A scalable fault-tolerant framework that combines coherent observable estimation with a space-time-efficient implementation of non-Clifford rotations is introduced, suppressing the residual logical errors that limit existing partially fault-tolerant approaches.
Abstract
While quantum computers promise to solve classically intractable problems, identifying the point at which fault-tolerant quantum computation outperforms the best classical algorithms for practical applications remains an outstanding challenge. Here we establish a concrete quantum-classical crossover for quantum many-body dynamics under realistic hardware conditions. We introduce a scalable fault-tolerant framework that combines coherent observable estimation with a space-time-efficient implementation of non-Clifford rotations, suppressing the residual logical errors that limit existing partially fault-tolerant approaches. A benchmark against state-of-the-art tensor-network and variational Monte Carlo algorithms reveals a concrete crossover for mixed-field Ising dynamics at modest system sizes. For a physical error rate of $p=10^{-3}$, fault-tolerant simulation requires approximately 2 hours and $3.7 \times 10^5$ physical qubits for a 100-site 1D system, whereas tensor network approaches would require about 100 years. For 2D models, where rapid entanglement growth limits the classical evolution time, we project quantum runtimes within minutes. A physical error rate of $p=10^{-4}$ leads to at least an order of magnitude reduction in qubit count ($3.1 \times 10^4$ physical qubits) and runtime (minutes for 1D and seconds for 2D). The reduction in quantum runtime arises from our improved rotation-state injection and co-design of quantum error correction and observable-estimation protocols, which jointly suppress logical-error accumulation and reduce sampling overhead. Our results establish a scalable route towards practical quantum advantage and identify quantitative engineering targets for future fault-tolerant architectures.
Quantum error-detecting codes offer a near-term path for improving the performance of quantum simulations on noisy hardware. Using IBM's superconducting quantum computer ibm_boston, we show that partially fault-tolerant encoded quantum simulations of the Ising model in 1+1D and 2+1D outperform their unencoded counterparts in estimating local observables. To represent 42 logical qubits on the heavy-hex quantum processor, 21 blocks of the [[4, 2, 2]] Iceberg code and up to 136 physical qubits are used. By pairing fault-tolerant syndrome extraction with non-fault-tolerant logical operations, this scheme preserves many of the benefits of error detection while avoiding the overhead typically required for a fully fault-tolerant logical gate set. The encoding's square logical connectivity, together with the freedom to place logical qubits within each block, enables simulations of a 2D spatial lattice with lower circuit depth than the unencoded implementation requires. We introduce Observable-Ranked Postselection, a selective-filtering technique based on syndrome correlations that recovers reliable results without the prohibitive shot loss of full syndrome postselection. Under the cumulative effect of device errors, this encoding improves local-observable accuracy over the unencoded baseline by 2-6% at intermediate times in 1+1D simulations, growing with circuit depth to over 200% in 2+1D at the latest times studied.
Henry F. Froland, Dorota M. Grabowska, S. Grieninger et al.· 2 citations
This work investigates how errors at module interfaces and within individual QPUs affect fault-tolerant computation when qubits are encoded using the rotated surface code, and develops an efficient protocol for preparing distributed fault-tolerant logical GHZ states.
S. Chelluri, R. Mengoni, Tom Darras et al.· 0 citations
An encoding-aware resource analysis comparing one-hot and binary amplitude encodings for QHD suggests that exploiting the analytic structure of the target function to compile the potential evolution in QHD more efficiently is needed for further resource reductions.
Chenxu Liu, Meng Wang, Mingze Li et al.· 0 citations
To maximize the value of fault-tolerant quantum computers, it is essential to develop concrete applications beyond well-established domains such as chemistry and condensed-matter physics. Here we construct and compile quantum algorithms to simulate the structure of atomic nuclei -- a topic that has received relatively little attention from the quantum computing community despite its similarities to the electronic structure problem in chemistry -- via effective shell-model Hamiltonians and no-core-shell-model Hamiltonians with three-body interactions derived from chiral effective field theory. Furthermore, we provide quantum resource estimates, in terms of Toffoli gate and qubit counts, for these algorithms, which, to our knowledge, are the first such estimates for fault-tolerant quantum simulation of atomic nuclei. Notably, the estimates for $^{32}$Mg and $^{219}$At shell-model Hamiltonians are comparable to recent estimates of Femoco simulations, a standard benchmark in chemistry. For no-core-shell-model Hamiltonians suitable for light nuclei (up to $^{40}$Ca or so), we find that resource requirements are significantly higher, suggesting that more bespoke strategies are required to make such simulations practicable. Throughout this work, we draw upon the similarities between nuclear and electronic structure problems, while also highlighting challenges that are specific to the former. We hope this work will spur long-term collaborations between the nuclear and quantum computing community with the ultimate goal of realizing useful nuclear simulations on quantum computers.
J. Benstead, Michael Garn, N. Gaspar et al.· 0 citations
Quantum error correction (QEC) is beginning to enable logical operations that outperform their unencoded physical counterparts, but useful fault-tolerant computation will require more than low-error quantum memory. An effective architecture must orchestrate efficient logical encoding, low-overhead logical operations, and access to the non-Clifford resources required for universal computation. Here, we introduce and experimentally validate such an architecture based on the $[[20,2,6]]$ $C_4$-Helix code, designed for the early fault-tolerant regime. Using Quantinuum Helios, a 98-qubit trapped-ion quantum processor, we experimentally demonstrate the principal components of this architecture: we perform repeated quantum error correction with an error of $4.6^{+6.2}_{-2.6}\times10^{-5}$ per logical qubit per QEC cycle. We benchmark the complete Clifford group on the two logical qubits of a single codeblock under active error correction, obtaining an error of $2.8^{+1.0}_{-1.6}\times 10^{-4}$ per two-qubit logical Clifford. We further demonstrate a fault-tolerant chain-map interface between $C_4$-Helix and a distance-5 surface code, preparing a heterogeneous three-logical-qubit GHZ state with a fidelity lower bound of $99.925^{+0.068}_{-0.245}\%$. In each case, the encoded implementation outperforms its corresponding unencoded physical baseline without relying on postselection. Circuit-level simulations indicate that improvements in physical fidelity bring the same architecture into the $10^{-6}$-$10^{-8}$ logical-error regime targeted for early fault-tolerant computation. Together, these results establish $C_4$-Helix as a hardware-validated fault-tolerant architecture rather than a bare quantum memory.
Noah F. Berthusen, Ali Lavasani, Asmae Benhemou et al.· 0 citations
Quantum computing has been championed as a ground-breaking technology due to its significant computational advantage over classical computing systems. At present, fault-tolerant, large-scale universal quantum computing remains elusive, and these issues remain central challenges in engineering, physics, and computer science. In theory, quantum advantage offers the potential to make many currently intractable computational problems practically solvable, with profound implications across science, industry, and computing. This paper examines the contemporary case for general-purpose quantum computing and the prevailing challenges that presently prevent its widespread adoption. It surveys the theoretical foundations of computation and quantum mechanics that underpin quantum computers, describes the quantum computational model and a working implementation on IBM's Qiskit platform, and evaluates the persistent barriers of noise, decoherence, and scalability that constrain quantum systems today. We conclude that quantum computing is best positioned, in the near term, as a specialized co-processor rather than a general-purpose replacement for classical computing.
Claude Cockfield, M. Garuba· Open Access Research Journal...· 0 citations
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