Tour de gross：基于双变量自行车代码的模块化量子计算机

We present thebicycle architecture, a modular quantum computing framework based on high-rate, low-overhead quantum LDPC codes identified in prior work. For two specific bivariate bicyclecodes with distances 12 and 18, we construct explicit fault-tolerant logical instruction sets and es-timate the logical error rate of each instruction under circuit noise.We develop a compilationstrategy adapted to the constraints of the bicycle architecture, enabling large-scale universal quan-tum circuit execution.Integrating these components, we perform end-to-end resource estimates Contents 1Introduction1.1Fault-tolerant architecture criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2The bicycle architecture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Fault-tolerant implementation of the bicycle architecture 2.1Review of bivariate bicycle codes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.2Idles and shift automorphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.3In-module measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.4Inter-module measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.5T injections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.6Benchmarking bicycle instructions. . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.7Future directions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Compiling to the bicycle architecture 3.1Distributing operations across data modules . . . . . . . . . . . . . . . . . . . . . . . .3.2In-module Pauli measurement synthesis. . . . . . . . . . . . . . . . . . . . . . . . . .3.3Small-angle rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.4Future directions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4End-to-end resource estimates 5Conclusions and opportunities AAppendices A.1Logical code bases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .A.2Shift automorphisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .A.3Logical processing units for logical measurements. . . . . . . . . . . . . . . . . . . . .A.4Logical measurement protocols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .A.5Circuit scheduling for logical measurements. . . . . . . . . . . . . . . . . . . . . . . .A.6Cost estimates for T state cultivation . . . . . . . . . . . . . . . . . . . . . . . . . . . .A.7Simulation of bicycle instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .A.8Distance validation of bicycle instructions. . . . . . . . . . . . . . . . . . . . . . . . .A.9Pauli-based computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Introduction Quantum computing offers the possibility to solve certain problems of interest, such as period-finding[Sho97], quantum chemistry [Bau+20; Mot+24], and dynamic simulation [KEA23; Shi+24], more effi-ciently than the best known algorithms on classical computers. The discovery that quantum computers can operate reliably despite noise [Sho96] sparked the field of fault-tolerant quantum computing [Rof19;Got22; Cam24].Translating fault-tolerant theory into practice requires afault-tolerant architecturespecifying qubit connectivity, allowed operations with their error rates and durations, and consistent,explicit procedures for fault-tolerant error correction and logical operations. In this work, we propose At the hardware level, the bicycle architecture differs from conventional surface code architecturesby integrating long-range qubit connectivity, see Figure 1a.The advantages of this capability aretwo-fold.Firstly, long-range qubit connectivity facilitates modularity [Mon+14; Bre+16; Bom+21],allowing for individual modules to be scalably optimized.In contrast to monolithic architectures,these modules can be interconnected or swapped out as needed without compromising overall per- By employing bivariate bicycle codes [KP13; PK21; Bra+24], the bicycle architecture significantlyreduces estimated qubit requirements for quantum computers executing specified algorithms, as shownin Figure 1b. Relative to conventional surface code architectures, it provides approximately an orderof magnitude more logical qubits for the same physical resources, thereby enabling access to a broaderrange of applications. (The application regions in Figure 1b reflect coarse resource estimates and areexpected to improve with continued algorithmic advances.) In Section 4, we show that scientifically hardware.(b) Comparison of logical capabilities at physical qubit counts (q:5k, 50k, 500k) anderror rates (p:10−3and10−4). The bicycle architecture (gross: filled red ellipse; two-gross: hollowblue ellipse) can reliably execute circuits with an order of magnitude more logical qubits than theconventional surf