Quantum Computing with Incoherent Resources and Quantum Jumps

Spontaneous emission and the inelastic scattering of photons are two natural processes usually associated with decoherence and the reduction in the capacity to process quantum information. Here we show that, when suitably detected, these photons are sufficient to build all the fundamental blocks needed to perform quantum computation in the emitting qubits while protecting them from deleterious dissipative effects. We exemplify this by showing how to efficiently prepare graph states for the implementation of measurement-based quantum computation.

Figure 1

Quantum-jump version of the building blocks for quantum computation. (1) Spontaneous emission (s.e.) is sufficient for measuring in the computational basis. [2(a)] The PBS erases which-process information, and a photon-detection produces a jump proportional to a unitary flip in the emitting qubit. [2(b)] More general rotations can be obtained through homodyne detection schemes [8]. (3) Entangling gates achieved through a second quantum erasing process: the standard balanced BSs erase which-qubit information, and a detection event in one of the available photocounters implements the corresponding maximally entangling operation indicated in the figure.

Figure 2

(a) Each qubit is encoded in the two lower levels $|g⟩$ and $|e⟩$ (corresponding to the logical $|0⟩$ and $|1⟩$) of a discrete emitter. The third level $|h⟩$ is introduced to produce the necessary inelastic scattering that incoherently pumps the qubit back into its excited state $|e⟩$ and complements spontaneous emission in order to generate the building blocks for quantum computation described in Fig. 1. (b) The two decoherence processes in the effective two-level system obtained after adiabatic eliminating level $|h⟩$.

Figure 3

The generation of a multiqubit state equivalent to a linear cluster state can be obtained by concatenating a variant of the entangling gate shown in Fig. 1.3. In (a) only the ${\sigma }_x$ channels are combined at the BS, while the ${\sigma }_y$ channels are detected independently (corresponding to the absence of ${\mathrm{BS}}_y$ in Fig. 1.3). (b) Single quantum trajectory simulation for the evolution of entanglement (given by the $N$ concurrence [34]) for 4 qubits initialized in the ground state. Detection events are marked with diamonds labeled by the corresponding detector. Jumps from combined detectors (blue-filled diamonds) generate entanglement: At $t\approx 0.5/\gamma$ a Bell state between qubits 3 and 4 is formed, and the subsequent jumps at $t\approx 1.16/\gamma$ and $2.7/\gamma$ complete the generation of a four-qubit cluster. Note that the intermediate local jumps change the state of the system but not the entanglement.

Figure 4

Average time for the preparation of a graph state for up to 100 qubits. Simulations used 5000 trajectories and confirm the logarithmic scale with the number of vertices explained in the text.