Practicality of Spin Chain Wiring in Diamond Quantum Technologies

Abstract

Coupled spin chains are promising candidates for 'wiring up' qubits in solid-state quantum computing (QC). In particular, two nitrogen-vacancy centers in diamond can be connected by a chain of implanted nitrogen impurities; when driven by a suitable global fields the chain can potentially enable quantum state transfer at room temperature. However, our detailed analysis of error effects suggests that foreseeable systems may fall far short of the fidelities required for QC. Fortunately the chain can function in the more modest role as a mediator of noisy entanglement, enabling QC provided that we use subsequent purification. For instance, a chain of 5 spins with inter-spin distances of 10 nm has finite entangling power as long as the T2 time of the spins exceeds 0.55 ms. Moreover we show that re-purposing the chain this way can remove the restriction to nearest-neighbor interactions, so eliminating the need for complicated dynamical decoupling sequences.Spin chains with nearest neighbor XY coupling mediate coherent interactions between distant spin qubits with fixed locations, and can thus serve as channels to transfer quantum information [1][2][3]. An important application would be to interconnect distant sub-registers of parallel parts in a scalable, solid-state quantum computer [4], e.g. in a diamond-based architecture at room temperature [5]. With an observed roomtemperature coherence time of 1.8 ms [6], the electron spin of individual nitrogen-vacancy (NV − ) defects in diamond is a promising candidate for a qubit [7]: Initialisation, coherent manipulation and measurement with nanoscale resolution (∼ 150 nm) have already been experimentally demonstrated using optical techniques under ambient conditions [8]. In addition, the long-lived 15 N nuclear spin (I = 1/2) associated with each NV − center can act as a local, coherent memory, accessible via the hyperfine coupling [9, 10]. A universal set of quantum operations between the nuclear memory spin and the processing electronic spin qubit within each NV − center is available with microwave and radio-frequency pulses [11][12][13]. Two NV − centers with only a small separation (r 10 nm) may be entangled through direct electron spin dipole-dipole coupling as long as a T 2 time on the order of milliseconds can be maintained [14]. However, individual addressability of the NV − center qubits demands larger separations of several tens or hundreds of nanometers [8], and the direct interaction becomes too weak.A recent proposal [15] suggested a chain of N implanted nitrogen impurities (each with a "dark" electronic spin-1/2) as a coherent quantum channel to transfer quantum states between distant NV − centers at room-temperature (see Fig. 1a). Here, the electron spins of the NV − centers and the nitrogen impurities interact with each other through nearest-neighbor dipoledipole coupling [16, 17]. Importantly, the scheme does not require individual control of the chain spins, instead relying on global resonant driving fields to turn the effective Hamiltonian into an XY exc...

Implementation of State Transfer Hamiltonians in Spin Chains with Magnetic Resonance Techniques

“…The transport Hamiltonian (either DQ or XX Hamiltonian) can then be engineered via the multiple-pulse techniques discussed in this chapter, while magnetic resonance control techniques can help in obtaining the desired couplings of the NV centers to the P1 spins (to achieve for example, the weakcoupling regime [152, 166-169, 186, 187]). While dephasing noise limits the transport fidelity [178] material engineering and dynamical decoupling techniques that can increase the coherence time [188,189] by orders of magnitude might make this scheme practical.…”

“…The NV center could be thus at the center of small quantum registers [175,176], where nuclear spins play the role of long-time storage qubits with fast access and control provided by the NV electronic spin. To connect the registers, other spins in the diamond lattice could be used, for example Nitrogen electronic spins [101,177,178]. While Nitrogen implantation can be done with improving precision [179][180][181][182], the Nitrogen to NV conversion is limited, as vacancies need to recombine with single Nitrogens by annealing at high temperature.…”

Smooth optimal control with Floquet theory

“…if dipole-dipole interaction is suppressed because of a large spatial separation of the spins [36]. Nevertheless, an interaction can still be possible by using the indirect coupling via neighboring spins, as proposed for nitrogen-vacancy centers [37,38]. With our method we can create entanglement between the end spins of a spin chain, even if the coupling strengths between the spins are only known up to a certain extent.…”

Robust state transfer with high fidelity in spin-1/2 chains by Lyapunov control

“…Because |0 is the ground state of spin-1/2 chain, and we choose the control Hamiltonian such that the ground state remains unchange in the dynamics, the state transfer mainly focuses on steering the initial state |1 into the target state |λ f . We should point out that the quantum information encoded in the first spin is almost perfectly transferred to the end spin in our system, like the other protocols [4][5][6][7][8][9][10][11][12][13] did for state transfer. The difference is that our resulting state is the eigenstate |λ f rather than the state |M in equation (5).…”

“…It is believed that almost all spins would participate in the dynamics of an unmodulated spin chain [4] due to spin-spin couplings, leading to dispersions of the chain that are harmful for quantum state transfer. Recently, several strategies have been proposed to avoid such dispersions (see, e.g., [5][6][7][8][9][10][11][12][13]). The first approach is mainly based on modulating coupling strengths between nearest neighbors to reduce the effect of dispersion [14][15][16].…”