# State of the Art¶

## Hardware¶

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]

## Software¶

- ASM / Machine Instructions
- currently
*Variational Quantum Algorithms*or*Quantum Annealing*:see Algorithms, also Quantum Approximate Optimization in QAOA.

Challenges:

## 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 annealing**: When can Quantum Annealing win? [31] (2016), see also State of the art of AQC.

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]