Manipulating a qubit through the backaction of sequential partial measurements and real-time feedback

Journal name:
Nature Physics
Volume:
10,
Pages:
189–193
Year published:
DOI:
doi:10.1038/nphys2881
Received
Accepted
Published online

Quantum measurements not only extract information from a system but also alter its state. Although the outcome of the measurement is probabilistic, the backaction imparted on the measured system is accurately described by quantum theory1, 2, 3. Therefore, quantum measurements can be exploited for manipulating quantum systems without the need for control fields4, 5, 6. We demonstrate measurement-only state manipulation on a nuclear spin qubit in diamond by adaptive partial measurements. We implement the partial measurement via tunable correlation with an electron ancilla qubit and subsequent ancilla readout7, 8. We vary the measurement strength to observe controlled wavefunction collapse and find post-selected quantum weak values8, 9, 10. By combining a novel quantum non-demolition readout on the ancilla with real-time adaptation of the measurement strength we realize steering of the nuclear spin to a target state by measurements alone. Besides being of fundamental interest, adaptive measurements can improve metrology applications11, 12, 13 and are key to measurement-based quantum computing14, 15.

At a glance

Figures

  1. Partial measurement of a spin qubit in diamond.
    Figure 1: Partial measurement of a spin qubit in diamond.

    a, The nitrogen vacancy centre is a natural two-qubit system where the system qubit is defined by the 14N nuclear spin and the ancilla qubit is defined by the electron spin. A solid immersion lens is deterministically fabricated on top of the selected nitrogen vacancy centre to increase the photon collection efficiency. Control fields for single qubit rotations are generated by applying a current to the gold stripline (yellow). b, A tunable strength measurement is implemented by a Ramsey-type gate on the ancilla. We plot the probability of measuring the state |0right fence for the ancilla, as a function of interaction time τ, for two system input states |right fence (red) and |right fence (blue). The Bloch spheres show the state of the system (purple) and ancilla (orange) after the entangling gate for the different input states (red and blue vectors). The colour bar represents the measurement strength, proportional to sin(θ), where θ=Aτ/2. Blue corresponds to a projective measurement and white to no measurement. Solid lines are a fit to the function y0+e−(τ/T2) 2 cos(Aτ+δ). From the phase offset δ we find the weakest measurement we can perform, corresponding to θ =5°. This is limited by free evolution of the ancilla during the pulses (see Supplementary Information). Error bars depict 68% confidence intervals. Sample size is 500 for each data point.

  2. Measurement backaction and quantum weak value.
    Figure 2: Measurement backaction and quantum weak value.

    a, We prepare an initial state of the system (|right fence,|xright fence and|yright fence), perform a partial measurement with strength θ, and characterize the measurement backaction on the system by quantum state tomography. Quantum state tomography is implemented by an ancilla-assisted projective measurement, performed with the same protocol, setting τ=229s for θ=90°. The nuclear spin basis rotation is performed with a π/2 radio-frequency pulse (along either x or y). The basis rotation pulse for the tomography is applied before the readout of the ancilla, to avoid the dephasing induced by the state-characterization measurement (see main text). The data is corrected for errors in the readout and initialization of the system qubit, both of which are obtained from independent measurements (see Supplementary Information). b,c, Measurement backaction for a partial measurement of increasing strength, independent of the measurement result for the ancilla qubit (b), or conditioned on the ancilla in |0right fence (c). d, Measurement of a generalized weak value for the nuclear-spin qubit, performed by a partial measurement of strength θ, followed by a strong measurement and post-selection of the state |right fence, as a function of the basis rotation angle ϕ of the strong measurement. Solid lines are simulations using independently determined parameters. The asymmetry in the curve can be explained by asymmetric nuclear spin flips arising during ancilla initialization by optical excitation of the forbidden transition of Ey (see Supplementary Information). Inset: the generalized weak value as a function of the strength θ of the partial measurement, setting the basis rotation angle of the strong measurement to the optimal value ϕ=π/2 − θ. All error bars depict 68% confidence intervals. The sample size varies per data point because each data point has a different post-selection criterion.

  3. Quantum non-demolition measurement of the ancilla and system qubit coherence during readout.
    Figure 3: Quantum non-demolition measurement of the ancilla and system qubit coherence during readout.

    a, The ancilla is initialized in |0right fence (|1right fence) by optically pumping the A2(Ey) transition. The ancilla is then read out by exciting the Ey transition for 100μs (conventional readout), or until a photon is detected (dynamical-stop readout). Finally, we verify the post-measurement state with a conventional readout. b, Fidelity of the post-measurement state of the ancilla for conventional readout (left graph) and dynamical-stop readout (right graph). Results are corrected for the infidelity in the final readout. c, Coherence of the system qubit state after ancilla readout. For the dynamical-stop protocol we define ancilla readout time as the predetermined maximum readout time. The graph shows the fidelity of the system with respect to |xright fence for conventional readout (red) and dynamical-stop readout (blue). The z-component of the system is unaffected, as shown by the constant fidelity with respect to |right fence (grey). All error bars depict 68% confidence intervals. Sample size per data point is 5,000 in b and 2,000 in c.

  4. Manipulation of a nuclear spin state by sequential partial adaptive measurements with real-time feedback.
    Figure 4: Manipulation of a nuclear spin state by sequential partial adaptive measurements with real-time feedback.

    a, Real-time adaptive measurement protocol. The ancilla qubit is initialized in |0right fence and the system qubit is prepared in |xright fence. The strength of the second measurement (θ2) is adjusted according to the outcome of the first measurement. The system is analysed by state tomography at each intermediate step. The result of the tomography is plotted on the Bloch spheres (blue vector) and compared with the ideal case (grey vector). b, Fidelity of the output state with respect to the target state as a function of ancilla readout time (dynamical-stop readout) with feedback (only the cases where the protocol heralds success). Upper panel: The grey line is obtained by performing one measurement and adding negative results to artificially increase the success probability to that of the adaptive protocol (red line in lower panel). In the lower panel we show the probability that the protocol heralds success for one measurement and for the adaptive protocol. Error bars depict 68% confidence intervals. The protocol is repeated 500 times for each step in the tomography.

References

  1. Guerlin, C.et al. Progressive field-state collapse and quantum non-demolition photon counting. Nature 448, 889893 (2007).
  2. Hatridge, M.et al. Quantum back-action of an individual variable-strength measurement. Science 339, 178181 (2013).
  3. Murch, K. W.et al. Observing single quantum trajectories of a superconducting quantum bit. Nature 502, 211214 (2013).
  4. Jordan, A. N. & Korotkov, A. N. Qubit feedback and control with kicked quantum nondemolition measurements: A quantum Bayesian approach. Phys. Rev. B 74, 085307 (2006).
  5. Ashhab, S. & Nori, F. Control-free control: Manipulating a quantum system using only a limited set of measurements. Phys. Rev. A 82, 062103 (2010).
  6. Wiseman, H. M. Quantum control: Squinting at quantum systems. Nature 470, 178179 (2010).
  7. Brun, T. A., Diosi, L. & Strunz, W.T. Test of weak measurement on a two- or three-qubit computer. Phys. Rev. A 77, 032101 (2008).
  8. Groen, J. P.et al. Partial-measurement backaction and non-classical weak values in a superconducting circuit. Phys. Rev. Lett. 111, 090506 (2013).
  9. Aharonov, Y., Albert, D. Z. & Vaidman, L. How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. Phys. Rev. Lett. 60, 1351 (1988).
  10. Pryde, G. J.et al. Measurement of quantum weak values of photon polarization. Phys. Rev. Lett. 94, 220405 (2005).
  11. Cappellaro, P.et al. Spin-bath narrowing with adaptive parameter estimation. Phys. Rev. A 85, 030301(R) (2012).
  12. Higgins, B. L.et al. Entanglement-free Heisenberg-limited phase estimation. Nature 450, 393396 (2007).
  13. Napolitano, M.et al. Interaction-based quantum metrology showing scaling beyond the Heisenberg limit. Nature 471, 486489 (2011).
  14. Raussendorf, R. & Briegel, H. J. A one-way quantum computer. Phys. Rev. Lett. 86, 51885191 (2001).
  15. Prevedel, R.et al. High-speed linear optics quantum computing using active feed-forward. Nature 445, 6569 (2007).
  16. Robledo, L.et al. High-fidelity projective read-out of a solid-state spin quantum register. Nature 477, 574578 (2011).
  17. Pfaff, W.et al. Demonstration of entanglement-by-measurement of solid-state qubits. Nature Phys. 9, 2933 (2013).
  18. Ristè, Det al. Deterministic entanglement of superconducting qubits by parity measurement and feedback. Nature 502, 350354 (2013).
  19. Chiaverini, J.et al. Realization of quantum error correction. Nature 432, 602605 (2004).
  20. Gillett, G. C.et al. Experimental feedback control of quantum systems using weak measurements. Phys. Rev. Lett. 104, 080503 (2010).
  21. Sayrin, C.et al. Real-time quantum feedback prepares and stabilizes photon number states. Nature 477, 7377 (2011).
  22. Vijay, R.et al. Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback. Nature 490, 7780 (2012).
  23. Dressel, J., Agarwal, S. & Jordan, A. N. Contextual values of observables in quantum measurements. Phys. Rev. Lett. 104, 240401 (2010).
  24. Williams, N. S. & Jordan, A. N. Weak values and the Leggett–Garg inequality in solid-state qubits. Phys. Rev. Lett. 100, 026804 (2008).
  25. Jiang, L.et al. Coherence of an optically illuminated single nuclear spin qubit. Phys. Rev. Lett. 100, 073001 (2008).
  26. Zhao, N.et al. Sensing single remote nuclear spins. Nature Nanotech. 7, 657662 (2012).
  27. Taminiau, T.H.et al. Detection and control of individual nuclear spins using a weakly coupled electron spin. Phys. Rev. Lett. 109, 137602 (2012).
  28. Kolkowitz, S.et al. Sensing distant nuclear spins with a single electron spin. Phys. Rev. Lett. 109, 137601 (2012).
  29. Bernien, H.et al. Heralded entanglement between solid-state qubits separated by three meters. Nature 497, 86 (2013).
  30. Dolde, F.et al. Room-temperature entanglement between single defect spins in diamond. Nature Phys. 9, 139143 (2013).

Download references

Author information

  1. These authors contributed equally to this work.

    • M. S. Blok

Affiliations

  1. Kavli Institute of Nanoscience Delft, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands

    • M. S. Blok,
    • C. Bonato &
    • R. Hanson
  2. Element Six Ltd, Kings Ride Park, Ascot, Berkshire SL5 8BP, UK

    • M. L. Markham &
    • D. J. Twitchen
  3. Ames Laboratory and Iowa State University, Ames, Iowa 50011, USA

    • V. V. Dobrovitski

Contributions

M.S.B., C.B., V.V.D. and R.H. designed the experiment. M.S.B. and C.B. performed the experiments and analysed the results. M.L.M. and D.J.T. designed and carried out synthesis of (111) engineered chemical vapour deposition diamond material. M.S.B., C.B. and R.H. wrote the manuscript. All authors discussed the results and commented on the manuscript.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Supplementary information

PDF files

  1. Supplementary Information (1291KB)

    Supplementary Information

Additional data