Quantum computing with superconducting circuits in the picosecond regime

TL;DR

This paper demonstrates that superconducting quantum circuits can achieve ultrafast quantum gates in the picosecond regime, enabling rapid quantum algorithms with minimal errors, thus significantly surpassing current state-of-the-art speeds.

Contribution

It establishes a fundamental speed limit for superconducting qubit gates based on nonlinearity and shows practical implementation of sub-100 picosecond gates with low errors.

Findings

Elementary gates can be performed in about 100 ps with errors below 10^-4.

A simplified Shor's algorithm can be executed in approximately 1 ns.

Superconducting circuits can be sped up by a factor of 100 compared to current technologies.

Abstract

We discuss the realization of a universal set of ultrafast single- and two-qubit operations with superconducting quantum circuits and investigate the most relevant physical and technical limitations that arise when pushing for faster and faster gates. With the help of numerical optimization techniques, we establish a fundamental bound on the minimal gate time, which is determined independently of the qubit design solely by its nonlinearity. In addition, important practical restrictions arise from the finite qubit transition frequency and the limited bandwidth of the control pulses. We show that for highly anharmonic flux qubits and commercially available control electronics, elementary single- and two-qubit operations can be implemented in about 100 picoseconds with residual gate errors below $10^{-4}$. Under the same conditions, we simulate the complete execution of a compressed version of Shor's algorithm for factoring the number 15 in about one nanosecond. These results demonstrate that compared to state-of-the-art implementations with transmon qubits, a hundredfold increase in the speed of gate operations with superconducting circuits is still feasible.