Photonic Architecture for Scalable Quantum Information Processing in Diamond

Physics and information are intimately connected, and the ultimate information processing devices will be those that harness the principles of quantum mechanics. Many physical systems have been identified as candidates for quantum information processing, but none of them are immune from errors. The challenge remains to find a path from the experiments of today to a reliable and scalable quantum computer. Here, we develop an architecture based on a simple module comprising an optical cavity containing a single negatively charged nitrogen vacancy center in diamond. Modules are connected by photons propagating in a fiber-optical network and collectively used to generate a topological cluster state, a robust substrate for quantum information processing. In principle, all processes in the architecture can be deterministic, but current limitations lead to processes that are probabilistic but heralded. We find that the architecture enables large-scale quantum information processing with existing technology.

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An international research effort is being directed at building a large-scale quantum computer to tackle computational tasks currently intractable with classical computers. One of the primary barriers to practical large-scale quantum computation has been finding quantum architectures compatible with current technologies. We propose a quantum architecture based on modules of negatively charged nitrogen-vacancy centers in diamond and show that this architecture is scalable.

Nitrogen-vacancy centers contain intrinsic nuclear and electron spins, which are important for quantum applications. Nuclear “spins” can serve as memory for storing quantum information, while electron spins can be coupled to a photon to promote interactions with distant nitrogen-vacancy centers. Previous experiments have successfully demonstrated that two remote electron spins can be entangled. We propose to use an optical cavity containing one negatively charged nitrogen-vacancy center in diamond and to connect these modules via photons. A scalable two-dimensional array is assembled from modules connected by optical fibers, single-photon detection devices, and control lines. A topological cluster state can be prepared by entangling each physical qubit with four of its nearest neighbors, creating a dagger-shaped cluster state. This fundamental unit is independent of the size of the network, ensuring scalability. The modules enable nondestructive readout by avoiding optical excitation of the centers. This method promises to greatly reduce the occurrence of errors due to spin flips in the optical cycle.

We find that our architecture is broadly consistent with present technology and that it is robust with respect to all known imperfections of the nitrogen-vacancy center. Our modular approach, which does not require extreme cryogenic temperatures, can be used for both computation and communication tasks. We propose that the challenges of time delays induced by increasing communication distances between modules in large arrays can be addressed via the long-lived nuclear-spin memory.

Figure 1

Schematic representation illustrating the module and the entanglement distribution scheme. The module contains an optical cavity with a four-level system. The entanglement distribution scheme is based on a Michelson interferometer where two modules are connected via an optical fiber [7, 8, 44, 46]. A single photon comes in from the right port and is conditionally reflected at each module depending on the state of the emitter. Erasing the path information at the beam splitter followed by detection at the dark port projects the system to the singlet Bell state.

Figure 2

${\mathrm{NV}}^{-}$ center is shown as a definite example of the artificial atom to realize the module. Its energy level structure for a low-temperature, low-strain sample [14, 64] is illustrated in (a). A static magnetic field of approximately 20 mT is used to separate the $m_s=\pm 1$ levels. The ${\mathrm{NV}}^{-}$ center possesses both an electron spin and a ${}^{15}\mathrm{N}$ nuclear spin, which will be used to store and grow a cluster state for quantum information processing. Panel (b) illustrates how the storage of entanglement in the nuclear spins is achieved. The protocol works as a repeat-until-success scheme for entangling the remote electron spins using a single photon–based Michelson interferometer. The successful event is the detection of a photon at the dark port. Once this has been achieved, the electrons are entangled with the nuclear spins followed by measurement of the electron spins to disentangle them. This allows our entanglement of the electron spins to be transferred to the nuclear spins [7]. Otherwise, the electron and nuclear spins will be decoupled completing the entangling cycle, only the electron spin reinitiated, and the protocol started again.

Figure 3

The repeat-until-success protocol is accurately time sequenced. This is required by the nature of the coupling, as entanglement between the electron spin and nuclear spin oscillates. Upon failure, we wait until the $2\pi$ point in the entangling cycle, where the nucleus and electron are decoupled. The nuclear spin is consequently protected from feedback errors through the hyperfine coupling by accurately timing the reinitialization of the electron spins. When the distribution of entanglement between two electrons succeeds, the entanglement bond will be transferred to the nuclear spins by waiting until a $\pi$ point where the electron and nuclear spins are maximally entangled.

Figure 4

Illustration of the sequence of operation to create a cluster state of five nuclear spin qubits. The scheme uses the repeat-until-success approach to create entanglement between two electron spins, before transferring upon success such entanglement to the corresponding nuclear spins.

Figure 5

Three-dimensional topological cluster state and module connectivity in a two-dimensional plane. (a) The topological cluster state cluster is a resource for fault-tolerant quantum computation. However, the whole state is not required at all times during the computation. Instead, only two layers of the cluster state need to be prepared and stored at any given time. (b) The physical unit cell composed of two layers. The back layer contains eight connected qubits arranged in a square (orange), while the front layer has five qubits arranged in a cross (blue). The two layers are connected by controlled-phase gates (green). Measurement of the front layer of the cluster will teleport the current state of the computer to the back layer, at which point the physical qubits we just measured can be reconnected in accordance with the geometry of the cluster state, and the information can be teleported back again. In this way, the two physical layers execute the even and odd temporal steps of the computation, allowing an arbitrarily deep computation to be performed with a fixed number of physical qubits. (c) A compact layout of modules on a two-dimensional plane.

Figure 6

Fault-tolerant thresholds and required component error rates. (a) Numerical simulation of topological error correction [74]. The logical error rate is plotted as a function of the physical error rate for various code sizes (distances $d$), where we assume that all gates and measurements are operating at the same error rate. Each point corresponds to at least $10^4$ trials. The value of the physical error rate at the intersection gives the threshold (in this case, approximately $7.3\times 10^{-3}$). For physical error rates below this threshold, the logical error rate can be reduced arbitrarily by increasing the code distance. (b) The required fidelity (1-error probability) for each physical parameter. In the Supplemental Material [58] details of the error calculations are shown for various physical parameters. The dots on the lines show the current best accuracy reported, all of which already meet the required accuracy, 99.27%. For a realistic implementation, the gate fidelity should be above 99.9%, corresponding to the green region in the plot. Electronic and nuclear spin coherence times are already in this regime, and the remaining parameters may soon meet the desired accuracy given the rapid development of quantum control of such systems. The fidelity does not converge to unity due to imperfections in the ${\mathrm{NV}}^{-}$ center.