A distillation-teleportation protocol for fault-tolerant QRAM
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arXiv
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| Autores principales: | , , , , , , , |
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| Formato: | Preprint |
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2025
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| _version_ | 1866918034948489216 |
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| author | Dalzell, Alexander M. Gilyén, András Hann, Connor T. McArdle, Sam Salton, Grant Nguyen, Quynh T. Kubica, Aleksander Brandão, Fernando G. S. L. |
| author_facet | Dalzell, Alexander M. Gilyén, András Hann, Connor T. McArdle, Sam Salton, Grant Nguyen, Quynh T. Kubica, Aleksander Brandão, Fernando G. S. L. |
| contents | We present a protocol for fault-tolerantly implementing the logical quantum random access memory (QRAM) operation, given access to a specialized, noisy QRAM device. For coherently accessing classical memories of size $2^n$, our protocol consumes only $\mathrm{poly}(n)$ fault-tolerant quantum resources (logical gates, logical qubits, quantum error correction cycles, etc.), avoiding the need to perform active error correction on all $Ω(2^n)$ components of the QRAM device. This is the first rigorous conceptual demonstration that a specialized, noisy QRAM device could be useful for implementing a fault-tolerant quantum algorithm. In fact, the fidelity of the device can be as low as $1/\mathrm{poly}(n)$. The protocol queries the noisy QRAM device $\mathrm{poly}(n)$ times to prepare a sequence of $n$-qubit QRAM resource states, which are moved to a general-purpose $\mathrm{poly}(n)$-size processor to be encoded into a QEC code, distilled, and fault-tolerantly teleported into the computation. To aid this protocol, we develop a new gate-efficient streaming version of quantum purity amplification that matches the optimal sample complexity in a wide range of parameters and is therefore of independent interest.
The exponential reduction in fault-tolerant quantum resources comes at the expense of an exponential quantity of purely classical complexity: each of the $n$ iterations of the protocol requires adaptively updating the $2^n$-size classical dataset and providing the noisy QRAM device with access to the updated dataset at the next iteration. While our protocol demonstrates that QRAM is more compatible with fault-tolerant quantum computation than previously thought, the need for significant classical computational complexity exposes potentially fundamental limitations to realizing a truly $\mathrm{poly}(n)$-cost fault-tolerant QRAM. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20265 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A distillation-teleportation protocol for fault-tolerant QRAM Dalzell, Alexander M. Gilyén, András Hann, Connor T. McArdle, Sam Salton, Grant Nguyen, Quynh T. Kubica, Aleksander Brandão, Fernando G. S. L. Quantum Physics We present a protocol for fault-tolerantly implementing the logical quantum random access memory (QRAM) operation, given access to a specialized, noisy QRAM device. For coherently accessing classical memories of size $2^n$, our protocol consumes only $\mathrm{poly}(n)$ fault-tolerant quantum resources (logical gates, logical qubits, quantum error correction cycles, etc.), avoiding the need to perform active error correction on all $Ω(2^n)$ components of the QRAM device. This is the first rigorous conceptual demonstration that a specialized, noisy QRAM device could be useful for implementing a fault-tolerant quantum algorithm. In fact, the fidelity of the device can be as low as $1/\mathrm{poly}(n)$. The protocol queries the noisy QRAM device $\mathrm{poly}(n)$ times to prepare a sequence of $n$-qubit QRAM resource states, which are moved to a general-purpose $\mathrm{poly}(n)$-size processor to be encoded into a QEC code, distilled, and fault-tolerantly teleported into the computation. To aid this protocol, we develop a new gate-efficient streaming version of quantum purity amplification that matches the optimal sample complexity in a wide range of parameters and is therefore of independent interest. The exponential reduction in fault-tolerant quantum resources comes at the expense of an exponential quantity of purely classical complexity: each of the $n$ iterations of the protocol requires adaptively updating the $2^n$-size classical dataset and providing the noisy QRAM device with access to the updated dataset at the next iteration. While our protocol demonstrates that QRAM is more compatible with fault-tolerant quantum computation than previously thought, the need for significant classical computational complexity exposes potentially fundamental limitations to realizing a truly $\mathrm{poly}(n)$-cost fault-tolerant QRAM. |
| title | A distillation-teleportation protocol for fault-tolerant QRAM |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2505.20265 |