Post-quantum cryptography currently rests on a small number of hardness assumptions, posing significant risks should any one of them be compromised. This vulnerability motivates the search for new and cryptographically versatile assumptions that make a convincing case for quantum hardness. In this work, we argue that decoding random quantum stabilizer codes -- a quantum analog of the well-studied LPN problem -- is an excellent candidate. This task occupies a unique middle ground: it is inherently native to quantum computation, yet admits an equivalent formulation with purely classical input and output, as recently shown by Khesin et al. (STOC '26). We prove that the average-case hardness of quantum stabilizer decoding implies the core primitives of classical Cryptomania, including public-key encryption (PKE) and oblivious transfer (OT), as well as one-way functions. Our constructions are moreover practical: our PKE scheme achieves essentially the same efficiency as state-of-the-art LPN-based PKE, and our OT is round-optimal. We also provide substantial evidence that stabilizer decoding does not reduce to LPN, suggesting that the former problem constitutes a genuinely new post-quantum assumption. Our primary technical contributions are twofold. First, we give a reduction from random quantum stabilizer decoding to an average-case problem closely resembling LPN, but which is equipped with additional symplectic algebraic structure. While this structure is essential to the quantum nature of the problem, it raises significant barriers to cryptographic security reductions. Second, we develop a new suit of scrambling techniques for such structured linear spaces, and use them to produce rigorous security proofs for all of our constructions. less

Whether the complex numbers of standard quantum theory are experimentally indispensable has remained open for decades. Real quantum theory (RQT), obtained by replacing complex amplitudes with real ones while retaining the usual Kronecker-product composition rule, reproduces all single-party and bipartite Bell correlations of quantum theory (QT), but its lack of local tomography suggested that the two theories might diverge in more general local experiments. This possibility appeared to be confirmed by Renou et al., who argued that a bilocal network experiment can falsify RQT without falsifying QT. Here we show that this conclusion relies on an experimentally untestable assumption. The key distinction is between product-state independence, which constrains the mathematical form of source states, and operational independence, which is defined entirely by the absence of observable cross-source correlations. We prove that, once source independence is imposed operationally, every finite network correlation achievable in QT is also achievable in RQT with the same locality structure of the measurements. We then extend this equivalence to arbitrary finite sequential multipartite protocols involving channels and measurements with prescribed locality structure. Thus, as long as no violation of QT is observed, RQT cannot be experimentally falsified. Our results restore the empirical indistinguishability of QT and RQT, while showing that they support markedly different pictures of the correlation structure underlying the same observed world. less

Quantum error correction (QEC), the lynchpin of fault-tolerant quantum computing (FTQC), is designed and validated against well-behaved Pauli stochastic error models. But in real-world deployment, QEC protocols encounter a vast array of other errors -- coherent and non-Pauli errors -- whose impacts on quantum circuits are vastly different than those of stochastic Pauli errors. The impacts of these errors on QEC and FTQC protocols have been largely unpredictable to date due to exponential classical simulation cost. Here, we show how to accurately and efficiently model the effects of coherent and non-Pauli errors on FTQC, and we study the effects of such errors on syndrome extraction for surface and bivariate bicycle codes, and on magic state cultivation. Our analysis suggests that coherent error can shift fault-tolerance thresholds, increase the space-time cost of magic state cultivation, and can increase logical error rates by an order of magnitude compared to equivalent stochastic errors. These analyses are enabled by a new technique for mapping any Markovian circuit-level error model with sufficiently small error rates onto a detector error model (DEM) for an FTQC circuit. The resulting DEM enables Monte Carlo estimation of logical error rates and noise-adapted decoding, and its parameters can be analytically related to the underlying physical noise parameters to enable approximate strong simulation. less

We present applications of quantum quadratic residue codes in magic state distillation. This includes showing that existing codes which are known to distill magic states, like the $5$-qubit perfect code, the $7$-qubit Steane code, and the $11$-qutrit and $23$-qubit Golay codes, are equivalent to certain quantum quadratic residue codes. We also present new examples of quantum quadratic residue codes that distill qubit $T$ states and qutrit Strange states with high thresholds, and we show that there are infinitely many quantum quadratic residue codes that distill $T$ states with a non-trivial threshold. All of these codes, including the codes with the highest currently known thresholds for $T$ state and Strange state distillation, are unified under the umbrella of quantum quadratic residue codes. less

Fermionic Gaussian circuits can be simulated efficiently on a classical computer, but become universal when supplemented with non-Gaussian operations. Similar to stabilizer circuits augmented with non-stabilizer resources, these non-Gaussian circuits can be simulated classically using rank- or extent-based methods. These methods decompose non-Gaussian states or operations into Gaussian ones, with runtimes that scale polynomially with measures of non-Gaussianity such as the rank and the extent -- quantities that typically grow exponentially with the number of non-Gaussian resources. Current fermionic rank- and extent-based simulators are limited to Gaussian circuits with magic-state injection. Extending them to mixed states and non-unitary channels has been hindered by the lack of known extent-optimized decompositions for physically relevant gates and noisy channels. In this work, we address this gap. First, we derive analytic decompositions for key non-Gaussian gates and channels, including decompositions for arbitrary two-qubit fermionic gates which are provably optimal for diagonal gates or those acting on Jordan-Wigner-adjacent qubit pairs. Second, we show that stochastic Pauli noise can reduce the effective extent of non-Gaussian rotation gates, but that fermionic magic is substantially more robust to such noise than stabilizer magic. Finally, we demonstrate how these decompositions can accelerate classical sampling from the output distribution of a quantum circuit. This involves a generalization of existing sparsification methods, previously limited to convex-unitary channels, to circuits involving intermediate measurements and feed-forward. Our decompositions also yield speedups for emulating noisy Pauli rotations with quasiprobability simulators in the large-angle/arbitrary-strength-noise and small-angle/low-noise parameter regimes. less

In the presence of qubit losses, the building blocks of fault-tolerant error correction (FTEC) must be revisited. Existing loss-tolerant approaches are mainly architecture-specific, and little attention has been given to optimizing the syndrome measurement sequences under loss. Schemes designed for the standard Pauli error model are not directly applicable because the syndrome patterns differ when both Pauli errors and erasures can occur. Based on recent advances in loss detection units and loss-tolerant syndrome extraction gadgets, we extend the study of adaptive Shor-style measurement sequences to the mixed error model. We begin by discussing how to adaptively convert correctable erasures into located errors. The minimal overhead is quantified by the number of stabilizer measurements, which can be reduced to a subgroup dimension problem for erasures arising in any FTEC circuit for qubits and prime-dimensional qudits. As a byproduct, we provide the construction of the canonical generating set with respect to a given bipartite partition for a stabilizer group on qudits of composite dimension. We then generalize both the weak and strong FTEC conditions. Finally, we present adaptive syndrome-measurement protocols for the mixed error model, generalizing the adaptive protocols for the standard Pauli error model. less

As early as 1935, Schrödinger recognized entanglement as ``not one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought''. Indeed, most remarkable phenomena in quantum information science, such as quantum computing and quantum teleportation, spring from clever uses of entanglement. Among them, pseudotelepathy enables two or more players to win systematically at some cooperative games with no need for communication between them, a restriction that would make the task impossible in a classical world. We investigate the power of multipartite entanglement for pseudotelepathy. Some known games that can be won with tripartite entanglement cannot be won with bipartite entanglement, but they can be won with bipartite nonsignalling resources such as the so-called Popescu--Rohrlich nonlocal box. We exhibit a five-player game that can be won with tripartite entanglement, but not with arbitrary bipartite nonsignalling resources even in the presence of arbitrary five-partite classical resources. This illustrates both the power of bipartite nonsignalling resources (over bipartite entanglement) and the even superior power of tripartite entanglement. less

Characterizing the relation between entanglement and Bell nonlocality is a long-standing open problem, notably challenging in the multipartite case. Here we investigate the effect of superactivation of genuine multipartite nonlocality. Specifically, we show that starting from multipartite states that feature only two-party entanglement (hence almost fully separable), it is possible to obtain GMNL in the many-copy regime. This represents the weakest possible resource for GMNL superactivation. On the technical side, we develop an efficient and practical criterion for certifying GMNL superactivation based on network entangled states, as well as a perfect parallel repetition result for the Khot-Vishnoi Bell game, which are of independent interest. less

We propose a general method for preparing stabilizer states with reduced two-qubit gate count and depth compared to the state of the art. The method starts from a graph state representation of the stabilizer state and iteratively reduces the number of edges in the graph using two-qubit Clifford gates to produce a unitary preparation circuit. We explore various heuristic search and AI-based approaches to optimally choose Clifford gates at each step, the most sophisticated of which is a combination of reinforcement learning and Monte Carlo tree search that we call QuSynth. We apply our method to synthesize code states of various quantum error correcting codes including the 23-qubit Golay code and the 144-qubit gross code, the latter of which is significantly beyond the qubit number that is accessible to prior optimal circuit synthesis methods. We demonstrate that our techniques are capable of reducing the required two-qubit gates by up to a factor of 2.5 compared to previous approaches while retaining low circuit depth. less

This paper introduces Witnessed Quantum Time Evolution (WQTE), a novel quantum algorithm for efficiently computing the eigen-energy spectra of arbitrary quantum systems without requiring eigenstate preparation-a key limitation of conventional approaches. By leveraging a single ancillary qubit to control real-time evolution operators and employing Fourier analysis, WQTE enables parallel resolution of multiple eigen-energies. Theoretical analysis demonstrates that the algorithm achieves Heisenberg-limited precision and operates with only a non-zero wavefunction overlap between the reference state and target eigenstates, significantly reducing initialization complexity. Numerical simulations validate the algorithm's effectiveness in molecular systems (e.g., H4 chains) and lattice models (e.g., Heisenberg spin systems), confirming that computational error scales inversely with maximum evolution time while maintaining robustness against sampling errors and quantum noise. Experimental implementation on an NMR quantum processor further verifies its feasibility in real-world noisy environments. Compared to existing quantum algorithms (e.g., VQE, QPE and their variants), WQTE exhibits superior circuit depth efficiency, resource economy, and noise resilience, making it a promising solution for eigen-energy computation on noisy intermediate-scale quantum (NISQ) devices. less

Extracting energy spectra from quantum Hamiltonians is a fundamental task for quantum simulation, yet remains challenging on noisy intermediate-scale quantum (NISQ) devices. We propose Measured Quantum Time Evolution (MQTE), an ancilla-free algorithm that estimates energy gaps by applying real-time evolution to a reference state and measuring time-resolved probabilities via repeated projective measurements. Spectral analysis of these signals reveals oscillation frequencies corresponding to eigenvalue differences. Crucially, MQTE exhibits inherent robustness to quantum hardware noise and sampling errors: these disturbances manifest as a white-noise background, which does not distort the underlying spectral structure but rather obscures the frequency information. By increasing the number of measurement samples, the intensity of the background white noise can be suppressed, thereby recovering the original spectral content. We validate the algorithm's performance via numerical simulations on one- and two-dimensional Heisenberg models, demonstrating accurate extraction of energy gaps and resilience against both sampling and circuit-level noise. Experimental implementation on the superconducting quantum processor Tianyan-176-II further confirms the practical feasibility and noise tolerance of MQTE under real hardware conditions. This work provides a robust and scalable framework for quantum spectral estimation in the NISQ era. less

The most widely used approach for simulating the dynamics of time-dependent Hamiltonians via quantum computation depends on the quantum-classical hybrid variational quantum time evolution algorithm, in which ordinary differential equations of the variational coefficients for determining time evolution are solved via classical simulations with a time discretization method. We here present a full-quantum approach, in which ordinary differential equations of the variational coefficients are transformed into static linear equations via the Chebyshev spectral discretization method and then solved via the quantum singular value transformation algorithm. Our full quantum algorithm avoids classical feedback, achieves exponential convergence for smooth Hamiltonians, and yields a quantum circuit depth that is independent of the number of time steps. We demonstrate two implementation strategies, with a global formulation designed for fault-tolerant architectures and a sequential formulation tailored to near-term devices, and validate the approach through numerical simulations of proton-hydrogen charge-transfer dynamics, a prototypical time-dependent quantum chemistry problem. This work establishes a systematic pathway from quantum-classical hybrid variational quantum algorithms to full-quantum solvers for general time-dependent Hamiltonians, particularly those whose dynamics admit compact variational descriptions, opening a route toward full quantum computational advantages in time-dependent simulations. less

Early demonstrations of fault tolerant quantum systems have paved the way for logical-level compilation. For fault-tolerant applications to succeed, execution must finish with a low total program error rate (i.e., a low program failure rate). In this work, we study a promising candidate for future fault-tolerant architectures with low spatial overhead: the Gross code. Compilation for the Gross code entails compiling to Pauli Based Computation and then reducing the rotations and measurements to the Bicycle ISA. Depending on the configuration of modules and the placement of code modules on hardware, one can reduce the amount of resulting Bicycle instructions to produce a lower overall error rate. We find that NISQ-based, and existing FTQC mappers are insufficient for mapping logical qubits on Gross code architectures because 1. they do not account for the two-level nature of the logical qubit mapping problem, which separates into code modules with distinct measurements, and 2. they naively account only for length two interactions, whereas Pauli-Products are up to length $n$, where $n$ is the number of logical qubits in the circuit. For these reasons, we introduce a two-stage pipeline that first uses hypergraph partitioning to create in-module clusters, and then executes a priority-based algorithm to efficiently assign clusters onto hardware. We find that our mapping policy reduces the error contribution from inter-module measurements, the largest source of error in the Gross Code, by up to $\sim36\%$ in the best case, with an average reduction of $\sim13\%$. On average, we reduce the failure rates from inter-module measurements by $\sim22\%$ with localized factory availability, and by $\sim17\%$ on grid architectures, allowing hardware developers to be less constrained in developing scalable fault tolerant systems due to software driven reductions in program failure rates. less

As we are entering an early-FTQC era, circuit execution protocols with logical qubits and certain error-correcting codes are being discussed. Here, we propose a circuit execution protocol for the space-time efficient analog rotation (STAR) architecture. Gate operations within the STAR architecture is based on lattice surgery with surface codes, but it allows direct execution of continuous gates $Rz(θ)$ as non-Clifford gates instead of $T = Rz(π/4)$. $Rz(θ)$ operations involve creation of resource states $|m_θ\rangle = \frac{1}{\sqrt{2}} (|0 \rangle + e^{iθ} |1\rangle ) $ followed by ZZ joint measurements with target logical qubits. While employing $Rz(θ)$ enables more efficient circuit execution, both their creations and joint measurements are probabilistic processes and adopt repeat-until-success (RUS) protocols which are likely to result in considerable time overhead. Our circuit execution protocol aims to reduce such time overhead by parallel trials of resource state creations and more frequent trials of joint measurements. By employing quadratic unconstrained binary optimization (QUBO) in determining resource state allocations within the space, we successfully make our protocol efficient. Furthermore, we proposed performance estimators given the target circuit and qubit topology. It successfully predicts the time performance within less time than actual simulations do, and helps find the optimal qubit topology to run the target circuits efficiently. less

Quantum state preparation and block encoding are versatile and practical input models for quantum algorithms in scientific computing. The circuit complexity of state preparation and block encoding frequently dominates the end-to-end gate complexity of quantum algorithms. We give algorithms with lower C-NOT counts for both the state preparation and block encoding. For a general $n$-qubit state, we improve the C-NOT count from Plesch-Brukner algorithm, proposed in 2011, from $(23/24)2^n$ to $(11/12)2^n$. For block encoding, our single-ancilla protocol for $2^{n-1}\times 2^{n-1}$ matrices uses the spectral norm as subnormalization and achieves a C-NOT count leading term $(11/48)4^n$. This result even exceeds the lower bound of $(1/4)4^n$ for $n$-qubit unitary synthesis. Further optimization is performed for low-rank matrices, which frequently arise in practical applications. Specifically, we achieve the C-NOT count leading term $(K+(11/12))2^n$ for a rank-$K$ matrix. Our approach builds upon the recursive block-ZXZ decomposition from Krol et al. and introduces a diagonal matrix migration technique based on the commutativity of the diagonal matrix and the uniformly controlled rotation about the $z$-axis to minimize the use of C-NOT gates. less

Quantum digital signatures (QDS) offer information-theoretic security for message integrity, authenticity, and non-repudiation, and constitute a fundamental cryptographic primitive for future quantum networks. Despite significant progress, the practical deployment of QDS has been severely constrained by limited signature rates and poor tolerance to channel loss, particularly in long-distance and metropolitan-scale networks. Here, we report a high-rate, loss-resilient QDS system that overcomes these two key bottlenecks simultaneously. Our implementation combines intrinsically phase-stable polarization modulation based on a Sagnac interferometer with gigahertz-rate quantum state encoding and low-timing-jitter superconducting nanowire single-photon detectors, enabling robust and continuous operation at high repetition frequencies. By integrating this hardware platform with a one-time universal hashing-based QDS protocol, we achieve a signature rate improvement of more than two orders of magnitude compared with existing QDS implementations under comparable channel-loss conditions. Notably, the system maintains a non-zero effective signature rate of approximately 1.25 times per second at a total channel loss of up to 49.05 dB, representing the highest loss tolerance reported for QDS to date. These results establish a practical and scalable technological pathway for deploying QDS in real-world quantum communication networks. less