Demonstration of Channel-Optimized Quantum Error Correction on Cloud-Based Quantum Computers

With the introduction of several cloud-based quantum computers, for example, from IBM and Rigetti, there is a growing interest in experimenting with quantum algorithms and protocols on such platforms. We are specifically interested in testing quantum error correction protocols since noise is an important factor that limits their performance. We demonstrate the channel-optimized quantum error correction protocol [R.L. Kosut, A. Shabani, and D.A. Lidar, PRL 100, 020502 (2008)] on the IBM and Rigetti machines. Our goal is to protect quantum states from noise. The noise on the IBM machine is characterized by standard process tomography. The optimal encoding and recovery map are found numerically by solving a bi-convex optimization problem which maximizes the average channel fidelity. We implement the optimal encoding and recovery maps by decomposing them into directly implementable gate operations. This error correction protocol does not require post-selection and is designed specifically for the physically relevant noise to the platform.