the maximum transfer fidelity exhibits an initial parabolic decay with disorder strength, followed by a linear decrease, for all the disorder models considered. We introduce a degree of scarness, and show that it is higher for memoryful disorder in comparison to memoryless disorders, implying a role of scarness in the quantum state transfer protocol. We further perform a scaling analysis, revealing that memory effect in disorder is not only beneficial for short-distance but also long-distance quantum state transfer. Finally, we show that the state yielding the maximum transfer fidelity has larger inverse participation ratio for memoryful disorder in comparison to the other two disorders, highlighting the role of nonergodicity in enhancing state transfer.

Quantifying coherence is an essential endeavor in both quantum foundations and quantum technologies. In this paper, we study the coherence measures in terms of the diagonal states in the strictly incoherent operations framework. Specifically, we propose a coherence measure in terms of fidelity and provide its analytical expression. The relations between the proposed coherence measure and some other coherence measures are derived. Furthermore, we prove its monotonicity under incoherent operations. As an application, we explore the role of the proposed coherence measure in characterizing the waveness in the multi-path interferometer. As a result, some wave-particle dualities in terms of fidelity are presented. This work not only deepens the interpretation of the diagonal states on characterizing quantum states, but also promotes the quantitative description of the wave-particle behaviors in the multi-path interferometer.

We characterize three-qubit controlled unitary gates of Schmidt rank three, establishing necessary and sufficient conditions for such gates to have Schmidt rank three. We construct explicit examples and analyze their entanglement capabilities, showing that gates with Schmidt rank three can generate output states ranging from fully separable to maximal GHZ-class states. Within this classification, we present a parameterized gate family that produces an output W-class state whose bipartite tangles for subsystems AB and AC are modulated as simple trigonometric functions of a single phase parameter. The examples also include gates implementable with only three CNOT gates, showing that this lower bound is achievable. Decompositions that achieve the minimum possible CNOT count for several other cases are provided as well. Our results bridge Schmidt rank classification, entanglement structure, and resource-efficient circuit synthesis.

We introduce the notion and reveal remarkable properties of quantum complexity resource contained in a mixed multimode Gaussian state and providing universal quantitative characterization of its quantum advantage. The notion is based on convex optimization, multimode photon number statistics, Hafnian Master Theorem, and #P-hard complexity. We consider pulsed OPAs targeting maximal quantum complexity resource and thousands of multipartite-entangled squeezed modes of output light via nonlinear, spatio-temporally nonadiabatic generation inside OPA and optimized extraction out of OPA. We show that such figure of merit is more realistic than Bloch--Messiah supermodes and guides to multimode OPAs opening new paths to important applications in quantum information science such as generation of 3D cluster states for one-way photonic quantum computing and demonstration of quantum advantage.

Variational quantum algorithms (VQAs) are among the leading approaches for near-term quantum computing, yet their performance can degrade in barren plateau regimes characterized by vanishing gradients. A widely held intuition is that increasing circuit expressivity, often associated with random-state behavior, leads to a loss of trainability. Existing results show that sufficiently random circuits can lead to barren plateaus. Here we show that standard statistical signatures of randomness can emerge well before this regime, without degrading trainability. We demonstrate this behavior in structured variational circuits applied to the one-dimensional cluster-Ising model and a generalized toric code Hamiltonian. To characterize state complexity, we analyze Porter-Thomas statistics, entanglement-spectrum level statistics, and inverse participation ratios. Across both models, increasing circuit depth drives these diagnostics toward random-state-like or random-matrix-like behavior, while variational optimization remains effective, with no evidence of exponential gradient suppression in the regime studied. We interpret this behavior in terms of locality. Spectral correlations develop at relatively shallow depth through locally generated structure, while global state randomization and the associated concentration-of-measure effects are not yet realized. These results show that commonly used statistical diagnostics of complexity do not by themselves determine trainability. Instead, they point to a separation between different aspects of complexity in finite-depth variational circuits.

We implement the Hadamard test with Trotterized time-evolution operators on IBM quantum computers to simultaneously extract ground- and excited-state energies of the transverse field Ising model (TFIM) and transverse longitudinal field Ising model (TLFIM). The Trotterization circuits for the TFIM admit constant-depth circuits (CDCs) for arbitrary time, allowing us to locate a large number of eigen-energies above the background noise for up to six spins. Via circuit synthesis we show that the three-spin TLFIM has constant-depth structure although it does not meet the known CDC criteria. The CDCs enable the extraction of the ground and first-excited state energies of the three-site TLFIM via its dynamics. We also address complications from the noisy background and discrete Fourier transform to enhance the reliability of the extraction process and compare the results from different generations of IBM hardware to highlight the improvement.

Barren plateaus are stated as an average-case phenomenon: pick an ansatz, initialize it naively, and concentration follows. This has led to the common view that a potential cure for barren plateaus is simply to initialize the parameters more carefully. Here we show that the situation is subtler. We introduce a first-moment framework that gives a simple operator-level diagnostic for when an initialization may escape the fully concentrated barren-plateau fixed point, and for comparing the biases induced by different initialization strategies. Our framework recovers several known initialization schemes such as identity and Gaussian initialization, but also shows that barren-plateau avoidance is highly non-unique. Indeed, many shifted, biased, and non-symmetric parameter distributions can avoid concentration, and these choices need not be equivalent. In fact, our results show that one can generate exponentially many families of inequivalent initialization strategies. Then, our numerics indicate that different first-moment-distinct initializations can lead to different attained minima, suggesting that avoiding barren plateaus via smart initializations can trade the exponential concentration problem for the challenge of selecting the right trainable pocket amongst many options.

A promising avenue for scaling quantum computing is to connect quantum processing units (QPUs) by generating entanglement between them. This requires circuit partitioning: partially rewriting quantum circuits to run on a distributed quantum system using quantum teleportation protocols, while preserving the unitary operation implemented by the circuit. The key metric to minimize when partitioning is the e-bit count, defined as the number of maximally entangled qubit pairs that must be generated between QPUs. We focus on partitioning the quantum Fourier transform (QFT) circuit, which is widely used as a subroutine in quantum algorithms such as quantum phase estimation and arithmetic circuits. Specifically, we present a partitioning scheme based on optimal gate-packing, compare it against prior analytical partitioning schemes for the QFT, and evaluate it against partitions produced by general-purpose circuit partitioning algorithms. We further validate our approach by implementing the partitioned circuit on quantum hardware.