Papers

We prove that every bipartite state $\rho$ of a qubit coupled to an $n$-level system whose operator Schmidt rank equals three can be written as a mixture of $\text{rank}(\rho)$ pure product states, and as a mixture of at most $n+1$ mixed product states in general. The second result is tight in the sense that there exist states that cannot be decomposed with a smaller number of terms. Our proof gives constructive methods to obtain the decompositions. It involves eigendecompositions of suitable unitary dilations of an operator explicitly determined by the state. Our framework recovers previously known results for the length of decompositions into pure product states and is also able to deal with decompositions into mixed states. For pure product states, our decomposition is different from existing ones.

In $\mathsf{QMA}(2)$, two computationally unbounded provers submit unentangled quantum witnesses to a polynomial-time quantum verifier. We ask whether allowing limited shared entanglement between the two provers changes the power of $\mathsf{QMA}(2)$. To this end, we formalize $\mathsf{QMA}(2;h)$, a variant in which the provers initially share $h$ EPR pairs, as suggested by Aaronson, Beigi, Drucker, Fefferman, and Shor (ToC~2009). We show that polynomially many shared EPR pairs give the provers no cheating advantage: $\mathsf{QMA}(2)\subseteq\mathsf{QMA}(2;h)$ for $h=\operatorname{poly}(n)$. For logarithmically many pairs, the power of $\mathsf{QMA}(2)$ remains unchanged, strengthening this inclusion to $\mathsf{QMA}(2)=\mathsf{QMA}(2;h)$ for $h=O(\log n)$. Finally, we introduce a variant that also allows classical communication between the provers when preparing the witnesses. This setting is particularly revealing for logarithmic-size witnesses: assuming $\mathsf{NP}\nsubseteq\mathsf{BQP}$, we show that superlogarithmically many shared EPR pairs strictly reduce the model's computational power.

Avalanche-based detection of small perturbations is commonplace in precision measurement devices from Geiger counters to single-photon avalanche detectors. Here, we expand this principle to sensing of light waves below the quantum shot noise limit, demonstrating numerically how atomic clouds trapped in photonic cavities can exhibit non-perturbative sensitivity to changes in the cavity field when the cavity mode is tuned to a parity-prohibited transition. We find that, when pumped by a continuous-wave laser, the atomic cloud creates emissions which amplify the initially sub-shot-noise fluctuation by two orders of magnitude. Crucially, this amplification is broadly tunable with respect to frequency and independent of atomic energy structure. Even more strikingly, our amplification mechanism preserves the phase imparted on the atoms by the original ultra-weak light wave, marking a qualitative improvement over conventional protocols. Our finding has implications for both quantum state characterization and detection of weak classical signals.

We present a family of quantum amplitude amplification algorithms that interleave ordinary Grover rotations with tunable weak measurements in loops. A successful measurement yields the target state and stops the algorithm, while after a failure, the loop resumes from the post-measurement state without restarting. We express the leading costs in expected Grover iterations as $p \to 0$. For a known target probability $p$, an exact weak measurement-conditioned loop for states near the angle $\pi/4$ uses $(\pi/8+1/4+o(1))/\sqrt{p}$ iterations, improving on the standard Grover constant $\pi/4$ and on optimised restart Grover, and matching the corresponding infimum in our continuous-angle analysis. When only a lower bound $0 < p_0 \leq p < 1/2$ is available, a discrete Lyapunov equation gives the exact expected oracle cost for every fixed measurement strength and a closed-form optimal strength. Using the strength selected from $p_0$, the expected number of Grover iterations is at most $\frac{1}{2\sqrt{2}}(\frac{1}{\sqrt{p}}+\frac{1}{\sqrt{p_0}})$, where the expected cost decreases as the actual $p$ increases, and gives the leading constant $1/\sqrt{2}$ at the promise boundary $p = p_0$. For completely unknown $p$, we identify measurement strength $\kappa(t)=\Theta(1/t)$ as the critical scale within the regular schedules considered here and analyse $\kappa_b(t)=\min\{1/2,b/t\}$. For each fixed $b > 2$, we rigorously derive a closed-form Gamma-function expression $C(b)$ giving $(C(b)/2+o(1))/\sqrt{p}$ expected iterations. Numerical minimisation of this explicit expression gives $b \approx 5.2$ and $C(b)/2 \approx 1.01$. The results show that weak measurements preserve the $\Theta(1/\sqrt{p})$ search scale while adding an explicit fixed-point control mechanism and provable oracle savings.

We present a hybrid quantum-classical algorithm for distribution network reconfiguration, a combinatorial optimization problem on power distribution networks, that combines a radiality preserving branch-exchange encoding with iterative warm-start quantum imaginary-time evolution to minimize active line losses. The encoding uses a fixed-width binary representation of sequential branch-exchange actions, ensuring that every register outcome decodes to a radial configuration. The quantum subroutine is informed by a surrogate model fit to classically-solved alternating current power flow (ACPF) labels. After a set budget of ACPF solves and circuit samples is exhausted, the algorithm returns the lowest-loss configuration seen. We employ our algorithm on ten test cases, including seven commonly-used benchmark cases and three cases we modified from these and similar standard systems. We include two methods to reduce problem size, which enable extensions of the algorithm to larger networks. We successfully reach minimal-loss configurations for six cases and find configurations with losses from 0.2 percent to 2.18 percent above the reported reference minimal loss for the other four.

Continuous quantum error correction (CQEC) replaces discrete syndrome measurements and recovery operations with continuous syndrome extraction and real-time Hamiltonian feedback. Here we investigate the thermodynamic resources required by this process by formulating measurement-based continuous quantum error correction as an information engine. We distinguish the system-side power associated with energy transfer between the feedback field and the protected system from the controller-side power associated with the feedback Hamiltonian. The framework is first developed for the one-qubit Ahn-Doherty-Landahl (ADL) protocol and subsequently extended to the three-qubit repetition code under continuous stabilizer monitoring. Numerical simulations show that increasing the feedback strength improves the steady-state fidelity and reduces the conditional-state entropy, while both energetic contributions continue to increase in magnitude after the fidelity begins to saturate. These results expose a direct tradeoff between logical stabilization and the energetic resources required for continuous feedback, closely related to previously established energy–precision tradeoffs in quantum measurement and quantum-Zeno stabilization.

We study the complexity of Local Hamiltonian problems under the restriction that every local term is an unweighted occurrence of the same fixed interaction. In the resulting Single-Interaction Hamiltonian (SIH) model, once the interaction is fixed, the Hamiltonian is specified entirely by its ordered interaction hypergraph. Our main technical tool is an exact compiler that converts any fixed finite alphabet of local interactions into a single interaction. On a designated auxiliary subspace, the compiled Hamiltonian reproduces the source Hamiltonian exactly, while the complete spectrum below a chosen separation scale is preserved with multiplicity. Combined with a finite-alphabet normalization, this gives a universal polynomial-time reduction from $k$-Local Hamiltonian to SIH$_{3k+3}$ up to a known global energy scale and inverse-polynomial approximation. Sharper constructions give QMA-completeness of SIH$_3$ and of geometrically local SIH$_8$ with bounded degree and interaction range. In the stoquastic setting, we obtain StoqMA-completeness of Stoq-SIH$_3$ and QMA-completeness of 1-Pinned Stoq-SIH$_4$. We also establish hardness results for uniformly system-size-dependent interactions and derive single-interaction formulations of the Hamiltonian quantum PCP conjecture, frustration-free, exponentially precise, and guided Local Hamiltonian problems. These results show that independently chosen local matrices and independently tunable coupling strengths are not necessary for a broad range of Hamiltonian-complexity phenomena.

We construct efficient information-theoretic non-malleable codes for classical messages that are secure against two noncommunicating local quantum tampering operations with arbitrary pre-shared entanglement. For every sufficiently small fixed $\xi>0$ and all sufficiently large first-share lengths $n$, the codes have rate at least $1/5-\xi$, perfect correctness, and error $2^{-n^{\Omega(1)}}$. Security holds for every message, with a single message-independent simulator for each attack. This resolves the constant-rate question for worst-case classical messages in the entangled two-split-state model. Our construction builds on the permutation-based two-split construction of Batra, Boddu, and Jain, which achieves rate approaching $1/5$ for uniformly random messages. We retain their architecture but replace the uniform message input to the permutation with a prescribed message concatenated with fresh uniform padding. Our main contribution is a worst-case security reduction for this modification.

Maximum-likelihood decoding provides an optimal decoding strategy for quantum error correction under stochastic Pauli noise. However, computing logical-class probabilities is challenging, and the leading exact tensor-network contraction requires time exponential in treewidth. In this work, we introduce a new decoding algorithm based on rank-decomposition dynamic programming (Rank DP). We express decoding partition functions with independent local fault factors as quadratic sums of powers and apply Rank DP. The resulting exact evaluator has arithmetic complexity polynomial in the input size and exponential in the Tanner graph's rank-width with respect to the fault partition, including decomposition construction. After Gaussian elimination, it gives polynomial-time decoding for punctured quantum Reed-Muller codes and a Steane-concatenated family with growing distance under independent single-qubit Pauli noise. Standard contraction of the corresponding tensor networks requires superpolynomial time. A nonnegative realization gives relative floating-point error bounds under explicit arithmetic assumptions. Numerical experiments demonstrate runtime advantages over the tested tensor-network implementations on selected code-capacity and circuit-level instances, with full likelihood evaluation for Reed-Muller codes up to $1{,}023$ qubits. We further use these likelihoods to learn circuit noise parameters from syndromes, evaluate rare postselection probabilities, and quantify decoder optimality gaps. Our work opens new avenues for exploiting algebraic structure in quantum decoding and noise characterization.

While color centers in diamond and other three-dimensional crystals are nowadays key elements of several types of sensors, color centers in two-dimensional materials are rapidly developing and promise high-tech applications. One of the interesting centers in 2D materials is the negatively charged boron vacancy in hexagonal boron nitride (h-BN), which has already shown some potential for magnetometry, but the reliable creation of boron vacancies remains challenging. Here, we demonstrate the fabrication of negatively charged boron vacancy color centers in bulk h-BN via implantation of helium ions at ~1 MeV, as confirmed by characteristic photoluminescence and optically detected magnetic resonance. The resonance has a width of 180 MHz and exhibits the expected Zeeman shift of the resonance lines. The depth of the color center along the c-axis of the h-BN crystal was measured and compared with predictions from Stopping and Range of Ions in Matter modeling. The experimental value and the modeled prediction are consistent within the reported uncertainties, as their 1{\sigma} intervals overlap, although the experiment shows a greater depth and a wider distribution.

We prove a local amplitude-ratio bound for positive ground states and an explicit reverse comparison for fidelity under finite-region erasure. An exact lattice calculation for a connected critical Ising chain gives amplitude exponent $1/8$, preserved by arbitrary optimal control on any fixed spin set and, at the level of logarithmic exponents, on $o(\log N)$ spins. We derive the finite Cauchy product and its uniform strip asymptotics, and document exact two-spin optimization and an interferometric protocol for measuring the recovery. A separate finite-mediator theorem quantifies local compression and a decoder while retaining the rest of the environment exactly. We also give a ground-preparation Ramsey bound, counterexamples to stronger projected-state inferences, and independent full-Hamiltonian calculations.

Layer codes are three-dimensional local CSS codes of check weight at most six, obtained by quasi-concatenating a CSS input code with unrotated surface code patches. What is established about them describes the code, not the circuit that measures it. In this work, we evaluate them as active memories under circuit-level noise. Doing so first requires a syndrome extraction circuit, and the junction stabilizers that couple the patches rule out borrowing a surface code patch's CNOT schedule. We present a decoder-free scheduler that constrains hook propagation first and compresses depth afterwards, generate circuits for eighteen layer codes across four input codes, and compare them with surface codes of the same distance, simulated and decoded in the same way. The circuits lose no distance to hook errors on [[4,2,2]]-input codes wherever a circuit-distance proof is affordable, and reach a lower logical error rate than those of a general-purpose scheduler for CSS codes at roughly half its CNOT depth per round. Our primary family built from a [[4,2,2]] input code reaches a circuit-level threshold of $5.06(7)\times10^{-3}$. The layer code outperforms the surface code in terms of idle robustness: at the same distance it tolerates an interval between syndrome extraction rounds 1.7-3.0 times longer than the rotated surface code. This comes at the cost of 1.7-5.0 times more operations per unit time and approximately five times more physical qubits, both per logical qubit. Finally, we model the cost of the beyond-2D cross-plane CNOTs that the construction demands, and find that their speed matters far more than their fidelity.

In graphene and other two-dimensional materials, periodic modulations of the electron density can significantly alter the energy spectrum and transport properties. Here, we report magnetotransport measurements in encapsulated monolayer graphene with ultra-high-quality patterned periodic antidot lattices that preserve the intrinsic electronic properties of the material. This lithographically defined platform enables controlled access to commensurability and superlattice phenomena at length scales otherwise difficult to achieve. By systematically tuning the lattice dimensions, we reveal a hierarchy of classical commensurability features arising from cyclotron orbits with comparable radii that follow multiple classical trajectories, resulting in broadened resistance peaks beyond the conventional single-orbit picture. Superimposed on these features, we observe pronounced Brown-Zak oscillations arising from the quantum commensurability between the magnetic flux quantum and the unit cell of the engineered Bravais lattices. We demonstrate that the intrinsic geometric phase of our system is directly measurable and show a precise matching of the magnetic field periodicity to the lithographic periodic patterning, where moiré-like electronic spectra can be geometrically generated in single-layer graphene without the need for twist, lattice mismatch, or multilayer stacking. Our results establish nanopatterned graphene as a clean, tunable, and scalable platform for realizing and exploring moiré physics through on-demand real-space design

High-precision measurement of oscillating signal is a ubiquitous issue in fundamental science and a critical task in practical technologies. In quantum metrology, quantum lock-in detection provide an efficient method for measuring such signal. In general, when the initial phase of the oscillating signal is unknown,quantum double lock-in detection can effectively extract complete information about the signal's amplitude, frequency, and initial phase. Conventional quantum double lock-in detection requires two individual quantum interferometry, each of which must undergo state preparation and readout. However, the time for state preparation and readout need not be negligible in practical experiments. In particular, the time for state preparation is longer than the time for sensing. To save experimental resources, it is challenging to achieve quantum double lock-in detection just via a single quantum interferometry while still extracting complete information about the signal's amplitude, frequency, and initial phase. Here, we present a general protocol for achieving a quantum double lock-in detection just via a single quantum interferometry under a sequential orthogonal periodic multipulse sequences. In particular, if the input state is a Greenberger-Horne-Zeilinger state and two interaction-based operations are applied during interferometry, the measurement precisions for frequency, amplitude, and initial phase can both approach the Heisenberg limit. Our study paves a new way for measuring oscillating signals with a single quantum interferometry, and provides a feasible method for achieving Heisenberg-limited detection of alternating signals.

Interactive proof systems with a laconic prover, studied by Goldreich, Vadhan, and Wigderson (CC, 2002), capture problems verifiable with logarithmic prover communication in the classical setting. For two-message quantum analogs, even a single-bit prover response contains quantum statistical zero-knowledge ($\sf QSZK$), introduced by Watrous (FOCS 2002). However, restricting the verifier's question to classical public coins collapses the corresponding class to $\sf BQP$, as shown by Beigi, Shor, and Watrous (ToC, 2011). We further study two-message quantum interactive proof systems with a laconic prover. To this end, we introduce the class ${\sf QIP}_{\ell\text{-}{\rm bit}}(2)$, where $\ell$ is the length of the prover's response, and establish: 1. A natural complete characterization of ${\sf QIP}_{\ell\text{-}{\rm bit}}(2)$ by Multi-State Distinguishability. In particular, Quantum State Distinguishability (QSD) is ${\sf QIP}_{\rm bit}$-complete. Since QSD is $\sf QSZK$-hard, our result places ${\sf QIP}_{\ell\text{-}{\rm bit}}(2)$, for $\ell\geq 2$, in a landscape "just above" $\sf QSZK$. 2. Easy regimes for ${\sf QIP}_{\ell\text{-}{\rm bit}}(2)$ collapsing to $\sf QSZK$. We prove that QSD$[a,b]$ (and thus ${\sf QIP}_{\rm bit}[a,b]$) is in $\sf QSZK$ when $a(n)-b(n)\geq 1/O(\log n)$, and combine this with an answer compression from ${\sf QIP}_{\ell\text{-}{\rm bit}}[2,c,s]$ to ${\sf QIP}_{\rm bit}$ to obtain another easy regime when $2c>(1+2^{\ell/2})s$. Remarkably, our improved polarization applies to SD and $\sf SZK$, resolving an open problem in Sahai and Vadhan (JACM, 2003). 3. Quantum public coins also make the interaction useless: ${\sf qc}\text{-}{\sf QAM}[O(\sqrt{\log{n}})]$ with constant gap is in $\sf BQP$, where ${\sf qc}\text{-}{\sf QAM}[\ell]$ is a subclass of ${\sf QIP}_{\ell\text{-}{\rm bit}}(2)$ in which the verifier's question is exactly halves of EPR pairs.

The Gottesman-Kitaev-Preskill encoding has emerged as a leading candidate for fault-tolerant quantum computation with continuous variables. For photonic architectures, the major challenge is preparing high-quality resource states, which can be deterministically synthesised from many large-amplitude cat states. Thus far, only modest-sized optical cat states have been prepared experimentally, and the implemented methods are highly probabilistic. We propose an all-optical scheme utilising quantum non-demolition interactions and photon-number measurements to prepare large-amplitude cat states with near-unity probability. Importantly, no particular photon-number outcome is postselected: all outcomes contribute to the accumulated photon number, with the protocol repeated until a required threshold is reached. We demonstrate that the scheme is robust to realistic levels of photon-loss, the dominant source of error in optical systems. Our results highlight the power of active Gaussian operations for state preparation and pave the way for efficient quantum error correction using bosonic codes.

Mathematically rigorous statements on the spectral gap of quantum many-body systems in the thermodynamic limit are notoriously difficult to prove – yet they are of fundamental importance for classifying quantum phases of matter. Here we prove the existence of a finite excitation gap for a particular Hamiltonian which was proposed in [T. F. Maier et al., PRX Quantum 6, 030340 (2025)] and is motivated by the Rydberg platform. The Hamiltonian exhibits only two-body blockade interactions between two-level systems and has a topologically ordered ground state in the toric code phase. We show that our result also applies to a broader class of blockade Hamiltonians which realize non-Abelian quantum double phases and were proposed in [H. P. Büchler et al., Phys. Rev. B 114, 065113 (2026)]. The proof builds on known gap stability results and exploits the local symmetry of the studied models.

Understanding randomness formation under conservation laws is important both for characterizing chaotic phenomena in isolated quantum systems and for symmetry-constrained quantum information processing. $U(1)$-symmetric random circuits on an $N$-qubit system provide a minimal tractable setting for this problem, in which the formation rate of unitary designs was conjectured to be governed by charge transport in the underlying circuit geometry. However, whether charge transport indeed sets the slowest relaxation mode has remained an open problem, due to the difficulty in deriving a tight lower bound on the symmetric design formation rate. In this work, we resolve this problem by determining the optimal scaling of the unitary $k$-design formation rate for $k\leq O(\sqrt{\log N})$ across a wide range of circuit geometries, including lattices, expander graphs, and all-to-all interactions. In particular, for $k\geq 2$, we find that the formation rate is governed by a two-particle encounter rate—the rate at which two random walkers encounter each other in a given circuit geometry. This encounter rate is parametrically smaller than the single-particle transport rate in many geometries, thereby disproving the previous conjecture. We further establish that this encounter mechanism indeed sets the design formation rate by deriving its matching lower bound with a novel proof technique based on an auxiliary subgroup ensemble. Although this encounter mode imposes a robust bottleneck on design formation in $U(1)$-symmetric random circuits, we also show that this bottleneck can be circumvented by using symmetry-breaking local gates and provide an explicit protocol that achieves faster design formation. These results establish a new picture of randomness formation under conservation laws and provide guiding principles for characterizing and efficiently generating symmetry-constrained randomness.

Quantum speed-ups have been obtained for many fundamental graph problems, including most variants of matching. A notable exception, however, is the maximum-weight perfect matching (MWPM) problem in general graphs with integer edge weights, which is arguably the most challenging variant of matching. We present a quantum algorithm for MWPM in general graphs that runs in \( \widetilde{O}(n m^{2/3}\log W) \) time, where $W$ is an upper bound on the magnitude of the edge weights. This is an improvement over the best known classical combinatorial bound of \( \widetilde{O}(m\sqrt n \log W) \) in the dense regime, where $m\ge n^{3/2}$. To the best of our knowledge, this is the first quantum algorithm to obtain an asymptotic improvement over the best classical combinatorial algorithm for the MWPM problem in general graphs. The running time of our method accounts for QRAM initialization and access overheads up to polylogarithmic factors, as well as all classical updates to the data structures. At a high level, our algorithm is based on a classical framework due to Duan, Pettie, and Su, but our algorithm requires replacing certain classical tasks with quantum methods, alternative analysis of classical procedures, and the use of alternative data structures that can be implemented effectively in the QRAM model.

The electron–electron Coulomb singularity forces cusp structure in electronic wavefunctions. This cusp structure limits wavefunction regularity and slows the convergence of expansions in smooth bases, requiring large basis sets to reach a target accuracy. The transcorrelated (TC) method incorporates this short-range behavior into the Hamiltonian, thereby improving the regularity of the transformed wavefunction and accelerating convergence toward the complete-basis-set limit. The resulting Hamiltonian is non-Hermitian and non-normal, which limits the direct applicability of standard quantum algorithms. For such non-normal operators, the complexity of several recent quantum algorithms depends explicitly on quantities related to eigenvector conditioning and eigenvalue sensitivity. Understanding these quantities is essential for assessing both algorithmic complexity and quantum resource requirements. In this work, we address these issues in two stages. We first study a solvable model, which provides a controlled setting for isolating how transcorrelation affects basis convergence and eigenvector conditioning. Within this setting, we investigate two distinct one-parameter Jastrow correlators. We derive the asymptotic energy-error scaling: $N^{-1/2}$ for the bare projection and $N^{-3/2}$ for both TC correlators at generic fixed parameters, with $N$denoting the basis size. Furthermore, we show that this faster convergence can yield a polynomial improvement in the asymptotic query-complexity upper bound. We then extend the analysis to second-quantized electronic-structure Hamiltonians and use particle-number-sector diagnostics to distinguish target-sector from auxiliary-sector conditioning. Our work provides a framework for understanding the central accuracy–cost trade-off in TC Hamiltonians.

We consider quantum circuits consisting of $d$ layers of nearest-neighbor two-qubit gates acting on $n$ qubits arranged on a line, where every qubit is independently depolarized with a constant probability before each layer. We describe a randomized parallel algorithm which samples from the output distribution of any such circuit to within total variation error $\delta$, with parallel runtime $2^{O(d)}\log\log(n/\delta)$ and $n 2^{O(d)}$ elementary real-arithmetic operations. Without noise, the same approach gives an exact sampler with parallel runtime $O(\log n)$. For constant depth, we further show that the input/output behavior of the noisy quantum circuit is reproduced up to a constant error by a randomized $\mathsf{AC}^0$-circuit, that is, a Boolean circuit of polynomial size and constant depth with unbounded fan-in AND and OR gates and NOT gates. Consequently, every relation problem solved by a noisy constant-depth quantum circuit in one dimension is also solved, with essentially the same success probability, by a randomized $\mathsf{AC}^0$-circuit. This rules out, for noisy circuits in one dimension, the unconditional quantum advantage established for noisy shallow circuits in two and three dimensions, where polynomial-size classical circuits over the same gate set require depth $\Omega(\log n/\log\log n)$. Our algorithm exploits the fact that depolarizing noise cuts a one-dimensional circuit into independent pieces of logarithmic width, each of which can be sampled exactly in parallel.

Scalable quantum processors require repeated qubit initialization throughout large arrays. In semiconductor spin qubits, fast initialization commonly relies on local reservoir access or measurement-based feedback, requiring dedicated infrastructure that becomes increasingly difficult to distribute as processors scale. Here, we demonstrate reservoir- and measurement-free initialization of a silicon spin-qubit pair in an industrially fabricated Si/SiGe quantum-dot device using a fixed sequence of microwave and baseband pulses. Odd spin-parity states relax to the singlet charge state, whereas blocked even spin-parity states are microwave-driven through the triplet manifold and subsequently converted to the singlet by singlet-triplet mixing and charge hybridization. Repeated cycles produce the singlet-associated charge outcome with a median probability of 99.4% across the sampled preparation states, while exchange spectroscopy independently verifies mapping to the target $|\uparrow\downarrow\rangle$ operational state. Microwave spectroscopy and time-domain measurements identify the dark-state-limited single-cycle transfer and the subsequent blockade-lifting dynamics that set the initialization time scale. The demonstrated pumping sequence uses approximately $12\,\mu\mathrm{s}$ of microwave bursts and mixing dwells, while we project sub-microsecond initialization under improved device conditions. These results establish fixed-sequence microwave initialization as a scalable control primitive for semiconductor spin-qubit processors, based on singlet-triplet physics that can be adapted to platforms with suitable Pauli-blockade transitions.

Free fermion dynamics is classically simulable, and a single non-Gaussian state makes it universal. We show that the same boundary governs quantum nonlocality. Measured as fermionic qubits, fermionic Gaussian states reach at most the biseparable bound of the Mermin inequality for three parties and, for any number of parties, violate the Mermin family by exactly the factor of a single entangled pair. They are never genuinely multipartite nonlocal. Genuine multipartite nonlocality and computational universality are thus one resource for fermions, the opposite of the stabilizer case. The mechanism is fermion parity. The bound is monogamous and certifies non-Gaussianity from measured correlations alone. On superconducting processors we watch nonlocality beyond free fermions switch on under an interaction between densities, confirm the monogamy law on 96 qubits, and measure the ground state of twelve interacting fermions on a ring cross the bound as the interaction grows, detecting the charge density wave transition.

The quantum breakdown model is a model of randomly interacting fermions, motivated by the physics of dielectric breakdown. Here, we establish classification of symmetry and quantum chaos in a zero-dimensional, all-to-all-interacting version of the quantum breakdown model. It exhibits the $\mathbb{Z}_4$ periodicity with respect to the number of fermionic modes, reminiscent of the symmetry classification of the Sachdev-Ye-Kitaev model. A unique feature of the quantum breakdown model is that it realizes all the five classes with chiral symmetry and hosts an exponentially large number of many-body zero modes protected by the chiral index. We elucidate the separation and scaling of the spectral gap and demonstrate the symmetry-enriched hard-edge spectral statistics as signatures of quantum chaos in the chiral symmetry classes.

It is widely expected that the von Neumann entanglement of a local operator grows at most logarithmically in integrable many-body systems in infinite volume. We give a counterexample in a four-state brickwork circuit whose gate is a permutation matrix solving the constant Yang–Baxter equation. The von Neumann operator entropy grows as $(\log2)\sqrt{t/\pi}+O(\log t)$, whereas fixed-index Rényi entropies grow linearly below index one and logarithmically above it. At fixed relative Hilbert–Schmidt error below one, matrix product operator simulations require a bond dimension growing at least as $\exp(c\sqrt t)$ for some $c>0$.

Bivariate bicycle (BB) quantum codes are a prominent finite-length family of quantum low-density parity-check codes, but their minimum distance is usually established numerically rather than read from the defining polynomials. We study the $Z$-logical quotient $K/S$ over $\mathbb F_2[x,y]/(x^\ell-1,y^m-1)$ and show that it fits into a short exact sequence with an annihilator quotient as kernel and a colon quotient as cokernel. The sequence gives an explicit logical basis, a dimension formula, and a componentwise distance identity $d_Z=\min(d_{\mathcal A},d_{\mathcal C})$. Using the Frobenius structure of the finite group algebra, we prove $r_{\mathcal A}=r_{\mathcal C}=k/2$ for every BB code, including repeated-root cases. The algebraic component of a logical class is distinct from the support shape of its lightest representatives: an annihilator class can have a lighter two-block representative, and a colon class can have a one-sided minimum. For lower bounds we show that every proper subset of a minimum-weight logical operator has nonzero syndrome, and that this property persists inside the colon component but not inside the annihilator component. A translation-anchored cluster search built on it proves the distances $4,6,10,10,12,18$ of the six standard BB codes of lengths $18$ to $288$ and enumerates every minimum-weight logical operator. The resulting census shows that $[[108,8,10]]$ is the only one of the six whose distance is attained in a single component, with $d_{\mathcal C}=10$ and $d_{\mathcal A}=12$.

We investigate a finite-time quantum-battery charging architecture in which a driven two-level working system transfers nonequilibrium resources to an interacting two-qubit battery through a weakly anharmonic three-level mediator. Finite-time driving generates coherence and ergotropy, while excitation-number conservation organizes the transfer into distinct dynamical sectors. The mediator then provides spectrally selective charging channels: its lower transition enables nearly complete single-excitation transfer with negligible residual mediator energy, whereas initial mediator loading activates a cross-resonant two-excitation cascade toward the doubly excited battery state. The latter exhibits a modest reduction in transfer efficiency due to the unequal collective matrix elements of the effective three-state chain. Detuning scans quantify the spectral tolerance, and the full mixed-state dynamics reveals distinct energy- and ergotropy-transfer profiles. Finite-time compression, thermal reset, and switching work close the cycle-level energy balance to numerical precision. The resulting scheme combines nonequilibrium resource generation, spectral selectivity, coherent multilevel charging, and thermodynamic cycle closure within a single architecture.

We establish efficient learning for a family of fermionic magic states under unknown number-conserving free-fermion evolution. Each input block has a definite particle number and is a superposition of Fock states, with occupied mode sets disjoint both within and across blocks. The key idea is to exploit the spectral structure of particle reduced density matrices (RDMs) to separate contributions from individual blocks from those involving several blocks, allowing us to reconstruct the hidden block structure. For a fixed upper bound on the particle number per block, our algorithm uses single-copy measurements and polynomial sample and classical computational complexity to recover a compact description of the state with prescribed fidelity and high probability, without prior knowledge of the block decomposition or the evolution. RDMs up to this upper bound suffice for reconstruction. We further show that this RDM order is necessary in general: two orthogonal states in the family can have identical RDMs at every lower order. These results show that an extensive number of non-Gaussian blocks can be compatible with efficient state learning.

We construct the first known fault-tolerant scheme for injecting states into quantum error-correcting codes with constant space and time overhead. That is, we construct a family of constant-rate quantum error-correcting codes for which a set of bare physical qubits can be injected, i.e. fault-tolerantly encoded, into a code block. Similarly, a code state can be ejected, i.e. fault-tolerantly decoded, back into bare physical qubits. We show that these injection and ejection procedures succeed under circuit-level locally stochastic noise, while incurring just a small constant probability of corrupting each qubit, which is unavoidable for bare physical qubits. We also show how to perform fault-tolerant error correction and code-state preparation under locally stochastic noise. All of our gadgets can be implemented with constant quantum circuit depth (i.e. are single-shot), and with a number of physical qubits growing linearly with the number of logical qubits, assuming the ability to run polynomial-sized noiseless classical circuits on the side. We construct our quantum codes by taking a high-dimensional hypergraph product of classical LDPC codes, which in turn are a simplified version of Spielman's linear-time encodable codes (STOC'95). As our resulting product codes are only resilient to physical errors occurring with non-uniform probabilities across qubits, we then show how to concatenate with inner codes of various sizes to obtain fault-tolerance against uniform noise.

For the three-qubit Shifts unextendible product basis (UPB), the minimum product-state expectation value $\lambda_{\mathrm{Shifts}}=1-3\sqrt6/8$ of the UPB projector is known, and four attaining product states were exhibited previously. We determine the complete equality set over all complex product states and prove that it consists of exactly eight product rays: two rays invariant under cyclic permutation of the three qubits and two cyclic orbits of size three. The proof combines exact phase analysis, a Gröbner-basis classification of all 28 finite real stationary points, and a complete treatment of the projective boundaries. Crucially, the eight contact rays span the full three-qubit Hilbert space, whereas the four previously known rays do not. The complete equality classification therefore establishes that the associated projector witness satisfies the spanning criterion and is optimal in the sense that no nonzero positive semidefinite operator can be subtracted while preserving block positivity. As a corollary, for the white-noise family $\rho(p)=(1-p)\rho_{\mathrm{Shifts}}+p\mathbb I/8$, where $\rho_{\mathrm{Shifts}}$ is the complementary-projector Shifts state, the same witness detects entanglement for $p<2-3\sqrt6/4\approx16.29\%$.