The Pinnacle Architecture: Reducing the cost of breaking RSA-2048 to 100 000 physical qubits using quantum LDPC codes

The realisation of utility-scale quantum computing inextricably depends on the design of practical, low-overhead fault-tolerant architectures. We introduce the \textit{Pinnacle Architecture}, which uses quantum low-density parity check (QLDPC) codes to allow for universal, fault-tolerant quantum computation with a spacetime overhead significantly smaller than that of any competing architecture. With this architecture, we show that 2048-bit RSA integers can be factored with less than one hundred thousand physical qubits, given a physical error rate of $10^{-3}$, code cycle time of $1$ \textmu s and a reaction time of $10$ \textmu s. We thereby demonstrate the feasibility of utility-scale quantum computing with an order of magnitude fewer physical qubits than has previously been believed necessary.

💡 Research Summary

The paper introduces the “Pinnacle Architecture,” a fault‑tolerant quantum computing framework that leverages quantum low‑density parity‑check (QLDPC) codes to dramatically cut the physical‑qubit overhead required for utility‑scale algorithms. Traditional surface‑code based architectures need on the order of a million physical qubits to run algorithms such as RSA‑2048 factoring or quantum chemistry simulations, because each logical qubit consumes thousands of physical qubits and the time overhead grows with the code distance.

Pinnacle is built from three modular components: (1) Processing Units, each consisting of several bridged QLDPC code blocks equipped with measurement‑gadget systems that enable arbitrary logical Pauli measurements within a single logical cycle; (2) Magic Engines, which embed a QLDPC block together with ancilla systems that inject noisy magic states while simultaneously distilling higher‑fidelity magic states for the next cycle, thereby delivering a fresh |T⟩ state per logical cycle to every processing unit; and (3) optional Memory blocks that store quantum data in QLDPC code blocks and can be accessed read‑only by multiple processing units through “Clifford frame cleaning.”

The key technical innovations are:

• Generalized Pauli measurement gadgets – extending the limited set of measurements available in earlier QLDPC proposals, allowing any logical Pauli product to be measured in parallel with syndrome extraction.
• Magic‑engine pipeline – decoupling magic‑state injection from distillation so that the supply of T‑gates does not become a bottleneck.
• Clifford‑frame cleaning – a new parallelisation technique that enables non‑Clifford gates to be executed across many processing units without costly routing.
• Constant‑depth syndrome extraction – thanks to the bounded check weight and qubit degree of QLDPC codes, each code cycle has fixed depth, making the architecture hardware‑agnostic and compatible with platforms that provide only quasi‑local connectivity.

Time scales are defined as follows: the code‑cycle time (t_c) (1 µs–1 ms depending on hardware), the logical‑cycle time (t_l = d_t t_c) where (d_t = Θ(d)) is proportional to the code distance, and the reaction time (t_r) (taken as (10 t_c)). Under these assumptions, Pauli‑based computation (PBC) can implement any quantum circuit using only Pauli measurements and injected magic states. A circuit with T‑count τ, κ logical qubits, and o adaptive measurements requires τ + κ + o logical cycles and ⌈κ/k⌉ QLDPC blocks, where k is the number of logical qubits per block.

Two benchmark applications are evaluated.

1. Fermi‑Hubbard ground‑state energy – Using generalized bicycle QLDPC codes, the authors achieve order‑of‑magnitude reductions in physical qubits compared with the best surface‑code estimates. For a 16 × 16 lattice (L = 16) at 0.5 % relative precision, only ~62 k physical qubits are needed at a physical error rate (p = 10^{-3}), and ~22 k at (p = 10^{-4}). The runtime ranges from a few minutes (with µs‑scale code cycles) to a few days (with ms‑scale cycles).

2. RSA‑2048 factoring – By compiling the algorithm of Ref.