Harnessing the Power of Long-Range Entanglement for Clifford Circuit Synthesis
In superconducting architectures, limited connectivity remains a significant challenge for the synthesis and compilation of quantum circuits. We consider models of entanglement-assisted computation where long-range operations are achieved through injections of large Greenberger–Horne&...
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2024-01-01
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| Series: | IEEE Transactions on Quantum Engineering |
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| Online Access: | https://ieeexplore.ieee.org/document/10531653/ |
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| author | Willers Yang Patrick Rall |
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| description | In superconducting architectures, limited connectivity remains a significant challenge for the synthesis and compilation of quantum circuits. We consider models of entanglement-assisted computation where long-range operations are achieved through injections of large Greenberger–Horne–Zeilinger (GHZ) states. These are prepared using ancillary qubits acting as an “entanglement bus,” unlocking global operation primitives such as multiqubit Pauli rotations and fan-out gates. We derive bounds on the circuit size for several well-studied problems, such as CZ circuit, CX circuit, and Clifford circuit synthesis. In particular, in an architecture using one such entanglement bus, we give a synthesis scheme for arbitrary Clifford operations requiring at most <inline-formula><tex-math notation="LaTeX">$2n+1$</tex-math></inline-formula> layers of entangled state injections, which can be computed classically in <inline-formula><tex-math notation="LaTeX">$O(n^{3})$</tex-math></inline-formula> time. In a square-lattice architecture with two entanglement buses, we show that a graph state can be synthesized using at most <inline-formula><tex-math notation="LaTeX">$\lceil \frac{1}{2}n\rceil +1$</tex-math></inline-formula> layers of GHZ state injections, and Clifford operations require only <inline-formula><tex-math notation="LaTeX">$\lceil \frac{3}{2} n \rceil + O(\sqrt{n})$</tex-math></inline-formula> layers of GHZ state injections. |
| format | Article |
| id | doaj-art-06721945587f4f48b0d960c6fc28d9de |
| institution | Kabale University |
| issn | 2689-1808 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IEEE |
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| series | IEEE Transactions on Quantum Engineering |
| spelling | doaj-art-06721945587f4f48b0d960c6fc28d9de2025-01-25T00:03:36ZengIEEEIEEE Transactions on Quantum Engineering2689-18082024-01-01511010.1109/TQE.2024.340208510531653Harnessing the Power of Long-Range Entanglement for Clifford Circuit SynthesisWillers Yang0https://orcid.org/0000-0001-5046-9147Patrick Rall1IBM Quantum, MIT-IBM Watson AI Lab, Cambridge, MA, USAIBM Quantum, MIT-IBM Watson AI Lab, Cambridge, MA, USAIn superconducting architectures, limited connectivity remains a significant challenge for the synthesis and compilation of quantum circuits. We consider models of entanglement-assisted computation where long-range operations are achieved through injections of large Greenberger–Horne–Zeilinger (GHZ) states. These are prepared using ancillary qubits acting as an “entanglement bus,” unlocking global operation primitives such as multiqubit Pauli rotations and fan-out gates. We derive bounds on the circuit size for several well-studied problems, such as CZ circuit, CX circuit, and Clifford circuit synthesis. In particular, in an architecture using one such entanglement bus, we give a synthesis scheme for arbitrary Clifford operations requiring at most <inline-formula><tex-math notation="LaTeX">$2n+1$</tex-math></inline-formula> layers of entangled state injections, which can be computed classically in <inline-formula><tex-math notation="LaTeX">$O(n^{3})$</tex-math></inline-formula> time. In a square-lattice architecture with two entanglement buses, we show that a graph state can be synthesized using at most <inline-formula><tex-math notation="LaTeX">$\lceil \frac{1}{2}n\rceil +1$</tex-math></inline-formula> layers of GHZ state injections, and Clifford operations require only <inline-formula><tex-math notation="LaTeX">$\lceil \frac{3}{2} n \rceil + O(\sqrt{n})$</tex-math></inline-formula> layers of GHZ state injections.https://ieeexplore.ieee.org/document/10531653/Clifford circuitsGreenberger–Horne–Zeilinger (GHZ) stateslong-range entanglementquantum circuit synthesis |
| spellingShingle | Willers Yang Patrick Rall Harnessing the Power of Long-Range Entanglement for Clifford Circuit Synthesis IEEE Transactions on Quantum Engineering Clifford circuits Greenberger–Horne–Zeilinger (GHZ) states long-range entanglement quantum circuit synthesis |
| title | Harnessing the Power of Long-Range Entanglement for Clifford Circuit Synthesis |
| title_full | Harnessing the Power of Long-Range Entanglement for Clifford Circuit Synthesis |
| title_fullStr | Harnessing the Power of Long-Range Entanglement for Clifford Circuit Synthesis |
| title_full_unstemmed | Harnessing the Power of Long-Range Entanglement for Clifford Circuit Synthesis |
| title_short | Harnessing the Power of Long-Range Entanglement for Clifford Circuit Synthesis |
| title_sort | harnessing the power of long range entanglement for clifford circuit synthesis |
| topic | Clifford circuits Greenberger–Horne–Zeilinger (GHZ) states long-range entanglement quantum circuit synthesis |
| url | https://ieeexplore.ieee.org/document/10531653/ |
| work_keys_str_mv | AT willersyang harnessingthepoweroflongrangeentanglementforcliffordcircuitsynthesis AT patrickrall harnessingthepoweroflongrangeentanglementforcliffordcircuitsynthesis |