Papers

We study the spectral gap of recently discovered families of KMS-detailed-balanced Gibbs-sampler Lindbladians for the mean-field Heisenberg model on $n$ spins. We show that the spectral gaps of these natural families of Lindbladians admit the same phase diagram: the gap is constant above the critical temperature (i.e., in the disordered phase), scales as $1/\sqrt{n}$ at the critical temperature, and as $1/n$ below the critical temperature (i.e., in the ordered phase). Our result builds on and extends the recent work of Basso et al.~(2026) which characterized this phase diagram for the GNS-detailed-balanced Davies generator, but only partially resolved the gap scaling at the critical temperature.

We study a Continuous-Variable Quantum Approximate Optimization Algorithm (CV-QAOA) for high-dimensional continuous optimization. Our formulation extends an earlier CV-QAOA proposal with a variationally optimized initial state and recovers the convergence guarantees of Quantum Hamiltonian Descent (QHD) in the high-depth limit. We prove rigorous performance guarantees of CV-QAOA on several families of cost functions. First, we show $d$-step CV-QAOA minimizes any $d$-dimensional strictly convex quadratic function with $2d$ quantum queries to the cost function. We then analyze a family of nonconvex "Rotated Double Well" (RDW) functions with $2^d$ local minima introduced by arXiv:2311.00811. While prior work showed QHD reaches its global minimum with $\tilde O(d^3)$ queries, we prove that 1-step CV-QAOA solves RDW with just two quantum queries. Although general-purpose classical solvers need superpolynomial time for RDW and structure-awareness can reduce the cost to polynomial time, we show that the 1-step CV-QAOA protocol can be efficiently dequantized, and that a gradient-aligned line search succeeds with $O(d)$ queries, nearly matching the information-theoretic $\Omega(d/\log d)$ query lower bound. To move beyond the dequantizable regime, we introduce a “Rotated Square Well” (RSW) problem, whose globally flat landscape suppresses useful local gradient information. For this family, we show that an adiabatic evolution simulated by CV-QAOA can reach the global minimum using $d^{o(1)}$ queries. On the other hand, any classical algorithm that learn the hidden rotation in RSW provably requires $\Omega(d^2/\log d)$ queries, a bound we nearly match with an explicit $\Theta(d^2\log d)$-query classical algorithm.Numerical simulations on deflected corrugated spring and Easom functions illustrate the promising performance of CV-QAOA on more general problems.

Publicly accessible fault-tolerant quantum computers must preserve scientific utility while limiting cryptanalytic power. We propose the restricted model of computation, 1/2BQP_1: a quantum server provides random computational-basis inputs, revealed only after execution, and one designated output bit. This interface permits arbitrary circuits and system sizes. We conjecture that a classical client making polynomially many adaptive requests cannot efficiently factor RSA moduli. The model subsumes the well-known one-clean-qubit model DQC1, retaining its applications to infinite-temperature multi-time correlations, out-of-time-order correlators, and suitably normalized partition functions. We propose a candidate for separating 1/2BQP_1 from DQC1 based on testing classical predictions of quantum spin dynamics. We argue security in two steps. First, we show that one-bit readout makes the quantum stages of standard factoring algorithms classically simulable, even when their preparation and postprocessing are redesigned within a broad family around a single arithmetic-oracle call. This covers the quantum stages of Shor, Ekera-Hastad, Kitaev, and Regev factoring constructions. Second, we examine the workaround of coherently implementing rational reconstruction to release a factor bit. Random inputs obstruct this straightforward attack: known techniques accommodate logarithmic-depth classical circuits, but rational reconstruction has resisted such parallelization for decades. Therefore, we show that security of our protocol is built on not only classical hardness for factoring, but also conjectured circuit lowerbounds for rational reconstruction.

We show that every intermediate state of a broad class of non-Clifford quantum error-correction circuits is a third-order phase-polynomial state, even under stochastic Pauli noise. The class includes magic state distillation and cultivation, code switching and gauge fixing, transversal non-Clifford gates with syndrome extraction, and injection of diagonal magic states. Third-order phase-polynomial states strictly generalize stabilizer states, and we prove that they are exactly the stabilizer states of the diagonal-Clifford-and-Pauli (DCP) stabilizer formalism that we introduce. We characterize these states and show that their representations can be updated in polynomial time. This yields an exact polynomial-time simulation algorithm for these circuits and, more broadly, a framework for reasoning about their internal states and about magic states in general. We provide an open-source implementation, merlin, and benchmark it against existing non-Clifford simulators on distillation, cultivation, and code switching circuits. The benchmarks demonstrate improved runtime and memory scaling as the number of logical outputs grows in Bravyi-Haah distillation, and simulation of a code switching circuit beyond the reach of all other tested simulators.

We study agnostic tomography of pure bosonic Gaussian states: given copies of an arbitrary $n$-mode bosonic state $\rho$, the goal is to output a pure Gaussian state whose infidelity with $\rho$ is at most $\mathrm{opt} + \epsilon$, where $\mathrm{opt}$ is the minimum infidelity achievable by any pure Gaussian state. We give efficient protocols achieving this in both the high and low fidelity regimes. When $\mathrm{opt}$ is below some universal constant, our protocol has runtime and copy complexity which is strongly polynomial in $n, 1/\epsilon$ and $\log \log E$, where $E$ is the energy of the closest pure Gaussian state. For arbitrary $\mathrm{opt}$, our protocol uses $(n+1)^{\mathrm{poly}(1/\epsilon)} \mathrm{poly}\left(1+\log\log(E)\right)$ copies and runtime. As a corollary, we obtain the first truly tolerant Gaussianity testing protocol for distinguishing whether $\mathrm{opt} > c + \epsilon$ or $\mathrm{opt} < c - \epsilon$, for any threshold $c\in(0,1)$. We also prove $\mathrm{poly}(n,1/\epsilon)$ runtime is impossible, unless $\mathrm{NP}\subseteq\mathrm{BQP}$. Our protocols follow a shared paradigm: first, we iteratively use general Gaussian measurements combined with techniques from classical robust statistics to obtain a good warm start estimate, then we leverage non-Gaussian measurements to refine this warm start using convex and non-convex optimization methods. Interestingly, we prove that non-Gaussian measurements are necessary to match the strong agnostic guarantees we obtain, and in fact these guarantees are provably superior to what is possible for robustly estimating classical Gaussians.

We consider the problem of quantum 1-PCA: given copies of an unknown $n$-qubit mixed state, recover a classical description of its leading eigenvector. Our goal is to do so using non-adaptive and single-qubit measurements. For an $n$-qubit state with top eigenvalue $\lambda$ and spectral gap at least $\Delta > 0$, we give an algorithm that recovers the leading eigenvector to fidelity at least $1 - \varepsilon$ with high probability using $\tilde{O}\left( {2^n \cdot \eta^2} / {\Delta^3 \varepsilon^3}\right)$ copies and $\tilde{O}((2^n/\Delta \varepsilon) \cdot \operatorname{poly}(\eta/\Delta\varepsilon))$ time, where $\eta = \max (1 - \lambda, \varepsilon)$. All of our measurements are non-adaptively chosen, and performed in single-qubit Pauli bases. When the spectral gap is constant and the desired accuracy is comparable to the noise level, i.e. $\varepsilon = \Omega (\eta)$, our runtime and copy complexity become $\tilde{O} (2^n / \varepsilon)$. This generalizes the guarantees of Grewal et al. [arXiv:2601.04444], who achieved similar rates, but under the assumption $\eta = 0$, i.e., that the state was pure. Our results show that the same rates hold in the presence of state misspecification, up to polylogarithmic factors. From a technical perspective, our algorithm works by recursively constructing low-dimensional subspaces that approximately preserve the target eigenvector. To achieve nearly linear runtime dependence on the dimension of the Hilbert space, we develop a novel structured Pauli sampling scheme that enables fast batched computation of exponentially many projected Pauli matrices.

The Sachdev-Ye-Kitaev model is a strongly interacting fermionic system that has been well-studied in condensed matter and high energy physics. It is highly quantum: Gaussian states are far from the thermal state (Hastings and O'Donnell, STOC'22) and representing the thermal state requires large polynomial-size quantum circuits (Anschuetz et al., QIP'25). Very recently, it was nonetheless proven that classical algorithms can estimate local thermal expectations at sufficiently high temperature in quasipolynomial time (Zlokapa, FOCS'26). We show that classical algorithms can in fact estimate local observables at all constant temperatures in polynomial time. Our techniques also extend straightforwardly to classical systems: we resolve an open question about computing thermal expectations of a classical spin glass up to its phase transition (Bencs et al., STOC'26). Our proof develops a fully rigorous quantum cavity method. Due to the success of the classical cavity method in optimization, sampling, inference and learning, we expect the quantum cavity method to find further applications of independent interest. As an example, we give a quantum algorithm that learns SYK Hamiltonians from the Gibbs state at any constant temperature with polynomial time and sample complexity.

We study hybrid quantum-classical algorithms in the query model. The computation consists of quantum subroutines that make at most $q$ oracle queries; between subroutines, all qubits are measured and discarded. We prove matching upper and lower bounds for several problems in this model: (i) (Unbiased) Phase estimation up to a precision $\epsilon$ requires $\Theta(\frac{1}{q \epsilon^2})$ queries; (ii) (Unbiased) Amplitude estimation up to a precision $\epsilon$ requires $\Theta(\frac{p(1-p)}{q \epsilon^2})$ queries; (iii) Search among $N$ items requires $\Theta(\frac{N}{q})$ queries; (iv) Two level AND-OR tree (AND of $m$ ORs, with $n$ inputs to each OR) requires $\Theta(\frac{nm}{q})$ queries. All of these bounds are optimal up to a constant factor, for all $q$ from 1, corresponding to the classical complexity, to $Q(f)$, the unrestricted quantum query complexity of the respective problem. We also derive a hybrid lower bound for distinguishing two distributions specified by a state-preparation unitary; this bound is tight up to a logarithmic factor. Besides specific lower bounds, an important contribution is developing methods for proving lower bounds on hybrid quantum algorithms (which have been very ad-hoc up to now). The first two bounds follow from a common framework: we analyze probability distributions over measurement transcripts and bound a progress measure that captures their distinguishability. The AND-OR bound requires a more delicate argument, combining two progress measures that track the information available to the algorithm classically and in quantum form, respectively.

Nonlocal games offer a conceptually clear way to reason about Bell nonlocality. However, we show that as originally defined, and most commonly used, i.e. with a deterministic predicate, they cannot be complete witnesses of nonlocality. Concretely, we prove the existence of nonlocal behaviours which do not violate any such nonlocal game. Furthermore, we also show that quantum mechanics can produce these game-classical nonlocal behaviours. We prove that this phenomenon exists in every bipartite scenario $(X,Y,A,B)$ with $X,Y\geq2$ and $A,B\geq4$.

We use an instanton-based analysis to show that Path Integral Stochastic Gradient Descent (PISGD), a classical optimization algorithm instantiated from path integral Monte Carlo (PIMC), can inherit the quantum tunneling mechanism. Quantum tunneling is the phenomenon in which a quantum particle passes through a potential barrier that a classical trajectory cannot cross in the same way. This mechanism can contribute to the performance of quantum optimization algorithms, since a common bottleneck in optimization is that the solution becomes trapped in a local minimum, separated from better solutions by a potential barrier. Classical noise-driven optimizers, such as stochastic gradient descent (SGD), have escape times that scale exponentially with the potential barrier height. For quantum tunneling, the escape time is instead exponential in the bounce action, which equals twice the Agmon distance between the two basins. When the barrier is tall but thin, quantum tunneling can allow escaping local minima faster than such classical methods. Remarkably, this scaling is not exclusive to algorithms with genuine quantum dynamics. For PISGD applied to classical nonconvex global optimization, we adapt Kramers' escape-rate theory to path space and obtain the same exponential scaling as quantum tunneling, in terms of the bounce action rather than the barrier height. We confirm this scaling numerically by implementing PISGD for both separable and nonseparable potentials. That said, PISGD retains only incoherent tunneling, since coherence among multiple tunneling paths is absent. Our analysis therefore does not rule out a potential quantum advantage for quantum-tunneling-based algorithms over classical ones in general.

Bosonic and fermionic Gaussian quantum states are families of quantum states that play a central role in quantum physics and quantum information processing. We study the problem of testing whether a given state is either Gaussian, or has bounded overlap with any Gaussian state. Previous analyses of this testing problem led to tests that require a number of copies of the state that scales with the number of modes (the system size). In this work we show that a constant number of copies of the state suffices. We derive these results based on the symmetries of identical copies of Gaussian states, and by bounding the distance to the set of Gaussian states through a gradient flow and a spectral bound studied previously for the Kac random walk on a sphere.

We propose a four-level scheme for generating a uniform imaginary magnetic field for ultracold atoms using Raman coupling and state-dependent particle losses. Eliminating two lossy auxiliary states and subsequently projecting onto one of the two remaining Raman-dressed atomic states, we find that the atomic motion is affected by an imaginary vector potential which is engineered to have a constant curl corresponding to a spatially uniform imaginary synthetic magnetic field. We analytically derive the Gaussian wavepacket dynamics for atoms in such a synthetic magnetic field and study the width-dependent transport, unlike motion in a uniform real magnetic field. We find numerical agreement between the two-level non-Hermitian Hamiltonian and the adiabatic projection description, confirming the applicability of the latter adiabatic approach.

Recent work has shown that syndrome information obtained during error-corrected quantum computation can be utilized for logical error mitigation (LEM), yielding exponential reductions in runtime overhead compared to "external” LEM methods, which do not make use of syndrome data. However, these syndrome-aware LEM methods (SALEM) generally require adaptive circuit operations based on real-time processing of syndromes. Here, we introduce syndrome-based offline logical error mitigation (SOLEM), a framework that utilizes syndrome data entirely in post-processing, without any modification to the given error-corrected circuit. In this sense, SOLEM is "built into” error-corrected circuits, and is in fact simpler to implement than external LEM protocols. The basic idea of SOLEM is to use naturally occurring syndrome-conditioned logical error channels in place of deliberate circuit modifications. We develop unbiased and heuristic estimators within this framework, including offline logical versions of probabilistic error cancellation (PEC) and zero-noise extrapolation (ZNE), as well as a global-regression estimator. SOLEM's fully offline nature leads to three significant advantages. First, SOLEM can post-process syndromes with a more powerful decoder than the one used in real time. Second, multiple estimators can be constructed from the same measured data and optimized using empirical statistical errors and related performance metrics. Third, logical error characterization is needed only in post-processing, allowing characterization data to be collected during circuit execution and reducing sensitivity to hardware drift. Remarkably, SOLEM estimators can achieve these advantages while attaining a runtime overhead which is exponentially lower than that of external LEM and is comparable to that of corresponding SALEM estimators.

Elastic scattering can generate entanglement and non-local magic between the spins of the two outgoing particles. The amount of entanglement and magic produced is encoded in the S-matrix; a unitary quantum gate that acts on the joint Hilbert space of the two spin-J particles. Previous work derived the entanglement power in terms of the scattering phase shifts for rotationally invariant S-matrices with J=1/2,1,3/2. In this paper, a closed form solution is derived for all J. We further prove that a broad class of non-local quantum resources depend to leading order only on the squared projective Hilbert-Schmidt distance from the nearest non-entangling gate. This holds for the entanglement power and non-local magic power, and the choice of resource simply changes the overall normalization. This universality establishes a common geometric origin for the leading resource-generating capacity of scattering, independent of the details of the interaction.

We study the one-way communication complexity of the $f$-Boolean Hidden Partition problem. Here, Alice is given an $n$-bit string and Bob is given $\Omega(n)$ disjoint blocks of its indices together with a string of labels. Under the promise that the evaluations of $f$ on these blocks either agree with all of the labels or disagree with all of them, Bob must determine which is the case using a single message from Alice. This problem generalizes the Boolean Hidden Matching and Hidden Hypermatching problems, which capture the special case where $f$ is the parity function. We establish classical and quantum communication bounds for $f$-Boolean Hidden Partition in terms of the sign degree $d$ of $f$, proving a conjecture of Doriguello and Montanaro (TQC 2020). Their prior work gave logarithmic communication upper bounds for classical protocols when $d \le 1$ and quantum protocols when $d \le 2$, as well as polynomial lower bounds for certain structured functions with larger sign degree. We show that for every $f$ of sign degree $d \ge 2$, the randomized classical communication complexity of this problem is $\Theta(n^{1-1/d})$ while its quantum communication complexity lies between $\Omega(n^{1-2/d})$ and $\bO{n^{1-1/\lceil d/2 \rceil} \log n}$. This completely characterizes the functions $f$ admitting polynomial quantum advantage as those for which $d \ge 2$, with a new infinite family of exponential separations given by the case $d = 2$.

The information-theoretic approach to entanglement typically relies on arbitrarily many input copies and unboundedly complex operations; however, the available resources are constrained in reality. This motivates the study of entanglement theory with limited resources. One of its central questions is which quantities characterize entanglement manipulations, and so far, only the idealized case of pure states has been well explored. In this work, we address entanglement distillation from mixed states and identify the Rényi coherent information as the quantity determining the optimal rate in the worst case under two distinct resource constraints. We first characterize the sample-efficient regime, in which unbounded computational power is allowed. Our universal protocol achieves this rate without knowledge of the input state under certain polynomial rank constraints. This rate is optimal among universal protocols: we construct states whose distillable entanglement is nearly extensive, yet from which no universal sample-efficient protocol attains a rate above their Rényi coherent information. We then push this characterization to the computationally efficient frontier: the same bound holds for any efficient protocol even when the input state is known, and another universal protocol achieves this rate efficiently under additional polynomial constraints on the marginal ranks. Overall, our results give the Rényi coherent information a novel operational meaning in two computational settings: universal distillation with limited copies and efficient distillation even with knowledge of the input state.

Closure phase enables imaging with ground-based interferometric arrays by canceling telescope-dependent phase errors due to atmospheric fluctuations. It can be obtained by measuring fringe phases on individual baselines forming a triangle and summing them. We show that closure phases can be measured more accurately with fewer photons by performing joint measurements on multiple photons. We first establish that at least three photons from the same atmospheric temporal phase-stability window are required for closure-phase information to survive the unknown telescope-dependent phase noise, and show that joint three-photon measurements already provide an advantage over single-photon measurements in the minimal three-telescope setting. We then turn to large arrays and consider estimating all bispectra—complex quantities whose phases are the closure phases—under a global mean-square error criterion. Although an $m$-telescope array contains $\Theta(m^2)$ independent triangle bispectra, we show that physical constraints on the visibilities make the total information content grow only nearly linearly with $m$ at fixed accuracy. Exploiting this structure, we construct an efficient protocol using at most three-photon joint measurements with photon cost $\tilde{O}(m)$, whereas any sequential single-photon protocol requires $\Omega(m^2)$ photons. When the number of detected photons per temporal stability window scales linearly with the array size, this allows the required exposure time to remain independent of $m$ up to logarithmic factors. We further analyze the complementary high-precision regime using multiparameter quantum metrology and find a similar advantage for collective measurements. Overall, our results show that quantum information processing techniques can substantially improve the sensitivity and robustness of optical interferometry.

We give a shadow tomography algorithm that uses $O(\log(m) \log(m/\delta) / \varepsilon^2)$ copies of the input state. Specifically, given a quantum state $\rho$ and observables $O_1,\ldots,O_m$, the algorithm outputs estimates of $\mathrm{tr}(O_i\rho)$ for all $i\in[m]$ that are all accurate to within $\pm\varepsilon$, except with probability at most $\delta$. The key idea is to work in the average-case setting: for a random state drawn from a known prior, a pretty good measurement on $O(\log(m)/\varepsilon^2)$ copies gives a constant-error guarantee on all but a small fraction of the prior. Boosting this guarantee gives an average-case shadow tomography algorithm, and the minimax principle then (non-constructively) implies the existence of a measurement with the same worst-case guarantee. We also identify an obstruction to further improvement with this approach. While pretty good measurements amplify success over the randomness of the prior, they do not amplify success over the randomness of measurement. This issue appears to be inherent, and gives rise to the remaining $\log(m)$ factor separating the complexity of the quantum problem from its classical counterpart.

The seminal Kyle model offers a framework to understand the price impact of an informed trader in a market model for a single asset. We study variants in which the asset's future value is modeled by a classical random walk and by a continuous-time quantum walk, respectively. With these assumptions, we analytically approximate and numerically identify the market equilibrium between risk-neutral market maker and informed trader. In the classical equilibrium, the informed trader possesses a linear strategy, whereas the market maker's pricing rule resembles a logistic curve. The informed trader's profit is also identified to grow sub-linearly with time t. In the quantum equilibrium, the informed trader's strategy forms multiple clusters and the pricing rule exhibits multiple jumps correspondingly. Despite the increasing non-linearity of the equilibrium, the informed trader's profit grows linearly with time t.

Fault-tolerant quantum computation typically relies on a fixed set of logical primitives, while realizing other desired operations can require substantial resources. We introduce irrep surface codes (ISCs), two-dimensional topological quantum error-correcting codes engineered to transversally implement a prescribed set of logical gates. The engineered gates only need to satisfy two conditions: (i) they generate a finite group, which, up to global phases, is forced by the Eastin-Knill theorem, and (ii) they are irreducible, meaning that any operator commuting with the set of gates must be proportional to the identity. This accommodates arbitrary finite groups of diagonal gates and arbitrary reversible classical gates, since each can be embedded into a larger irreducible finite group of gates. It also enables logical gates outside every finite level of the Clifford hierarchy. To incorporate these operations into surface-code computations, we further develop lattice-surgery protocols to transfer the encoded information between surface codes and ISCs obeying either of two sufficient conditions. Together, these results establish a systematic method for tailoring topological codes to desired logical operations and integrating them into conventional computations.

We establish general conditions for the rapid convergence of propagation algorithms for computing expectation values of local observables in quantum many-body systems, covering both spin and fermionic systems. Our results apply to evolutions that are sufficiently contractive, providing a general mechanism by which contractivity controls the growth generated by local interactions and enables efficient classical simulation. As a first application, we consider noisy time evolution generated by local Hamiltonians on arbitrary interaction graphs. We show that the dynamics can be efficiently simulated when the noise strength $\lambda$ is sufficiently large compared to the degree of the interaction graph. More generally, for systems with an interaction strength $u$, our bounds determine a time horizon $t_{\text{max}}$ as a function of the interaction strength $u$, the noise strength $\lambda$, and the interaction structure below which the algorithm is efficient. In the noiseless limit, $\lambda=0$, our analysis extends the efficiently simulable time scale from $\log(1/u)$ proved in Facelli, Fawzi, and Fawzi (2026) to $t_{\text{max}} \sim 1/u$ matching the recent improvement by Zhao, Marvian and Tong (2026). As a second application, we apply the same framework to the computation of local observables in Gibbs states of local Hamiltonians. We consider a pseudo-Lindbladian whose steady state is the Gibbs state and show that, at sufficiently high temperature, its propagation algorithm converges rapidly. In particular, for weakly-interacting systems with interaction strength $u$, our result applies up to inverse temperatures $\beta\sim\log(1/u)$.

Clifford and matchgate circuits are canonical families of classically simulable quantum circuits. Their intersection, the matchgate-Clifford group, plays an important role in randomized fermionic protocols and in matchgate synthesis. Its adjoint action is isomorphic to the group of unit-determinant signed permutations of $2n$ Majorana modes, and we study optimal exact synthesis in this group. That is, given a target unitary and a gate set, output an $n$-qubit circuit implementing the target using the fewest operations. We show that the complexity of this problem strongly depends on the gate set. In particular, we study gate sets consisting of Majorana braids with different connectivity graphs. For path and complete graphs, we prove that the problem is classically solvable in $\mathcal{O}\left(n^2\right)$ time, and we provide explicit gate-optimal compilers. In addition, we prove that when the connectivity graph is a tree, the decision version of the optimal synthesis problem becomes NP-complete. Finally, we benchmark our optimal compiler on chains of up to $n=80$ qubits against those of Qiskit and Tket, obtaining circuits with constant factor improvements $\times2.57$ and $\times2.28$ in the total number of gates, respectively.

In a previous work, we showed that real quantum theory (RQT) cannot be experimentally distinguished from ordinary quantum theory (QT). In this paper, we investigate whether this indistinguishability survives two natural extensions of the setting: allowing separated measurements to be represented by commuting rather than tensor-product observables, and imposing superselection rules, as in fermionic information theory. We show that it does in both cases. Our first result is a positive answer to the Tsirelson problem in RQT: commuting and tensor-product measurements generate the same finite-dimensional correlations. This is surprisingly not a trivial consequence of the standard complex proof, as it does not carry over to the reals. The proof obstruction becomes particularly relevant in the presence of superselection rules, which is why we first establish the equivalence in RQT before extending the framework to superselected RQT. Our second result is a local, real quantum formulation of superselected theories. We extend the RQT framework to accommodate a representation of superselection over the reals and show, in particular, that it admits a fermionic version whose predictions are experimentally indistinguishable from those of fermionic information theory. More generally, the construction extends to all superselected QTs.

We derive rates of exponential relative-entropy decay for a broad class of infinite-dimensional quantum Gibbs samplers. A key technical ingredient is a perturbative stability theory for hypercontractive estimates and logarithmic Sobolev inequalities. For suitably chosen dissipative couplings, we obtain exponential entropy decay for full multimode Bose-Hubbard samplers with arbitrary hopping and repulsive density interactions. For harmonically confined quantum Coulomb gases and molecular systems, we prove exponential entropy decay for every fixed finite-rank low-energy truncation of the interaction. Finally, we exhibit a periodic charging model with a positive spectral gap but no finite-time $L^2$-to-$L^p$ bound for any $p>2$.

We exhibit a classical oracle relative to which QMA \neq QMA(2). The separation is based on a separable Hamiltonian problem defined by signed edge constraints on a graph. The YES instances have zero-energy product states, while the NO instances, constructed using the antisymmetric subspace, have entangled zero-energy states but no low-energy product states. For the QMA lower bound, we use compressed-oracle techniques to track the information learned by a quantum computation making few queries to a YES instance. The key step is to map the resulting superpositions of partial oracle records to the NO family without significantly changing the verifier's behavior.

We study collective state preparation and channel encoding in fermionic systems under parity superselection and composition governed by the canonical anticommutation relations. For a two-mode Gaussian state $\tau$, we obtain the exact entanglement of formation, $E_{\mathrm F}^{\mathrm{phys}}(\tau^{\otimes m})=\lceil m/2\rceil\log2$ for every $m\geq1$. Two copies have the same formation value as one, violating additivity and strong superadditivity, while regularization halves the single-copy value. For an associated Gaussian channel, we determine the minimum output entropy and Holevo information at every blocklength and prove nonadditivity of both. Together, these results give exact answers to the fermionic counterparts of the four additivity questions associated with Shor and Hastings. One physical use carries no classical information, whereas two uses transmit one bit perfectly. The unassisted classical and zero-error classical capacities both equal one half bit per mode. A sharp finite-block bound gives a strong converse: the decoding success probability vanishes at every rate above capacity. These optimizations cover all physical pure-state decompositions and channel inputs, with Gaussian ensembles and classical codes attaining the optima. The formation and minimum output entropy formulas hold for every Rényi order $\alpha\in(0,\infty]$. We also determine the unassisted quantum and zero-error quantum capacities, both equal to one half logical qubit per mode, and prove a strong converse: entanglement fidelity vanishes at every rate above capacity. For a noisy Gaussian family, we determine the one- and two-copy formation values and prove strict nonadditivity at full rank. For $\tau$, Bell violation under local parity-preserving measurements first appears at three copies.

Self-testing certifies quantum states and measurements from observed correlations alone, without requiring a description of the devices that produce them. In this work we establish, to the best of our knowledge, the first robust self-test of the full continuous family of measurements generated by Majorana operators. We achieve this by showing that the Grothendieck game, a two-player nonlocal game in which the players receive directions on a sphere and return binary answers, is a self-test of Majorana observables. That is, any near-optimal performance certifies an entire continuously parameterized family of quantum measurements. We further extend this certification to products of Majorana observables, obtaining a robust self-test of the spin representation of the continuous pin group.

We study the emergent randomness in projected ensembles generated by dual-unitary circuits. Specifically, we consider evolution by solvable dual-unitary brickwork circuits followed by measurements on part of the system, which induce an ensemble of states on the unmeasured subsystem. Previous work has established that this projected ensemble of states forms a quantum state design in the limit where the bath size is large, but the rate of convergence at finite bath size has not been rigorously established. Under three inverse-polynomial assumptions, local permutation mixing, a bound on recurrent backward motion, and contraction at the measured boundary, we fill this gap and prove that a bath of polynomial size suffices to form approximate $k$-designs. In establishing our results, we develop a microscopic transport interpretation of emergent randomness in the projected ensemble, in which deviations from local permutation operators appear as defects, and make connections with the theory of quantum walks.

Decoded quantum interferometry (DQI) uses classical error correction to solve optimization problems, but it is hard to tell which problems could give it a quantum advantage. We develop soundness rules that screen candidate problems by their code parameters, decoding guarantees and classical baselines. For the standard objective of counting satisfied constraints, we prove that under worst-case Hamming decoding DQI's guarantee can exceed Prange completion by at most $(\sqrt{2}-1)/2$. Optimal polynomial intersection (OPI) attains this margin cap asymptotically, so no candidate in this setting can exceed OPI's margin. We also derive a performance law for real-valued objectives: the objective fixes both the solution quality and which errors the decoder must correct. An AI-agent search guided by these rules found two candidate applications. Alternant max-agreement on McEliece-type public keys tests what a secret decoder is worth to DQI against classical solvers that see only the public instance. Multiplicative polynomial intersection, a knapsack-type problem built from discrete logarithms, pairs a cosine objective with a public decoder for signed errors. For both we prove decoding guarantees and finite-length comparisons with Prange restarts, and on the larger instances we tested, DQI's expected quality exceeds what our classical solvers reach within fixed budgets.

Quantum low-density parity-check (qLDPC) codes offer a promising route to reducing the qubit overhead of fault tolerance, with recent ultra-high-rate constructions achieving encoding rates above one half. In this work, we develop fast and parallel logical computation methods for ultra-high-rate codes. We first utilize the group symmetries of the codes to partition the logical qubits into orbits, and then apply parallel surgery methods to implement group-invariant collections of logical Pauli-product measurements. These measurements are highly programmable, as we may arbitrarily couple logical orbits as long as each measurement is repeated across the whole orbit(s). To reduce the space and time overheads, we develop a technique called chain-map convolution, which uses the group structure to boost both the spatial and temporal distances of our protocol in a highly efficient manner. As case studies, we construct distance-preserving parallel measurement gadgets for the [[256, 68, 12]], [[576, 148, 18]] pair-partition codes, and a [[1152, 580, 12]] rate-$1/2$ code, with only around $2.5\times$ space overhead and 3-4 rounds of syndrome extraction each. The same methods also enable parallel injection of cultivated magic states into high-rate codes. Finally, we extend programmability through subgroup restrictions, revealing a tradeoff between logical control and the spacetime resources required for fault tolerance and highlighting the crucial role structured parallelism plays in reducing overhead. These results provide new methods for designing qLDPC logical operations with low spacetime overhead, opening a route toward more efficient fault-tolerant quantum architectures.