Fault-tolerant fermionic quantum computing

• URL: http://arxiv.org/abs/2411.08955v2
• Date: Wed, 16 Jul 2025 17:58:47 GMT
• Title: Fault-tolerant fermionic quantum computing
• Authors: Alexander Schuckert, Eleanor Crane, Alexey V. Gorshkov, Mohammad Hafezi, Michael J. Gullans,
• Abstract summary: We introduce fermionic fault-tolerant quantum computing, a framework which removes this overhead altogether.<n>We show how our framework can be implemented in neutral atoms, overcoming the apparent inability of neutral atoms to implement non-number-conserving gates.
• Score: 39.58317527488534
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Simulating the dynamics of electrons and other fermionic particles in quantum chemistry, materials science, and high-energy physics is one of the most promising applications of fault-tolerant quantum computers. However, the overhead in mapping time evolution under fermionic Hamiltonians to qubit gates renders this endeavor challenging. We introduce fermionic fault-tolerant quantum computing, a framework which removes this overhead altogether. Using native fermionic operations we first construct a repetition code which corrects phase errors only. Within a fermionic color code, which corrects for both phase and loss errors, we then realize a universal fermionic gate set, including transversal fermionic Clifford gates. Interfacing with qubit color codes we introduce qubit-fermion fault-tolerant computation, which allows for qubit-controlled fermionic time evolution, a crucial subroutine in state-of-the-art quantum algorithms. As an application, we consider simulating crystalline materials, finding an exponential improvement in circuit depth for a single time step from $\mathcal{O}(N)$ to $\mathcal{O}(\log(N))$ with respect to lattice site number $N$ while retaining a site count of $\tilde{\mathcal{O}}(N)$, implying a linear-in-$N$ end-to-end gate depth for simulating materials, as opposed to quadratic in previous approaches. We also introduce a fermion-inspired qubit algorithm with $O(\mathrm{log}(N)$ depth, but a prohibitive number of additional ancilla qubits. We show how our framework can be implemented in neutral atoms, overcoming the apparent inability of neutral atoms to implement non-number-conserving gates. Our work opens the door to fermion-qubit fault-tolerant quantum computation in platforms with native fermions such as neutral atoms, quantum dots and donors in silicon, with applications in quantum chemistry, material science, and high-energy physics.

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