** **

**Solid-State Qubits **

**Research will extend spin-based qubits toward greater numbers of coupled qubits, explore a variety of coupling for sensing and qubit coupling, including exchange-only qubits made from three coupled dots, extend control of the nuclear environment, realize spin qubits in predominantly zero-nuclear-spin materials, explore qubits in large spin-orbit systems coupled to small spin-orbit systems using different materials or oriented magnetic fields, and explore dynamical decoupling beyond the single qubit regime. **

*Nuclear environmental control *

In most implementations to date, the dominant source of decoherence of separated spins is hyperfine coupling to host nuclei, which appears as local Zeeman fields about which the separate spin precess.

The hyperfine environment is dynamic, evolving over time scales from microseconds to minutes, and is itself a rich and interesting system related to the so-called central spin problem [1,2]. In the past few years, several experiments have demonstrated control over the nuclear ensemble using single-electron dynamic nuclear polarization (DNP) [3,4]. We plan to extend these studies by creating materials with specific nuclear-spin regions, so that spin information can be intentionally coupled to nuclei, opening the possibility of storing coherent quantum information in nuclear ensembles [5]. Nuclear spin-free materials (Si, C) can be made with specific regions of nuclear spin ½ (respectively ^{29 }Si and ^{13 }C) inserted during growth [6,7].

*Zero-nuclear-spin materials *

Hyperfine coupling can be avoided by using predominantly zero-nuclear-spin materials such as silicon, germanium, or carbon. Holes within the Ge core have a small hyperfine coupling to the ~7% of nonzero-spin nuclei, because hole wave functions vanish at each nucleus. Long coherence lifetimes are anticipated in this system but have not yet been measured. The single nanowire is a good platform to investigate one-dimensional arrays of quantum dots that can be entangled using exchange, and entanglement swapped between neighbors [8].

*Dynamical decoupling *

Rapid dephasing of prepared entangled electrons upon spatial separation, observed in GaAs, ^{13 }C, and InAs spin qubits to occur in under 10 ns, can be recovered using dynamical decoupling schemes that generalize and improve conventional spin echo [9]. Coherence times including dynamical decoupling exceed gate operation time by more than five orders of magnitude. It is not known in general how to interleave decoupling into quantum algorithms, nor is it known how well these schemes work to reduce hyperfine dephasing beyond two electrons. How decoupling can be applied, for instance, in the three-spin exchange-only qubit has not been described theoretically nor attempted experimentally. This straightforward first step will initiate this direction in the Center.

*Multi-particle qubits, and multi-qubit systems *

The simplest realizations of spin qubits are individual electrons. It appears feasible that quantum dots containing tens or hundreds of electrons will function equally well, particularly if interactions are intentionally screened using dielectrics or metallic gates. Moving to higher occupancy qubits will greatly increase yield. This is important because investigating entanglement beyond our present understanding will require more than a few coupled electrons. Progress in device fabrication will require numerical simulation, using multi-electron dots, developing shallow heterostructure materials, growing barriers into nanowires, and automating device tuning.

## References cited:

- A. V. Khaetskii, D. Loss, and L. Glazman,
*Electron spin decoherence in quantum dots due to interaction with nuclei*, Phys. Rev. Lett.**88**, 186802 (2002). - G. Chen, D. L. Bergman, and L. Balents,
*Semiclassical dynamics and long-time asymptotics of the central-spin problem in a quantum dot*, Phys. Rev. B**76**, 045312 (2007). - J. R. Petta, J. M. Taylor, A. C. Johnson, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard,
*Dynamic nuclear polarization with single electron spins*, Phys. Rev. Lett.**100**, 067601 (2008). - S. Foletti, H. Bluhm, D. Mahalu, V. Umansky, and A. Yacoby,
*Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization*, Nature Physics**5**, 903 (2009). - J. M. Taylor, C. M. Marcus, and M. D. Lukin,
*Long-lived memory for mesoscopic quantum bits*, Phys. Rev. Lett.**90**, 206803 (2003). - H. O. H. Churchill, F. Kuemmeth, J. W. Harlow, A. J. Bestwick, E. I. Rashba, K. Flensberg, C. H. Stwertka, T. Taychatanapat, S. K. Watson, C. M. Marcus, Relaxation and Dephasing in a Two-electron 13C Nanotube Double Quantum Dot, Phys. Rev. Lett. 102, 166802 (2009).
- H. O. H. Churchill, A. J. Bestwick, J. W. Harlow, F. Kuemmeth, D. Marcos, C. H. Stwertka, S. K. Watson, C. M. Marcus, Electron-nuclear interaction in 13C nanotube double quantum dots, Nature Physics 5, 321 (2009)
- Y. Hu, F. Kuemmeth, C. M. Lieber, C. M. Marcus, Hole spin relaxation in Ge–Si core–shell nanowire qubits, Nature Nanotechnology 7, 47 (2012).
- H. Bluhm, S. Foletti, I. Neder, M. Rudner, D. Mahalu, V. Umansky, and A. Yacoby,
*Dephasing time of GaAs electron-spin qubits coupled to a nuclear bath exceeding 200 mu s*, Nature Physics**5**, 1 (2010).