Sampling-based proposals are prominent candidates for demonstrating quantum computations beyond the reach of classical supercomputers. However, it has been difficult to combine their complexity-theoretic hardness with two capabilities needed for scalable quantum computing more generally: suppressing hardware errors, and verifying the quantum computation itself. Here we address both issues by introducing structured circuits, which, in addition to provable hardness guarantees, admit an encoding in a quantum code. This allows us to simultaneously reach high fidelities at high circuit depths, and to certify an experimental fidelity via the circuit structure and measurement of code syndromes. The resulting certificate is device dependent, but requires substantially weaker noise assumptions than existing fidelity proxy benchmarks. We demonstrate our proposal with a $70$-qubit, depth-$70$ Clifford circuit doped with $468$ $T$ gates. We use a total of $97$ physical qubits to encode this computation in spacetime codes, effectively suppressing gate error rates by $10\times$ after syndrome post-selection, and yielding a state with a fidelity lower bound of $0.284$ with $95\%$ confidence. Our construction is a systematic method for promoting a stabilizer state to a magic state while keeping an error-detected fidelity certificate.
Suppressing errors is the central challenge for useful large-scale quantum computing. While quantum error correction promises a viable solution to this challenge, existing codes typically suffer from trade-offs among encoding efficiency, error threshold, and hardware feasibility. Here, we introduce Cornucopia codes, a family of practical, hardware-efficient quantum low-density parity-check codes that achieve an ultra-high encoding rate exceeding $1/2$ while maintaining a pseudo-threshold exceeding $0.4\%$ under the standard circuit-level noise model. Inspired by recent affine-permutation-based code constructions and the long-range connectivity available in reconfigurable neutral-atom arrays, we adopt a structured code geometry in which the code layout, atom rearrangement, and syndrome-extraction schedule are co-designed. This structure enables nonlocal syndrome measurements through simple, parallel atom rearrangements. A complete syndrome extraction cycle measures all $X$- and $Z$-type checks in parallel with $12$ entangling layers, independent of the code size. The resulting threshold is comparable to those of the surface code and bivariate bicycle codes. In particular, a single code block $[[2844,1426,18]]$ encodes $1{,}426$ distance-$18$ logical qubits, achieving an extrapolated logical error rate of $2.6\times10^{-16}$ ($1.9\times10^{-31}$) per logical qubit per cycle, assuming the physical error rate of $0.1\%$ ($0.01\%$). By comparison, a bivariate bicycle code implementation would require more than $68{,}000$ physical qubits to encode the same number of logical qubits at a comparable logical error rate. These results bring demonstrations of ultra-low-overhead quantum error correction within the reach of near-term quantum processors.
We give a sampling problem that is solvable by shallow quantum circuits, hard for polynomial-time classical algorithms under lattice-based assumptions, and efficiently verifiable by a classical computer. The quantum sampler admits two implementations: one uses log-logarithmic-depth quantum circuits with one- and two-qubit gates, i.e., $\mathsf{QNC}^0[\log\log]$ circuits, while the other uses constant-depth quantum circuits with unbounded fan-in gates, i.e., $\mathsf{QAC}^0$ circuits. Our construction can be seen as compiling the Learning with Errors (LWE)-based single-round proof of quantumness of Arabadjieva et al. (2025) to very low depth. The price paid for this compilation is the reliance on less standard, though well-motivated, assumptions: in addition to the lattice knowledge assumption used by Arabadjieva et al. (2025), we require a strengthened variant of the adaptive-hardcore-bit property of LWE, for which we provide supporting evidence. Unlike previous low-depth proofs of quantumness, the quantum computation here requires no mid-circuit measurements or feed-forward: it consists only of running a shallow circuit and sampling from its output distribution. This shows that shallow quantum circuits have sufficient structure to solve certain classically hard tasks whose solutions can be verified efficiently.
Can a high-quality quantum gate be certified when uncharacterized state-preparation and measurement errors are dominant? Can this be achieved with low experimental overhead? Here, we introduce a sound black-box certification protocol for a single-qubit gate based on a small set of fixed, deterministic sequences. From the data, the protocol derives finite-sample bounds on the gate's rotation eigenvalue, a gauge-invariant property. Its phase reveals the accuracy of the rotation angle, while its modulus quantifies the loss of coherence under repeated gate applications. We implement the protocol on a $^{40}\mathrm{Ca}^{+}$ trapped-ion processor and certify the $\sqrt{\mathrm{X}}$-gate rotation eigenvalue using $22\,000$ circuit executions, and demonstrate the robustness of certification to state-preparation and measurement errors by deliberately degrading the readout. Finally, we prove that these spectral constraints imply, up to a physically meaningful unitary change of basis, a rigorous average gate-fidelity lower bound for every time-independent qubit model compatible with the data. In both readout settings, the spectral bounds yield the same fidelity certificate of $99.94(3)\%$ with $99\%$ confidence. Our results establish a new standard for quantum-gate certification by combining soundness and experimental efficiency without requiring trusted reference operations, randomized circuits, or model fitting.
Nikolai Miklin, Jan Nöller, J. Martínez et al.· 0 citations
The threshold theorem states that quantum computations can be made reliable below a physical error threshold, at the cost of additional physical qubits and circuit depth. Recent work has reduced these space and time overheads to polylogarithmic or nearly logarithmic scalings, but whether the cumulative spacetime overhead can be constant has remained unclear. Here, we show that even for the simplest task of preserving quantum information in a quantum memory, under an optimistic noise model and allowing general adaptive protocols, there is an unavoidable logarithmic contribution to the cumulative spacetime overhead. This additional cost can nevertheless be shared among many logical qubits, so sufficiently wide computations, including standard implementations of Shor's algorithm, may still achieve constant relative overhead. We further give a positive-rate CSS code construction that attains the memory bound, identify sufficient conditions under which the same scaling extends from quantum memory to fault-tolerant circuit implementations, and derive circuit-size bounds for subsystem spacetime codes. Our work establishes fundamental limits on the resources required for quantum fault tolerance.
Kishor Bharti, Tobias Haug, Andrew Tanggara· 0 citations
Preparation and verification of specific quantum states is an important capability for quantum devices to realise advantages over classical computations and algorithms. In this work, we have demonstrated an end-to-end framework that combines resource-efficient quantum state preparation with rapid, robust fidelity verification on near-term quantum hardware. By experimentally preparing and validating a structured complex quantum state encoding a digitized acoustic signal on the Quantinuum H2-1 trapped-ion platform, we achieved a high hardware fidelity of $F_{\mathrm{hw}} = 0.929$. Crucially, this milestone was realized without relying on idealized assumptions or deep fault-tolerant overhead, but rather through resource-minimal circuits optimized for NISQ-era and early fault-tolerant devices. Furthermore, we addressed a key limitation in current quantum state certification. While validation methods like shadow overlap work well for random states, their sample complexity can become prohibitively high for the structured states used in practical algorithms. We mitigate this by introducing a pre-measurement basis-change technique that reduces the verification parameter, $\tau$, by over 10 orders of magnitude for structured targets. This approach tightens the theoretical certification guarantees of the shadow overlap method and integrates tensor-network preparation and shadow validation into a unified workflow. These results shift the paradigm of how structured classical data can be mapped to and verified on quantum hardware under realistic noise and measurement budgets. By compressing a robust verification procedure to just 1,000 measurement shots, this framework offers an immediate, scalable benchmarking standard.
Archie Butterworth, Josh Green, Yu-Sen Wu et al.· 0 citations
This work considers a qubit noise model where the probability of phase-flip errors is exponentially smaller (in qubit number) compared to the probability of bit-flip errors that occur with probability p, and demonstrates that Heisenberg scaling can be attained for times up to T\propto 1/p^{(N+1)/2} for a N-qubit repetition code.
Lorcán O. Conlon, Yu-Xin Wang, E. Abbasgholinejad et al.· 1 citation
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
