Papers

State convertibility represents a fundamental concept used to determine whether a transformation is possible given a specific set of resources. Within the field of Thermodynamics, where physical process are required to preserve a reference state typically in microcanonical or canonical form, this translates into the notions of majorization and thermo-majorization —criteria that require constructing and comparing state-dependent Lorenz curves. In this work, we firstly unify and extend these notions to an arbitrary and possibly time-dependent reference distribution $g(t)$, introducing the concept of $g(t)$-majorization; we then introduce a dual picture whereby state convertibility is turned into a one-dimensional convex-order problem, which allows us to demonstrate that a transition is admissible if and only if the associated real-valued distributions of relative populations $ k_j(t)/g_j(t)$ are connected by a martingale. Building on it, we then derive an exact fluctuation theorem for a reference-relative entropy production whose average violation certifies, through a $\chi^{2}$-divergence bound, the mismatch between an assumed and the true reference evolution—a model-independent diagnostic that requires no independent characterization of the latter and turns an observed breakdown of the fluctuation relation into a certified lower bound on the reference error.

We investigate the growth of the black hole interior in three-dimensional gravity from the boundary theory. For the two-sided BTZ black hole, we propose a boundary reconstruction of the time dependence of a codimension-one surface in terms of correlation functions of smeared operators in the thermofield double state, reproducing the characteristic late-time linear growth predicted by the complexity-volume proposal. Using the Chern–Simons formulation of three-dimensional gravity, these nonlocal correlators are represented by bulk Wilson lines with smeared endpoints, extending the familiar connection between Wilson lines and codimension-two observables underlying holographic entanglement entropy to codimension-one observables. We then ask whether the same geometric growth is captured by Krylov complexity. For the smeared operators, we extract the Lanczos data from their correlation functions and find that operator Krylov complexity reproduces the late-time linear growth of the black hole interior, extending previous connections between operator growth and bulk geometry to AdS$_3$. By contrast, the Krylov spread complexity of the thermofield double state, obtained from the semiclassical gravitational partition function, does not exhibit the linear growth of the bulk volume within the regime accessible to our analysis. Our results therefore point to a distinguished role for operator Krylov complexity in encoding black hole interior growth beyond two-dimensional gravity, while highlighting a qualitative distinction between operator and state notions of Krylov complexity.

These notes develop four interconnected ways of reading a quantum circuit. A circuit for us begins as an operational composition of gates; then, it becomes a diagram whose local equalities may be used as calculations; next, it becomes a protected process once errors, syndromes, and logical degrees of freedom are separated; and finally, it becomes geometric when its connectivity, topology, and boundary data are treated as physical design parameters. The development begins at the level of bits and qubits before appealing to Deutsch's and Grover's algorithms as basic examples of quantum circuits. With the basics in hand, we interpret quantum circuits diagramatically, leading us to compact closed string diagrams and the ZX-calculus. After that, we consider how to correct quantum circuits by introducing the Knill–Laflamme condition, homological surface codes, and related concepts with a view towards thinking of these as operations on diagrams. The lectures eventually arrive at the properties of hyperbolic quantum codes and the prospect of physical superconducting circuits emulating the negatively-curved lattices needed to support those codes. These mathematical ideas and physical experiments, taken together, represent one way to impart a geometric layer onto quantum circuits. By the very end, we bring the ideas nearly full circle by assessing the extent to which these device physics experiments operationalize the basic ZX diagrams encountered much earlier in the story. While the later material reports on original research, and while the discussion becomes increasingly mathematical as the sections progress, no prior knowledge of quantum information, quantum computing, or quantum error correction is actually assumed.

Hybrid quantum-classical computing has emerged as the dominant paradigm for near-term quantum applications, yet hybrid workflows are typically described by individual algorithms rather than their underlying execution behavior. We introduce the Quantum Execution Locality Framework (QELF), a qualitative framework for characterizing hybrid quantum-classical workflows according to recurring dataflow structures and quantum execution locality, the extent to which computation remains resident on the Quantum Processing Unit (QPU) before host intervention or classical synchronization. From a representative cross-section of applications, QELF identifies five recurring computational patterns with distinct locality characteristics and discusses their implications for communication overhead, workflow organization, and future hybrid computing architectures. By providing a common vocabulary for reasoning about hybrid workloads, QELF establishes a foundation for future quantitative validation and the co-design of algorithms, runtime systems, and hybrid computing architectures.

We study symmetry-resolved Krylov complexity in finite-dimensional chaotic quantum many-body systems. When both the Hamiltonian and the initial operator commute with a conserved charge, the operator dynamics decomposes into independent symmetry sectors, each with its own Krylov chain. We show that, after saturation, the unresolved Krylov complexity is additive over symmetry sectors. In the absence of additional Liouvillian degeneracies, the late-time contribution of a sector with Hilbert-space dimension $d_q$ is controlled by $d_q(d_q-1)$, leading to a dimension-weighted equipartition that approaches the simple large-sector scaling $d_q^2/\sum_{q'}d_{q'}^2$. This late-time rule differs from the early-time weighted-average discussed in the literature and is governed instead by the dimensions of the accessible operator spaces. We support the analytic prediction with numerical studies of the real and complex SYK models, a chaotic bosonic spin model, and the mixed-field Ising chain. Our results show that resolving exact symmetries is essential for interpreting the saturation value of Krylov complexity as a diagnostic of chaotic operator growth.

We investigate quantum thermometry in Ohmic-type reservoirs using two-qubit probes within an exactly solvable pure-dephasing framework. By analyzing the individual variance associated with temperature estimation, we identify optimal regimes governed by the Ohmicity parameter $s$, the deviation angle $\theta$, and the decay coefficients $\alpha$ and $\beta$, thereby determining the conditions that minimize estimation errors. The Quantum Fisher Information (QFI) exhibits pronounced maxima at finite interaction times, especially in sub-Ohmic and Ohmic environments at low temperatures, whereas super-Ohmic reservoirs flatten the QFI peak and shift the optimal sensitivity toward higher temperatures. Consistently, the quantum signal-to-noise ratio (QSNR) is suppressed at low temperatures, increases with thermal excitation, and saturates in the high-temperature regime, where the influence of spectral details becomes negligible. A comparative study of mutual and local estimation strategies shows that common-bath configurations, particularly for $\Sigma^+$ and $\Sigma^0$ probes, outperform local baths at short interaction times due to bath-induced correlations, while local environments become advantageous at longer times. The analysis further reveals finite optimal values of both the interaction time $t_{\rm opt}$ and the temperature $T_{\rm opt}$, as well as a strong reduction of the variance with increasing measurement number in the low-temperature regime. In addition, our study of hyperon-antihyperon channels ($\Lambda$, $\Sigma^+$, $\Sigma^0$, $\Xi^-$, $\Xi^0$) shows that entanglement and quantum discord remain remarkably robust over broad angular domains, whereas steering and Bell nonlocality are confined to narrower regions. Overall, the interplay between spectral structure, particle-dependent parameters, and estimation strategy provides valuable ...

A chiral superconductor carries chiral Majorana modes along its boundary, and the integer that counts them fixes everything that follows, yet that integer has never been measured together with a local parity observable on one object. Proximitized one-dimensional wires read fermion parity rapidly but diagnose bulk topology through a separate protocol. Here we show that a reconfigurable domain wall between regions of opposite Chern number in an intrinsic two-dimensional chiral superconductor performs both functions. Opened to its contacts the wall is a ballistic channel whose quantized thermal conductance counts its Majorana modes; closed, the same wall is a Fabry–Pérot resonator whose spectrum shifts by half a level spacing when the parity of the enclosed vortices changes, giving a two-level heat conductance. We derive the exact transmission, the elastic heat full counting statistics, and a theorem showing that linear-response heat scattering of a fixed quadratic problem resolves vortex parity but not the fusion channel of well-separated cores. An outside vortex hybridized with the wall is an intrinsic false positive; temperature, geometry and a finite-bias mean–noise test separates it. Rhombohedral-graphene parameters place submicron loops in the resolved regime at millikelvin temperatures, where chiral-domain reconfiguration and noise thermometry are both established.

We show that the conventional multipolar Hamiltonian is qualitatively modified when the photonic vacuum breaks inversion or time-reversal symmetry. By explicitly applying the Power-Zienau-Woolley transformation, we derive the resulting multipolar Hamiltonians for two idealized chiral photonic environments: a spatial-chiral vacuum, which breaks inversion symmetry, and a temporal-chiral vacuum, which breaks time-reversal symmetry. In the spatial-chiral case, the transformation generates an inversion-breaking self-energy, whereas in the temporal-chiral case it produces an additional Zeeman-like energy. Using a trapped hydrogen-like atom and a charged harmonic oscillator in cavities as minimal examples, we show that these symmetry-dependent terms lead to characteristic spectral shifts. Our work provides a general framework for describing light-matter interactions in chiral quantum electrodynamics and identifying the associated symmetry-dependent effects on cavity-embedded atoms, molecules, and quantum materials.

Mid-circuit measurements provide direct access to trajectory-level observables, revealing dynamical structures in many-body systems that are invisible in ensemble-averaged quantities. We exploit this capability to realize and study an instance of the Floquet-East model on a superconducting quantum processor. Here, the combination of mid-circuit measurements, kinetically constrained unitary operations and hardware noise gives rise to intricate many-body phenomena. Analyzing trajectories obtained from temporally and spatially resolved mid-circuit measurements, we identify dynamical heterogeneity — a hallmark of glassy dynamics. We quantify this emergent behavior by studying the probability of finding inactive space-time regions of a given size. This quantity displays a crossover from area- to perimeter-dominated scaling, which is a characteristic property of glasses and is associated with the proximity to a dynamical first-order phase transition. Our results establish current noisy intermediate-scale quantum devices as scalable testbeds for investigating correlated many-body phenomena at the level of measurement trajectories.

One of the proposed platforms in which both quantum and general relativistic effects can become observable is an atom interacting with the electromagnetic field in a gravitational-wave background. The periodic modulation of field modes induced by variations of the spacetime metric modifies the atomic emission spectrum. Notably, the temporal modulation of the mode-frequency induced by a plane gravitational wave can be simulated through modulated boundary conditions, such as moving cavity mirrors. We analyze the impact of this modulation on atom-field interactions in the strong atom-cavity coupling regime, where Rabi oscillations occur. We show analytically that the modulation is resonantly enhanced, leading to measurable imprints in the atomic transition probability. This establishes a realistic and experimentally accessible platform for probing analogue general relativistic effects in quantum optical systems.

Monitored many-body quantum systems can undergo sharp learnability transitions characterized by how much information can be learned by the observer. When the dynamics conserves a non-Abelian charge, such as an $SU(2)$ spin, understanding how the observer learns the total charge remains an outstanding problem. Unlike the Abelian case, where charge measurements on distinct sites commute, the $SU(2)$-symmetric readouts are noncommuting fusion measurements, making learning a genuinely quantum inference problem. In this work, we propose a theory of $1+1d$ monitored quantum dynamics with $SU(2)$ symmetry, and show that it can be described by an effective replicated loop model comprised of a replica-pairing field and a diffusive ($z=2$) background sector that carries the $SU(2)$ charge and remains gapless throughout the phase diagram. Our theory predicts that the "spin-sharpening” and entanglement transitions coincide as a single transition. Ordering of the pairing field produces volume-law entanglement and hides the background sector from measurements, leading to a learning time of $t\sim L^{3}$ for the total spin. When the pairing field disorders, the background sector alone gives logarithmic entanglement and a diffusive learning time $t\sim L^{2}$. Our analysis is controlled by a large-loop-fugacity expansion.

The Jarzynski equality provides a strict link between nonequilibrium work and equilibrium free energy changes. Its typical quantum formulations, however, rely on measurement protocols that destroy coherence. In this Letter, we use the resource-theoretic approach to derive a non-destructive quantum Jarzynski equality conditioned on the outcomes of an arbitrary bath observable. This yields the Rényi-Jarzynski equality, which quantifies a finite bath's drift from equilibrium under a non-adiabatic drive via the Rényi $k$-divergence. We further demonstrate that the Rényi-Jarzynski equality provides a tunable cost function for quantum optimal control problems where minimizing bath drift is desired, such as state preparation and gate design, enabling the minimization of cross-talk in finite quantum systems. Our toy model exhibits a transition between competing minima for some critical value of $k$, illustrating how the Rényi order tunes sensitivity to different regions of a bath distribution. Strikingly, when drive parameters vary across bath energy levels, minimizing bath drift requires generating system-bath entanglement.

We implement a chiral spin-chain black hole simulator on IBM superconducting quantum hardware and probe, within a common microscopic framework, both semiclassical horizon physics and interacting quantum scrambling. We first measure the dispersion relation across the exterior, horizon and over-tilted interior regimes, reproducing the predicted evolution of the effective light-cone structure. To probe Hawking thermality, we prepare a localised excitation inside the horizon and monitor its density response at an exterior site, observing the predicted inverse relation between the peak arrival time and the surface gravity, thereby establishing a calibrated dynamical estimator of the Hawking temperature. Beyond the semiclassical regime, we continuously tune the interactions and distinguish non-exponential operator spreading in the free-fermion limit from Lyapunov-like OTOC decay in the strongly interacting chiral regime. These measurements use observable-specific Floquet circuits derived from the same parent chiral model, including its mean-field and coordinate-equivalent XY descriptions, to reduce circuit depth while preserving the physics relevant to each probe. Our results provide a unified programmable platform for studying horizon geometry, Hawking thermality and interacting scrambling on quantum hardware.

Quantum state transfer on qubit lattices is a crucial step in a panoply of quantum information processing tasks. Understanding its fundamental limits in the presence of practical imperfections remains a pressing open question. In particular, it is unclear how thermal noise in the intermediate ancilla sites impedes transfer. In this work, we derive tight lower bounds on the necessary growth of commutator norms to achieve approximate state transfer. Specializing to 1D power-law systems with thermal ancilla states, we demonstrate that state transfer runtimes depend sensitively on the scaling of temperature with system size, improving logarithmic bounds to algebraic ones. Our work extends previous results on exact state transfer to the qualitatively different and more practically relevant regime of approximate state transfer.

Gaussian boson sampling (GBS) is a sampling task proposed to demonstrate quantum advantage. We consider Gaussian boson sampling on $M$ optical modes, with $K$ equally squeezed input modes and $N$ observed photon counts. We complete the proof of the hiding conjecture for Gaussian boson sampling with an arbitrary number of squeezers $K$, which is a part of the argument for classical hardness of GBS. In particular, we show that for any $K$ and $N=o(\sqrt{K})$, the symmetric product $MK^{-1/2}U_{NK}U_{NK}^T$, for $U_{NK}$ the top left $N\times K$ submatrix of an $M\times M$ Haar random unitary $U$, is close in total variation distance to both an $N\times N$ symmetric complex Gaussian matrix $\mathbf G$ with independent entries, and the symmetric product $GG^T/\sqrt{K}$ for $G$ an $N\times K$ matrix of iid standard complex Gaussians. We show however that the density-based instance generating method of [Aaronson and Arkhipov, Theory Comput. 9, 143 (2013), Lemma 5.8] used to efficiently implement a hiding procedure fails for Gaussian boson sampling with $K=cM$ if $c<1/2$. Instead we use approximate instance generating to implement the hiding for the usual classical hardness reduction.

Fractional quantum Hall-superconductor (FQH-SC) heterostructures are predicted to host defect-bound parafermion zero modes (PZMs). We propose two related configurations to probe their fusion structure. In a Josephson junction coupled to a single quantum point contact (QPC), quasiparticle tunneling switches the defect fusion channel, producing stochastic transitions between branches of the fractional Josephson spectrum. Embedding the junction in a two-QPC Fabry-Pérot interferometer provides a complementary probe. Weak zero mode tunneling produces fusion-channel-dependent interference while strong tunneling makes the interferometer probe a superposition of fusion channels and strongly suppresses the signal: in the topological limit it vanishes exactly, revealing the defects' non-Abelian nature even when the parent FQH state is Abelian.

We study the Yukawa-Sachdev-Ye-Kitaev model, a disordered model of $N$ Majorana fermions and $R=\gamma N$ bosons in which the bosons are linearly coupled to independent realizations of SYK $p$-body interactions, in the presence of dissipation, modeled by a Lindblad master equation. Motivated by recent proposals for implementing SYK models in quantum simulators, we focus on bosonic leakage at rate $\kappa$. Initializing the system in the steady state, we analyze the late-time fermionic relaxation rate and the Lyapunov exponent, solving the large-$N$ theory both numerically and for $p$ large, finding a rich landscape of dynamical behaviors. Most notably, the Lyapunov exponent remains positive for every value of $\kappa$ and, for $p>2$, can even grow as $\kappa$ increases. The QED case $p=2$, which lies between the fully chaotic regime $p>2$ and the integrable case $p=1$, exhibits special features. We also identify a critical value of the boson-to-fermion ratio $\gamma_c \approx 2/p^2$ separating distinct dynamical regimes.

Given a set of input states, we consider the task of predicting the expectation value of a Pauli observable at the output of an unknown quantum evolution, using only a limited number of measurements. Recently, quantum Gaussian process (QGP) regression was introduced for this task across various classes of unitary evolution. Here, we extend the QGP framework beyond unitary dynamics. In particular, we prove convergence of the channel's outputs to a QGP and derive the associated closed-form kernel under a uniform (Lebesgue measure) prior over quantum channels. The kernel's dimensional factor, however, dictates the required observation precision. While manageable when the channel and observable are restricted to small subsystems, exponential suppression precludes learning when the subsystem grows extensively with the system size. Since the Lebesgue prior is overly broad for many applications, we propose an empirical Bayes heuristic that replaces the dimensional factor with a learnable scale parameter while retaining the kernel's state-overlap correlation structure. In numerical simulations of up to 64 qubits, channel QGP regression with the Lebesgue kernel exhibits a strong inductive bias for local channels, enabling faithful extrapolation. For global 64-qubit channels, the rescaled kernel restores learnability, with predictions improving systematically with the shot budget. Results from a noisy quantum computer further demonstrate the robustness of QGP regression under experimental conditions. Beyond regression, we validate QGPs as Bayesian-optimization surrogates for state preparation under noisy XXZ dynamics.

We investigate the holographic dictionary relating point particles carrying longitudinal momentum or angular momentum in asymptotically AdS$_3$ spacetimes to suitably regulated, time-evolved states created by local primary operators in the dual two-dimensional conformal field theory (2D CFT). We find that asymmetric left/right Euclidean smearing of local operators produces states carrying momentum, and the corresponding bulk excitation is a particle with conserved momentum. We compute the energy density and entanglement entropy in these states and in their dual back-reacted geometries, finding exact agreement between the CFT and gravity descriptions. We further extend this correspondence to particles with intrinsic spin, whose CFT duals are primary operators with unequal holomorphic and anti-holomorphic scaling dimensions. We again find a precise match between CFT and holographic calculations of energy densities and entanglement entropies. Finally, we explore applications of these setups beyond holography by deriving the evolution of Rényi entropies in 2D rational CFTs and introducing a new class of local quantum quench protocols with conserved longitudinal or angular momentum.

We revisit a proposed correction to the muon magnetic anomaly measurement and compare it with energy-binned scans reported by the Fermilab $g-2$ collaboration. The central point is that, for a relativistic three-body decay inferred from an ensemble of detected positrons, the relevant neutrino partial trace is defined on the asymptotic state at the detector, not on an idealised state at the decay vertex. Because the fitted positron sample mixes events with different decay times, flight times, energies and acceptances, tracing over the unobserved neutrino helicities leaves a time-dependent mixed state in the observed sector. Using angular-momentum balance, we obtain an energy-dependent correction in the positron energy interval $E_p \in (1.5,2.9)$ GeV. The corrected experimental interval for the muon anomaly moves towards the BaBar- and $\tau$-based determinations, while remaining compatible at the $1\sigma$ level with both data-driven and lattice-based Standard Model evaluations. We then fit digitised public $R(E_p)$ scans for Fermilab's runs $1$ to $6$, with two one-parameter hypotheses: a constant shift and the entanglement-motivated energy-dependent shift. Within digitisation accuracy, the differences in $\chi^2$ remain modest and the current binned data do not provide decisive discrimination between them.

The recent creation of a Bose-Einstein condensate (BEC) of dipolar molecules has opened a new frontier for many-body quantum systems in which dipolar interactions can drive novel self-organization phenomena. Here, we observe electrostriction in a molecular BEC, an elliptical deformation driven by anisotropic dipolar interactions. We use double microwave dressing, involving $\sigma$- and $\pi$-polarized fields, to control non-axially symmetric dipolar interactions. We compare the experimental observations of electrostriction to a model based on an extended Gross-Pitaevskii equation and find excellent agreement in the regime of weak to moderate interactions. Using electrostriction, we demonstrate that the molecular BEC can be torqued by dynamically changing the orientation of the elliptical $\sigma$ microwave field. This provides a route to setting molecular quantum gases into rotation, opening opportunities to probe vorticity, superfluidity, and supersolidity in strongly dipolar matter.

We develop a geometry for transporting stationary-state response across the control space of an open quantum system. A physical model is represented by the ordered pair of its stationary state and dynamical generator. Embedding these pairs in a common ambient space induces a metric, a response one-form, and a closed two-form on the control manifold. The ambient space admits a canonical complex structure that exchanges state and generator directions, but the Liouvillian null-state condition restricts physical models to a submanifold that need not preserve this structure. For an amplitude-damped optical Bloch model, the metric and response two-form are compatible at the single point $\omega=0$ and $g/\Gamma=1/\sqrt{2}$; the physical manifold is non-Kähler elsewhere. The induced metric defines the Levi–Civita connection, geodesics, and parallel transport without requiring Kähler compatibility. We compute the connection by automatic differentiation through the stationary Liouvillian solve and recover the symbolic result to machine precision. A two-point calculation then shows that the resulting geodesic differs from linear interpolation in control space and follows a shorter path through the family of state–generator models. This geometry supplies the intrinsic derivative and transport structure needed to carry observable response, including multidimensional spectra, between admissible stationary models.

One of the most basic conjectures in quantum complexity theory states that every $t$-query quantum algorithm can be simulated on most inputs by a $\mathrm{poly}(t)$-query classical algorithm. If true, this would provide broad justification for the need for structure in quantum speedups. We settle this conjecture for parallel quantum algorithms, showing that every $t$-query $d$-round quantum algorithm can be simulated on most inputs with $t^{O(d^2)}$ classical queries. This suggests that for unstructured problems, superpolynomial speedups would require quantum circuits of superconstant depth, and exponential speedups would further require polynomial depth. In contrast, most known speedups for structured problems are achieved by highly parallel, low-depth algorithms. Our techniques also carry new implications for the status of $\mathsf{BPP}$ vs. $\mathsf{BQP}$ relative to a random oracle, a similarly longstanding problem.

In this work, we study the limitations and advantages of using entanglement battery and entanglement catalyst in local state discrimination problems. We consider both cases of such tools, i.e., exact and approximate cases. We show that to distinguish any set of orthogonal pure bipartite entangled states perfectly under local operations and classical communication using an (exact) entanglement battery or an (exact) entanglement catalyst, it is necessary to consider that the cardinality of the set must be smaller than the total dimension of the given Hilbert space. Then, we construct a nontrivial case where an exact entanglement battery can provide huge advantage. We also construct other nontrivial cases where exact or approximate entanglement battery or entanglement catalyst can be useful. In fact, we find that the approximate tools are particularly useful in the local discrimination of certain sets which can be derived from many-copy indistinguishable ensembles.

Adding links generally improves classical transport by increasing the number of available paths. We show that coherent quantum transport can display the opposite behavior. Using continuous-time quantum walks on a percolated hierarchical small-world network, we identify a coherent overconnectivity penalty: root-to-boundary transport is maximized at intermediate bond probability and decreases as the network approaches full connectivity. The effect is quantified by the final-layer limiting probability $\chi_N$ and by the penalty $P_Q=1-\chi_N(p=1)/\max_p\chi_N(p)$, which measures the loss caused by making the architecture fully connected. The optimum results from a competition between shortcut-assisted spreading and interference-induced intra-layer recirculation. Spectral analysis shows that bond dilution creates motif-induced degeneracies and reorganizes the eigenstates connecting the root to the outermost layer. A comparison with dephased and classical transport shows that the non-monotonic landscape is not a purely geometrical percolation effect, but a coherent architecture-dependent phenomenon. These results provide a design principle for coherent transport in disordered photonic and quantum-network architectures.

The practical implementation of quantum algorithms on noisy intermediate-scale quantum devices encounters operational limitations due to decoherence and other sources of noise inherent in real hardware. To mitigate these errors while preserving the original functionality of the algorithm, shorter quantum circuits are therefore preferred. This motivates the development of effective quantum circuit optimization algorithms. Learning-based approaches have emerged as a leading candidate, yet existing autonomous agents remain inefficient, spending most of their training capacity rediscovering elementary reductions that deterministic rule-based methods already handle reliably. To address this challenge, we propose a reinforcement learning framework that embeds a deterministic Commutation-and-Reduction (CR) algorithm directly into the training environment. After every agent action, the CR algorithm automatically resolves elementary commutations and cancellations, enabling the agent to focus its learning capacity on the non-trivial optimizations where reinforcement learning adds real value. Empirical evaluation across two gate sets, the universal Clifford+T basis and the CNOT+Pauli basis, shows that RL+CR produces shorter circuits than a standard RL agent at all tested scales. We demonstrate that RL trained on smaller quantum circuits can be applied to larger quantum circuits. On 20-qubit Clifford+T circuits, five times larger than the training circuits, RL+CR removes twice as many gates as standard RL. This work provides a robust approach that could accelerate the compilation and optimization processes for future fault-tolerant and utility-scale quantum systems.

Quantum magic, or nonstabilizerness, is a quantum resource associated with computational advantage in quantum systems. In high energy collisions, Quantum Electrodynamics (QED) is inefficient at generating magic while the weak mixing angle, a fundamental constant of nature, sits near a value that minimizes magic production in charged-lepton scattering. These observations were made in the laboratory (lab) basis, in which spin is projected along the incoming beam axis. An alternative choice is the helicity basis, in which spin is projected along the direction of motion of each particle. The transformation between these two bases is, in general, not a Clifford operation and therefore can change the amount of magic. We present a detailed study of magic production in both bases for QED and electroweak processes, and compare these results with the basis-invariant non-local magic. In the ultra-relativistic limit, magic production is generally smaller in the helicity basis due to helicity selection rules, while the lab basis generally yields less magic in the non-relativistic regime. We provide circuit realizations of the ultra-relativistic Bhabha amplitudes using linear combinations of unitaries and show that the lab basis construction contains a larger $T$-gate count at generic scattering angles. Interestingly, in both bases the physical weak mixing angle lies close to the value that minimizes magic production.

Calderbank-Shor-Steane (CSS) codes, constructed from nested classical codes $C_2 \subseteq C_1$, are typically optimized for good code parameters. However, practical quantum computing equally demands fault-tolerant logical gates. In this work, we characterize nested pairs $(C_1, C_2)$ whose resulting CSS codes realize a target logical diagonal gate via transversal physical $Z$-rotations. In doing so, we recover a result of Camps-Moreno et al. that CSS codes can realize only logical single-qubit $Z$-rotations and multi-qubit controlled $Z$-rotations via transversal physical $Z$-rotations. Building on our characterization, we develop the ”appending construction”, that takes as input an $[[n',k']]$ CSS code $Q'$ and a target logical $Z$-rotation (single-qubit or multi-controlled) $U_L$, and extends $Q'$ by systematically appending $n''$ physical qubits to obtain an $[[n,k]]$ CSS code $Q$ with $n = n'+n''$ and $k=k'$. The target logical gate $U_L$ is realized in $Q$ by applying a well-chosen physical transversal $Z$-rotation to the $n''$ appended physical qubits. Moreover, any logical gate realized via transversal physical $Z$-rotations in the input code $Q'$ remains transversally realizable in the extended code $Q$. The CSS code $Q$ may incur a loss in minimum distance, but the loss can be controlled through the parameter choices made in the construction. By repeatedly applying the appending construction, we can extend any CSS code $Q'$ to obtain a CSS code $Q$ that supports fault-tolerant implementations of multiple desired logical $Z$-rotations. The cost to be paid for this is the increased physical qubit overhead as the number of target logical gates grows. To illustrate our methodology, we construct CSS code families that transversally realize addressable logical single-qubit and multi-controlled $Z$-rotations.

Non-local search-to-decision asks whether the difficulty of two non-communicating (non-local) parties both predicting x given a bipartite state (that possibly depends on x) implies the difficulty of non-local parties both predicting the inner product <r,x>, for a uniformly random r. This problem and its variants have been extensively studied and are motivated by applications to unclonable cryptographic primitives such as unclonable encryption and copy-protection. We study the identical-challenge setting, in which both parties receive the same uniformly random vector r, in contrast to the independently sampled challenges considered in prior works. We demonstrate positive results for the cases when $x$ and r are vectors over F_2 and over large finite fields. As a consequence, we obtain a conceptually different proof of indistinguishability-secure unclonable encryption.

We identify different regimes of quantum state transfer in long-range coupled spin-$\frac{1}{2}$ systems, where naturally occurring power-law interactions enable rapid, high-fidelity transfer with minimal engineering. Across a broad range of interaction profiles, from effectively nearest-neighbour coupling to Coulomb interactions, we show how long-range connectivity fundamentally reshapes the mechanisms underlying information propagation within such systems. For effectively short-range interactions, transfer follows familiar ballistic transfer dynamics: an initially localised excitation spreads across many eigenmodes concentrated within the approximately linear region of the spectrum, enabling robust wavepacket motion. In contrast, increasing long-distance interactions via lowering the power-law exponent $\alpha$ ($\alpha=1-2$) drives a striking transformation, where the initial state becomes confined to progressively fewer eigenmodes, ultimately reducing the dynamics to the coherent participation of only a few states corresponding to the highest eigenenergies. This spectral localization gives rise to emergent long-range oscillations between distant sites, revealing a distinct – and faster – transfer mechanism arising from the intrinsic structure of long-range quantum interactions rather than from full-system engineering pathways.