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Ancilla-error-transparent swap tests in circuit quantum electrodynamics

  1. 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. 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. 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. 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. 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. 6. Swap gates Swap tests Kerr-cat qubits
  7. 7. Kerr-cat qubits
  8. 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. 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. 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. 11. Swap gates
  12. 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. 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. 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. 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. 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. 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. 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. 19. Swap tests | + ⟩ = |0⟩ + |1⟩ X
  20. 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. 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. 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. 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. 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. 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

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