High-fidelity quantum state evolution in imperfect photonic integrated circuits

We propose and analyze the design of a programmable photonic integrated circuit for high-fidelity quantum computation and simulation. We demonstrate that the reconfigurability of our design allows us to overcome two major impediments to quantum optics on a chip: it removes the need for a full fabrication cycle for each experiment and allows for compensation of fabrication errors using numerical optimization techniques. Under a pessimistic fabrication model for the silicon-on-insulator process, we demonstrate a dramatic fidelity improvement for the linear optics controlled-not and controlled-phase gates and, showing the scalability of this approach, the iterative phase estimation algorithm built from individually optimized gates. We also propose and simulate an experiment that the programmability of our system would enable: a statistically robust study of the evolution of entangled photons in disordered quantum walks. Overall, our results suggest that existing fabrication processes are sufficient to build a quantum photonic processor capable of high-fidelity operation.

Figure 1

(a) Schematic of the QPP composed of interconnected MZIs. (b) The six-mode cnot gate proposed in Ref. [16]. (c) The same cnot protocol implemented on the QPP. The upper number in each box represents the splitting ratio $\eta \equiv {sin}^2\left(\theta \right)$, where $\theta$ is the internal phase setting, and the lower number represents the output phase offset $\varphi$. (d) The MZI unit cell. (e) Cross section of the directional coupler showing the dominant mechanisms for disorder in the splitting ratio, variation in the height of the waveguide $h$, the width $w$, and the waveguide spacing $g$. (f) Cross section of the phase shifter illustrating free carrier absorption, the dominant loss mechanism [17].

Figure 2

(a) Performance of the cnot gate for 1000 instances of the QPP. The blue (green) histogram plots the fidelity before (after) optimization of the phase settings. (b) Results pre- and postoptimization for the cphase gate over 300 instances of the QPP. For each simulation, the reported fidelity is the minimum over six different choices of $\varphi$ (the phase applied by the controlled operation), equally distributed from zero to $2\pi$.

Figure 3

(a) Quantum circuit for the IPEA, as outlined in Ref. [35]. (b) The IPEA fidelity with unoptimized (blue) and optimized (green) performance. By optimizing the circuit to account for fabrication imperfections, the QPP enables very high process fidelities. Again, note the logarithmic scaling to capture both unoptimized and optimized performance on the same axes.

Figure 4

Simulation of the DTQRW in the QPP postselected on detecting two photons for various levels of time-dependent (TD) and time-independent (TID) disorder. (a.i)–(e.i) Correlation functions for output waveguide positions in the QPP lattice. (a.ii)–(e.ii) Particle density distributions as a function of waveguide position [same as the last layer of (a.iii)–(e.iii), marked in red]. (d.ii) and (e.ii) have logarithmic scales. (a.iii)–(e.iii) Dynamics of QRW where the $x$ axis and $y$ axis represent the waveguide output position and MZI layer, respectively. (a.i)–(a.iii) Propagation of input state $({|20\rangle }_{\text{LR}}+{|02\rangle }_{\text{LR}})/\sqrt{2}$ revealing bunching effect seen for continuous-time QRWs. (b.i)–(b.iii) A single realization of TID and TD disorder in the QPP resulting in highly irregular propagation. (c.i)–(c.iii) Average of 1000 realizations of weak TID disorder showing the coexistence of bunching and localization. (d.i)–(d.iii) Average of 1000 realizations of TID disorder showing an exponential density distribution—the hallmark of Anderson localization. (e.i)–(e.iii) Average of 1000 realizations of TID and TD disorder, showing delocalization and a Gaussian distribution.