Extending the Frontier of Quantum Computers with Qutrits
We advocate for a fundamentally different way to perform quantum computation by using three-level qutrits instead of qubits. In particular, we substantially reduce the resource requirements of quantum computations by exploiting a third state for temporary variables (ancilla) in quantum circuits. Past work with qutrits has demonstrated only constant factor improvements, owing to the lg(3) binary-to-ternary compression factor. We present a novel technique using qutrits to achieve a logarithmic runtime decomposition of the Generalized Toffoli gate using no ancilla - an exponential improvement over the best qubit-only equivalent. Our approach features a 70× improvement in total two-qudit gate count over the qubit-only decomposition. This results in improvements for important algorithms for arithmetic and QRAM. Simulation results under realistic noise models indicate over 90% mean reliability (fidelity) for our circuit, versus under 30% for the qubit-only baseline. These results suggest that qutrits offer a promising path toward extending the frontier of quantum computers.
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NSF-PAR ID:
10191000
Journal Name:
IEEE Micro
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1 to 1
ISSN:
0272-1732
The quantum simulation of quantum chemistry is a promising application of quantum computers. However, forNmolecular orbitals, the$${\mathcal{O}}({N}^{4})$$$O\left({N}^{4}\right)$gate complexity of performing Hamiltonian and unitary Coupled Cluster Trotter steps makes simulation based on such primitives challenging. We substantially reduce the gate complexity of such primitives through a two-step low-rank factorization of the Hamiltonian and cluster operator, accompanied by truncation of small terms. Using truncations that incur errors below chemical accuracy allow one to perform Trotter steps of the arbitrary basis electronic structure Hamiltonian with$${\mathcal{O}}({N}^{3})$$$O\left({N}^{3}\right)$gate complexity in small simulations, which reduces to$${\mathcal{O}}({N}^{2})$$$O\left({N}^{2}\right)$gate complexity in the asymptotic regime; and unitary Coupled Cluster Trotter steps with$${\mathcal{O}}({N}^{3})$$$O\left({N}^{3}\right)$gate complexity as a function of increasing basis size for a given molecule. In the case of the Hamiltonian Trotter step, these circuits have$${\mathcal{O}}({N}^{2})$$$O\left({N}^{2}\right)$depth on a linearly connected array, an improvement over the$${\mathcal{O}}({N}^{3})$$$O\left({N}^{3}\right)$scaling assuming no truncation. As a practical example, we show that a chemically accurate Hamiltonian Trotter step for a 50 qubit molecular simulation can be carried out in the molecular orbital basis with as few as 4000 layers of parallel nearest-neighbor two-qubit gates, consisting of fewer than 105non-Clifford rotations. We also apply our algorithm to iron–sulfur clusters relevant for elucidating the mode of action of metalloenzymes.