Scalable, High-Speed Measurement-Based Quantum Computer Using Trapped Ions

We describe a scalable, high-speed, and robust architecture for measurement-based quantum computing with trapped ions. Measurement-based architectures offer a way to speed up operation of a quantum computer significantly by parallelizing the slow entangling operations and transferring the speed requirement to fast measurement of qubits. We show that a 3D cluster state suitable for fault-tolerant measurement-based quantum computing can be implemented on a 2D array of ion traps. We propose the projective measurement of ions via multiphoton photoionization for nanosecond operation and discuss the viability of such a scheme for Ca ions.

Figure 1

(a) Hexagonal ion-trap architecture with 120° junctions. Single channel electron multiplier (CEM) detectors for high-efficiency electron detection are indicated. For entangling operations, atoms can be shuttled into close proximity with high fidelity to remain in the ground state. To entangle non-nearest-neighbor atoms, one atom could be moved out of the way as indicated by arrows. Alternatively, swap operations between qubits at a junction could minimize movement of atoms. (b) Underlying hexagonal array and resulting cluster states for non-nearest-neighbor interactions. The hexagonal array is decomposed into two rhombic lattices (red solid and blue dashed lines show the edges of the cluster state layers). Each lattice can again be broken down into further sublattices. For example, 4 sublattices of the solid line rhombic lattice are indicated by circles, squares, triangles, and diamonds. These, together with 4 sublattices of the dashed rhombic lattice, can create an eight-layer 3D cluster state (see text for details). Qubits belonging to the eight different layers are numbered from 1 to 8.

Figure 2

Relevant levels for ionization-readout scheme of the (a) $S$ state and (b) $D$ state in ${}^{43}\mathrm{Ca}^{+}$. Contributing transitions are shown with black arrows. The ionization threshold at 11.87 eV is indicated as thick solid line.

Figure 3

(a)–(c) Time evolution of the emitted electron wave packet in the ion-trap saddle potential at three different times, (a) 0.25 ns, (b) 1.0 ns, (c) 1.5 ns. We assume an initial 4-photon kick of the electrons in the positive $x$ direction. (d) If we place one detector $30\mu \mathrm{m}$ away on the $x$ axis, we can detect the electron with up to 90% fidelity [see dashed line in (d)]. A second detector can be placed on the negative $x$ axis to detect the part of the wave packet that escaped along the saddle in this direction. The detection efficiency is then above 99% within a 3 ns time window [solid line in (d)].