State of the Art


  • NISQ era (Noisy Intermediate-Scale Quantum Computers) [108]

  • Superconducting qubits: current state of play [R10]
  • Challenges (scale, quality, speed):

    • number of qubits: more qubits on a chip, or “extend quantum systems with quantum optical channels” [M15], see also Entanglement across separate silicon dies [49]

    • quality of qubits: error-rate, coherence time

    • manufacturing: e.g. avoid defects introducting splitting of levels [M33]

    • connectivity of qubits: strong impact on performance, (but simple ladder connectivity may be good enough for current hardware [62] [M24])

    • data I/O: performance of loading classical data, faster read out (measurements) [M24]

    • control electronics: “Reduce the wiring: move the controller to cryogenic temperature (4K) - cryogenic CMOS” [M8]


  • ASM / Machine Instructions
  • currently Variational Quantum Algorithms or Quantum Annealing:
  • Challenges:

    • quantum compiler (LLVM): optimization of qubit usage, “mapping & scheduling” [M8], “randomized compiling” [M13]

    • Error correction

Quantum Advantage

Also refered to as Quantum Supremacy e.g. by Google. The term Quantum Advantage was preferred by IBM.

  • Google’s 2019 Quantum Supremacy claim with 53 qubits [7] for an academic problem.
  • More from Google AI Quantum Research in the dedicated section: Quantum Advantage
  • Estimate of the number of qubits to achieve Quantum Supremacy (2020) [30]

    “An IQP circuit with 208 qubits, a QAOA circuit with 420 qubits, and a boson sampling circuit with 98 photons each would require at least one century to be simulated using a classical simulation algorithm”

  • Focus beyond Quadratic Speedups for Error-Corrected Quantum Advantage (2021) [14]

    “We discuss conditions under which it would be possible for a modest fault-tolerant quantum computer to realize a runtime advantage by executing a quantum algorithm with only a small polynomial speedup over the best classical alternative. […] We conclude that quadratic speedups will not enable quantum advantage on early generations of such fault-tolerant devices unless there is a significant improvement in how we realize quantum error correction.”

  • About quantum chemistry: Gate-count estimates for performing quantum chemistry on small quantum computers? (2014) [131]
  • About quantum machine learning: Quantum advantage in learning from experiments (2022) [65]
  • About optimization problems: Where is the quantum advantage? (2021) [M32]
  • About quantum annealing: When can Quantum Annealing win? [31] (2016), see also State of the art of AQC.
  • About boson sampling: Quantum computational advantage with a programmable photonic processor (2022) [86] (YouTube)

The important questions to investigate:

  • A list of problems solved more efficiently on quantum computers.

  • For what problems can we expect an exponential speedup?

Balanced Opinions

  • “Quantum Computing: A bubble ready to burst?”, Nov-11-2020 [M6],

  • “Will Quantum Computing ever live up to its hype?”, Apr-20-2021 [M17]

  • “Quantum computing has a hype problem”, Mar-28-2022 [M12]

  • “Quantum Computing will change our lives. But be patient, please”, Dec-14-2022, [M36]

Further readings

  • “Status of quantum computer development” by the German Federal Office for Information Security [M42]