Recently there has been increased efforts to build large-scale quantum computers for solving certain types of hard computational problems. These efforts are mainly motivated by the prospect of enabling quantum algorithms with a quadratic, polynomial or potentially exponential speedup. When the size of the problem is sufficiently large, this scaling advantage implies that a quantum computer will outperform its classical counterpart, independently of the time it takes to execute a single gate. However, for any real-world application, not only the scaling but also the

total computation time will be of importance, hence the realization of faster gate operations becomes a necessity to further improve the fidelity of the computation.

In the work we highlight today, the authors discuss the realization of a universal set of ultrafast single- and two-qubit operations with superconducting quantum circuits along with investigating the physical and technical limitations for achieving faster gates. The work establishes a fundamental bound on the minimal gate time, which depends on the qubit nonlinearity and bandwidth of the control pulse over a large parameter range, being independent of the qubit design. The numerical results suggest 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, authors estimate that the complete execution of a compressed version of Shor’s algorithm for factoring the number 15 would take about one nanosecond on such a hypothetical device.

The numerical results claim that there exists a lower bound for both single-qubit gates and two-qubit gates, which holds without the often assumed three-level approximation for the whole range of qubit parameters explored in this work. For very fast gates in the range of hundred picoseconds, additional limitations arise from the finite qubit oscillation time.

The authors also addressed the implementation of larger quantum circuits composed out of many ultrafast gates. A full multi-level simulation of a basic three-qubit circuit consisting of eleven elementary single- and two-qubit gates is performed taking the finite qubit rotation time into account which introduces a natural cycle time according to which gates must be clocked. For realistic qubit nonlinearities and control bandwidths, the simulated execution times for the whole circuit are observed to be about 1-2 ns, which is about two orders of magnitude faster than what is achievable in most superconducting quantum computing experiments today. The results demonstrate that significant improvements in this direction are still possible.

In their analysis, the authors have restricted the gate times down to about 50 picoseconds, which requires absolute nonlinearities and larger control bandwidth than contemporary state-of-the-art experiments. Although such parameters are highly non-standard for current superconducting qubit experiments, they are still within physical and technological bounds. For the implementation of even faster gates, additional physical constraints will come into play and also the applicability of the usual effective circuit model must be re-evaluated. For example, at a certain value, the energy of the third circuit level is comparable to twice the superconducting gap of aluminum. Any components of the control field above this frequency will excite quasiparticles and strongly degrade the qubit coherence. However, in other materials the superconducting gap can be substantially higher, which suggests that at least in principle, gate times in the range of 1-10 picoseconds could become accessible in the future.

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. Despite its long-term relevance, the implementation of quantum gates in the picosecond regime still remains highly unexplored and the ultimate limit for the speed of superconducting quantum processors is still a research question to be addressed with a hope for pushing towards faster gates. In such a scenario, decoherence will be a less limiting factor, since gates will take less time to be applied. Furthermore, algorithms that require a large circuit depth will be able to be implemented, allowing researchers to solve more complex problems. Finally, processes like quantum error correction and decoding of errors will be much easier to implement, therefore taking us beyond the NISQ era.

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