Precisely Timing Dissipative Quantum Information Processing

Dissipative engineering constitutes a framework within which quantum information processing protocols are powered by system-environment interaction rather than by unitary dynamics alone. This framework embraces noise as a resource and, consequently, offers a number of advantages compared to one based on unitary dynamics alone, e.g., that the protocols are typically independent of the initial state of the system. However, the time independent nature of this scheme makes it difficult to imagine precisely timed sequential operations, conditional measurements, or error correction. In this work, we provide a path around these challenges, by introducing basic dissipative gadgets which allow us to precisely initiate, trigger, and time dissipative operations while keeping the system Liouvillian time independent. These gadgets open up novel perspectives for thinking of timed dissipative quantum information processing. As an example, we sketch how measurement-based computation can be simulated in the dissipative setting.

Figure 1

(a) Depiction of an initialization gadget. The central circle depicts the target qubit, the outer circles the auxiliary qubits. The full red lines connecting the timer qubit to the auxiliary ones illustrate the conditional state preparation local Liouvillians ${\mathcal{L}}_j^{\mathrm{cp}}$, and the dotted circles around the auxiliary qubits illustrate unconditional amplitude damping Liouvillians ${\mathcal{L}}_j^{\mathrm{ad}}$; i.e., ${\mathcal{L}}^{\mathrm{ini}}={\mathcal{L}}^{\mathrm{cp}}+{\mathcal{L}}^{\mathrm{ad}}$. (b) Depiction of the linear timer gadget. The circles represent the timer qubits, the lines connecting the timer qubits are the local Liouvillians ${\mathcal{L}}_j^{\mathrm{cut}}$, and the boxes illustrate the initialization devices from (a).