STAR-Magic Mutation: Even More Efficient Analog Rotation Gates for Early Fault-Tolerant Quantum Computer

TL;DR

The paper introduces STAR-magic mutation, a protocol that significantly improves the efficiency of implementing logical rotation gates on early fault-tolerant quantum computers, reducing error and execution time for small-angle rotations.

Contribution

It presents a novel protocol combining state preparation techniques to achieve better error scaling and introduces a new quantum architecture for early fault-tolerant quantum computing.

Findings

Achieves a two-order-of-magnitude reduction in error and time for small-angle rotations.

Demonstrates the architecture's ability to simulate complex quantum systems with hundreds of thousands of qubits.

Provides theoretical bounds on circuit size and spacetime costs for the proposed architecture.

Abstract

We introduce STAR-magic mutation, an efficient protocol for implementing logical rotation gates on early fault-tolerant quantum computers. This protocol judiciously combines two of the latest state preparation protocols: transversal multi-rotation protocol and magic state cultivation. It achieves a logical rotation gate with a favorable error scaling of $\mathcal{O}(\theta_L^{2(1-\Theta(1/d))}p_{\text{ph}})$, while requiring only the ancillary space of a single surface code patch. Here, $\theta_L$ is the logical rotation angle, $p_{\text{ph}}$ is the physical error rate, and $d$ is the code distance. This scaling marks a significant improvement over the previous state-of-the-art, $\mathcal{O}(\theta_L p_{\text{ph}})$, making our protocol particularly powerful for implementing a sequence of small-angle rotation gates, like Trotter-based circuits. Notably, for $\theta_L \lesssim 10^{-5}$, our protocol achieves a two-order-of-magnitude reduction in both the execution time and the error rate of analog rotation gates compared to the standard $T$-gate synthesis using cultivated magic states. Building upon this protocol, we also propose a novel quantum computing architecture designed for early fault-tolerant quantum computers, dubbed ``STAR ver.~3". It employs a refined circuit compilation strategy based on Clifford+$T$+$\phi$ gate set, rather than the conventional Clifford+$T$ or Clifford+$\phi$ gate sets. We establish a theoretical bound on the feasible circuit size on this architecture and illustrate its capabilities by analyzing the spacetime costs for simulating the dynamics of quantum many-body systems. Specifically, we demonstrate that our architecture can simulate biologically-relevant molecules or lattice models at scales beyond the reach of exact classical simulation, with only a few hundred thousand physical qubits, even assuming a realistic error rate of $p_{\text{ph}}=10^{-3}$.