Quantum Computing in the NISQ era and beyond

I’ve already emphasized repeatedly that it will probably be a long time before we have fault-tolerant quantum computers solving hard problems. Nevertheless, we can make significant progress in the near term by developing better methods and hardware for implementing quantum error correction, guided by relatively small-scale experiments with quantum error-correcting codes. We expect that, in the next few years, enhanced control of an error-corrected qubit will be demonstrated convincingly in the lab for the first time. Further near-term experiments exploring quantum error correction are bound to advance our understanding of noise in quantum devices, and to suggest more effective techniques for noise mitigation [53, 54] and device validation [55].

Nevertheless, solving really hard problems (like factoring numbers which are thousands of bits long) using fault-tolerant quantum computing is not likely to happen for a while, because of the large number of physical qubits needed. To run algorithms involving thousands of protected qubits we’ll need a number of physical qubits which is in the millions, or more [56]. That’s a very large leap from where we will be for the next few years, with of order a hundred qubits. Crossing the “quantum chasm,” from hundreds of physical qubits to millions of physical qubits, is going to take some time, but we’ll get there eventually.

Throughout the NISQ era it will remain important to strive for lower gate error rates in the various quantum platforms. With more accurate quantum gates, quantum computers operating without error correction will be able to go further by executing larger circuits. Better gates will also lower the overhead cost of doing quantum error correction when we eventually move on to fault-tolerant quantum computing in the future. (Microsoft’s current program [57], focused on advancing topological quantum computing, is founded on the notion that much lower gate error rates will pay offhandsomely sometime in the

14 future.)

It is important to realize that we will need significant advances — in basic science as well as in systems engineering — to attain fully scalable fault-tolerant quantum computers. Therefore, the challenge of scalability poses compelling problems for scientists and engineers. Because we still have so far to go, new insights, developments, and innovations have the potential to substantially alter the long-term outlook.