Two Tsinghua University researchers have presented a proof that reduces the theoretical slowdown needed to protect large quantum calculations from errors. Zhengyi Han and Zi-Wen Liu's September 23 preprint improves an earlier mathematical bound by combining parallel operations with reusable workspace. The result concerns how a fault-tolerant computer could scale, rather than a speed increase measured on a processor.
Quantum hardware makes errors. Fault-tolerant computation protects a calculation by encoding each useful unit of quantum information, called a logical qubit, across multiple physical qubits. Keeping that information intact while computing requires extra operations as well as extra hardware.
Reducing both costs together is difficult. Earlier theoretical work had kept the physical-qubit count within a fixed multiple of the logical-qubit count, but still required a time penalty slightly greater than logarithmic growth. Han and Liu's construction removes that extra factor under specified conditions.
The slowdown grows slowly as the calculation gets larger
The new bound is logarithmic: the slowdown factor rises comparatively slowly as the calculation grows or the required accuracy increases. It depends on how many logical qubits the calculation uses, how many sequential layers of operations it needs, and how much error is allowed.
This describes the growth of the overhead at large scales. It does not specify a runtime in seconds or establish that the construction would beat today's methods on a particular machine.
Parallel operations share reusable workspace
The main construction uses quantum locally testable codes, error-correcting codes that use checks on small parts of the encoded information to detect corruption. These codes also allow many operations on protected data to run at once.
The construction moves batches of logical qubits from compact storage into working space for those operations. Different groups can run in parallel, and the same extra workspace serves successive batches. Reusing it avoids setting aside a separate large workspace for every operation, helping limit the hardware cost while parallel execution limits the time cost.
The guarantee depends on circuit size and control assumptions
The promise of constant space overhead does not mean a fixed number of physical qubits can do any job. It means the physical-qubit count can stay within a fixed multiple of the logical-qubit count. That guarantee applies only when the calculation uses enough logical qubits to absorb the extra workspace needed to prepare states, move information and change how it is encoded. Narrower calculations do not receive the same guarantee from this theorem.
The proof also assumes that physical errors remain below a threshold, that classical control is error-free, and that qubits can interact without restrictions imposed by their positions. It counts the time taken by classical processing. Extending the result to noisy controllers and restricted physical connections remains an open problem identified by the authors.
Han and Liu disclose substantial generative-AI assistance with proof details and presentation, and take responsibility for the results.
Sources
- Zhengyi Han and Zi-Wen Liu, “Purely-logarithmic-time- and constant-space-overhead fault-tolerant quantum computation” (2026)
- Quynh T. Nguyen and Christopher A. Pattison, “Quantum fault tolerance with constant-space and logarithmic-time overheads”
- Yiming Li, Zimu Li and Zi-Wen Liu, “Transversal non-Clifford gates on good quantum locally testable codes”
- Lead image: Oak Ridge National Laboratory quantum lab, CC BY 2.0, via Wikimedia Commons
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