Deterministic Bethe state preparation
We present an explicit quantum circuit that prepares an arbitrary $U(1)$-eigenstate on a quantum computer, including the exact eigenstates of the spin-$1/2 XXZ$ quantum spin chain with either open or closed boundary conditions. The algorithm is deterministic, does not require ancillary qubits, and d...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2024-10-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2024-10-24-1510/pdf/ |
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| author | David Raveh Rafael I. Nepomechie |
| author_facet | David Raveh Rafael I. Nepomechie |
| author_sort | David Raveh |
| collection | DOAJ |
| description | We present an explicit quantum circuit that prepares an arbitrary $U(1)$-eigenstate on a quantum computer, including the exact eigenstates of the spin-$1/2 XXZ$ quantum spin chain with either open or closed boundary conditions. The algorithm is deterministic, does not require ancillary qubits, and does not require QR decompositions. The circuit prepares such an $L$-qubit state with $M$ down-spins using $\binom{L}{M}-1$ multi-controlled rotation gates and $2M(L-M)$ CNOT-gates. |
| format | Article |
| id | doaj-art-7ec6e6a3650447bebf6bdfd5536edabc |
| institution | DOAJ |
| issn | 2521-327X |
| language | English |
| publishDate | 2024-10-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-7ec6e6a3650447bebf6bdfd5536edabc2025-08-20T02:40:27ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2024-10-018151010.22331/q-2024-10-24-151010.22331/q-2024-10-24-1510Deterministic Bethe state preparationDavid RavehRafael I. NepomechieWe present an explicit quantum circuit that prepares an arbitrary $U(1)$-eigenstate on a quantum computer, including the exact eigenstates of the spin-$1/2 XXZ$ quantum spin chain with either open or closed boundary conditions. The algorithm is deterministic, does not require ancillary qubits, and does not require QR decompositions. The circuit prepares such an $L$-qubit state with $M$ down-spins using $\binom{L}{M}-1$ multi-controlled rotation gates and $2M(L-M)$ CNOT-gates.https://quantum-journal.org/papers/q-2024-10-24-1510/pdf/ |
| spellingShingle | David Raveh Rafael I. Nepomechie Deterministic Bethe state preparation Quantum |
| title | Deterministic Bethe state preparation |
| title_full | Deterministic Bethe state preparation |
| title_fullStr | Deterministic Bethe state preparation |
| title_full_unstemmed | Deterministic Bethe state preparation |
| title_short | Deterministic Bethe state preparation |
| title_sort | deterministic bethe state preparation |
| url | https://quantum-journal.org/papers/q-2024-10-24-1510/pdf/ |
| work_keys_str_mv | AT davidraveh deterministicbethestatepreparation AT rafaelinepomechie deterministicbethestatepreparation |