Second-quantized fermionic operators with polylogarithmic qubit and gate complexity

Abstract

We present a method for encoding second-quantized fermionic systems in qubits when the number of fermions is conserved, as in the electronic structure problem. When the number $F$ of fermions is much smaller than the number $M$ of modes, this symmetry reduces the number of information-theoretically required qubits from $\Theta (M)$ to $O(F\log M)$. In this limit, our encoding requires $O(F^2{\log }^{4}M)$ qubits, while encoded fermionic creation and annihilation operators have cost $O(F^2{\log }^{5}M)$ in two-qubit gates. When incorporated into randomized simulation methods, this permits simulating time-evolution with only polylogarithmic explicit dependence on $M$. This is the first second-quantized encoding of fermions in qubits whose costs in qubits and gates are both polylogarithmic in $M$, which permits studying fermionic systems in the high-accuracy regime of many modes.

arXiv commentup to date with published version; 19 pages, 4 figures

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• Low-depth simulations of fermionic systems on square-grid quantum hardware
• Solving reaction dynamics with quantum computing algorithms
• Hardware-efficient entangled measurements for variational quantum algorithms
• Parallelization techniques for quantum simulation of fermionic systems
• Optimal Particle-Conserved Linear Encoding for Practical Fermionic Simulation
• Optimizing Quantum Chemistry Simulations with a Hybrid Quantization Scheme
• Benchmarking Quantum Simulation of Chemical Hamiltonians using the Sorted-List Encoding