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Bulletin of the American Physical Society

Design and Analysis of Superconducting Qubits for Extensible Surface Coding

Nadia Haider, Stefano Poletto, Alessandro Bruno, David J. Michalak, Román Caudillo, Nandini Muthusubramanian, Ramiro Sagastizabal, Brian Tarasinski, Cornelis Christiaan Bultink, Michiel Adriaan Rol, James S. Clarke, L. DiCarlo

Published Mar 8, 2018• 0 citations
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Quantum error correction (QEC) is the central building block of fault-tolerant quantum computation but the design of QEC codes may not always match the underlying hardware. To tackle the discrepancy between the quantum hardware and QEC codes, we propose a synthesis framework that can implement and optimize the surface code onto superconducting quantum architectures. In particular, we divide the surface code synthesis into three key subroutines. The first two optimize the mapping of data qubits and ancillary qubits including syndrome qubits on the connectivity-constrained superconducting architecture, while the last subroutine optimizes the surface code execution by rescheduling syndrome measurements. Our experiments on mainstream superconducting architectures demonstrate the effectiveness of the proposed synthesis framework. Especially, the surface codes synthesized by the proposed automatic synthesis framework can achieve comparable or even better error correction capability than manually designed QEC codes.
We analytically designed the control bias pulses to realize new multi-qubit parity detector gates for 2-Dimensional (2D) array of superconducting flux qubits with non-tunable couplings. We designed two 5-qubit gates such that the middle qubit is the target qubit and all four coupled neighbors are the control qubits. These new gates detect the parity between two vertically/horizontally coupled neighbor qubits while cancelling out the coupling effect of horizontally/vertically coupled neighbor qubits. For a 3 by 3 array of 9 qubits with non-tunable couplings, we simulated the effect of our new 5-qubit horizontal and vertical parity detector gates. We achieved the intrinsic fidelity of 99.9% for horizontal and vertical parity detector gates. In this paper we realize Surface Code memories based on the multi-qubit parity detector gates for nearest neighbor superconducting flux qubits with and without tunable couplings. However, our scheme is applicable to other superconducting qubits as well. In our proposed memory realization, error correction cycles can be performed in parallel on several logical qubits or even on the entire 2D array of qubits, this makes it a desirable candidate for large scale and longtime quantum computation. In addition to extensive reduction of the number of control parameters in our method, the error correction cycle time is reduced and does not grow by increasing the number of qubits in the logical qubit layout. Another advantage of this approach is that there will not be any dephasing from idle qubits since all the qubits are used in the error correction cycles.
As discussed in previous chapters, the Qiskit Metal framework plays a crucial role in designing superconducting qubits. Moving forward, we will use this framework extensively for simulations, where we’ll need to code specific parameters to generate simulations, matrices, and desired outputs. The framework is built using the Python programming language, and Qiskit Metal supports a Python IDE, which facilitates efficient coding. In this chapter, we will explore how to write Python code to develop superconducting circuits. However, before diving directly into the code for superconducting qubits, it is essential to understand some basic concepts.