Simulating fermionic systems on qubit-based quantum computers often demands significant computational resources due to the requirement to map fermions to qubits. Thus, designing a fault-tolerant quantum computer that operates directly with fermions offers an effective solution to this challenge. Here, we introduce a protocol for fault-tolerant fermionic quantum computation utilizing fermion-to-fermion low-density parity-check (LDPC) codes. Our method employs a fermionic LDPC memory, which transfers its state to fermionic color code processors, where logical operations are subsequently performed. We propose using odd-weight logical Majorana operators to form the code space, serving as memory for the fermionic LDPC code, and provide an algorithm to identify these logical operators. We present examples showing that the encoding rate of fermionic codes often matches that of qubit codes, while the logical failure rate can be significantly lower than the physical error rate. Furthermore, we propose two methods for performing fermionic lattice surgery to facilitate state transfer. Finally, we simulate the dynamics of a fermionic system using our protocol, illustrating effective error suppression.

翻译：在基于量子比特的量子计算机上模拟费米子系统通常需要大量的计算资源，因为需要将费米子映射到量子比特。因此，设计一种直接以费米子运行且具备容错能力的量子计算机，为这一挑战提供了有效的解决方案。本文介绍了一种利用费米子到费米子的低密度奇偶校验码进行容错费米子量子计算的方案。我们的方法采用费米子LDPC存储器，将其状态传输至费米子颜色码处理器，随后在其中执行逻辑操作。我们提出使用奇数权重逻辑马约拉纳算符来构成码空间，作为费米子LDPC码的存储器，并提供了一种识别这些逻辑算符的算法。我们给出的示例表明，费米子码的编码率通常与量子比特码相当，而其逻辑错误率可以显著低于物理错误率。此外，我们提出了两种执行费米子晶格手术的方法，以促进状态传输。最后，我们使用该方案模拟了费米子系统的动力学，展示了有效的错误抑制效果。