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Ancilla-error-transparent swap tests in circuit quantum electrodynamics
- 1. Ancilla-error-transparent swap tests in circuit quantum electrodynamics Ondřej Černotík Department of Optics, Palacký University Olomouc Department of Condensed Matter Physics, Charles University, 27 May 2021
- 2. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ Superconducting circuits are the workhorse of quantum computing. 2 IBM Research Google
- 3. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ Superconducting quantum bits are enabled by the nonlinearity of the Josephson junction. 3 A. Blais et al., RMP 93, 025005 (2021)
- 4. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ Losses and noise can be combatted using quantum error correction. 4 C. K. Andersen et al., Nat. Phys. 16, 875 (2020) Z. Chen et al., arXiv:2102.06132 (2021)
- 5. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ Alternatively, qubits can be encoded into harmonic oscillators. 5 A. Joshi et al., QST 6, 033001 (2021) |0L⟩ = ∑ n cn |n⟩ |1L⟩ = ∑ n dn |n⟩ ⟨0L |1L⟩ = ⟨0L |a† a|1L⟩ = 0
- 6. Swap gates Swap tests Kerr-cat qubits
- 7. Kerr-cat qubits
- 8. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ Coherent states can be used to encode quantum information. 8 a|α⟩ = α|α⟩ a| − α⟩ = − α| − α⟩ |0L⟩ = |α⟩ |1L⟩ = | − α⟩ Protected against bit fl ips Amplitude damping
- 9. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ Kerr nonlinearity and two-photon driving stabilise a cat qubit. 9 H = − Ka†2 a2 + ϵ(a2 + a†2 ) = − K(a†2 − α2 )(a2 − α2 ) + Kα4 α = ϵ/K A. Grimm et al., Nature 584, 205 (2020) S. Puri et al., PRX 9, 041009 (2019)
- 10. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ The noise of a Kerr-cat qubit is biased towards phase fl ips. 10 Photon loss → phase fl ips κα2 S. Puri et al., PRX 9, 041009 (2019) S. Puri et al., Sci. Adv. 6, eaay5901 (2020) Photon gain → phase fl ips Photon gain → leakage Photon gain → bit fl ips ∼ exp(−α2 )
- 11. Swap gates
- 12. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ Swap gates are important non-Clifford gates for bosonic qubits. 12 H.-K. Lau and A. A. Clerk, PRL 117, 100501 (2016) Controlled-swap gate |0⟩⟨0| ⊗ I + |1⟩⟨1| ⊗ S Exponential-swap gate exp(iθS) = cos θ I + i sin θ S S|ϕ⟩|ψ⟩ = |ψ⟩|ϕ⟩
- 13. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ Bosonic swap gates have been implemented but with limited quality. 13 Y. Y. Gao et al., Nature 566, 509 (2019)
- 14. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ A controlled-phase beam splitter can be implemented with a Kerr-cat ancilla. 14 Hint = − ζ(a† bc† + ab† c) ≃ ∓ ζα(a† b + ab† ) |0L⟩⟨0L | ⊗ U† BS + |1L⟩⟨1L | ⊗ UBS ωa ωb ωc −ωa + ωb − ωc
- 15. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ A controlled beam splitter can be turned into a controlled- swap gate. 15 ωa ωb −ωa + ωb + +|1L⟩⟨1L | ⊗ U2 BS |0L⟩⟨0L | ⊗ I ωa ωb ωc −ωa + ωb − ωc
- 16. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ The full system contains additional interactions and imperfections. 16 H = − Kc†2 c2 + ϵ(c†2 + c2 ) − χ(a† a + b† b − N)(c† c − α2 ) +ζ1(t)(a† b + b† a) − ζ2(t)(a† bc† + ab† c) + losses and thermal noise of the Kerr-cat qubit CPBS BS Free evolution
- 17. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ The full system contains additional interactions and imperfections. 17 CPBS BS Free evolution
- 18. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ The controlled-swap gate inherits the Kerr cat's noise bias. 18 Z error non-Z error
- 19. Swap tests | + ⟩ = |0⟩ + |1⟩ X
- 20. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ A swap test is an important protocol in quantum information science. 20 | + ⟩ = |0⟩ + |1⟩ X R. Filip, PRA 65, 062320 (2002) overlap measurement state puri fi cation purity estimation entanglement witness P± = 1 2 (I ± S) Projection onto (anti-)symmetric space
- 21. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ Swap test performance suffers from ancilla errors. 21 Phase fl ips: incorrect result Solution: repeated swap test | + ⟩ | − ⟩ | + ⟩ Z (I + S)ρ(I + S) ρ Bit fl ips: imperfect swap X ≠ (I + S)ρ(I + S) | + ⟩
- 22. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ Swap tests can be used for precise phase estimation. 22 |n⟩ |0⟩ |n⟩|0⟩ − |0⟩|n⟩ e−inφ |n⟩|0⟩ − |0⟩|n⟩ Δ = p+ − p− = − cos(nφ)
- 23. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ High sensitivity is possible also with classical input states. 23 Input states: |α⟩, | − α⟩ |α⟩, |0⟩
- 24. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ Kerr-cat qubits open new paths in quantum optics and quantum information. 24 Noise bias Ef fi cient quantum gates | + ⟩ = |0⟩ + |1⟩ X Low-noise swap tests
- 25. Ondrej Cernotík (UP Olomouc): Ancilla-error-transparent swap tests in circuit quantum electrodynamics ˇ ˇ 25 UP Olomouc Iivari Pietikäinen Radim Filip Yale Quantum Institute Shruti Puri Steven M. Girvin Funding