Quantum computing Supremacy is when quantum computers perform computational tasks beyond the capabilities of classical (regular) computers for a significant range of important problems.

There are also some proposed technical metrics using cross entropy

*A critical question for the field of quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond the capabilities of state-of-the-art classical computers, achieving so-called quantum supremacy. We study the task of sampling from the output distributions of (pseudo-)random quantum circuits, a natural task for benchmarking quantum computers. Crucially, sampling this distribution classically requires a direct numerical simulation of the circuit, with computational cost exponential in the number of qubits. This requirement is typical of chaotic systems. We extend previous results in computational complexity to argue more formally that this sampling task must take exponential time in a classical computer. We study the convergence to the chaotic regime using extensive supercomputer simulations, modeling circuits with up to 42 qubits – the largest quantum circuits simulated to date for a computational task that approaches quantum supremacy. We argue that while chaotic states are extremely sensitive to errors, quantum supremacy can be achieved in the near-term with approximately fifty superconducting qubits. We introduce cross entropy as a useful benchmark of quantum circuits which approximates the circuit fidelity. We show that the cross entropy can be efficiently measured when circuit simulations are available. Beyond the classically tractable regime, the cross entropy can be extrapolated and compared with theoretical estimates of circuit fidelity to define a practical quantum supremacy test.*

1. Dwave Systems (has a 2000 qubit system superconducting quantum annealing system)

Dwave’s next chip will revamp their design. Dwave will likely try to address aspects of qubit coherence time and perhaps error correction to match the competing chips from Rigetti, Google and IBM.

2. Rigetti computing is currently testing a three-qubit chip made using aluminum circuits on a silicon wafer, and the design due next year should have 40 qubits. Rigetti says that’s possible thanks to design software his company has created that reduces the number of prototypes that will need to be built on the way to a final design. Versions with 100 or more qubits would be able to improve on ordinary computers when it comes to chemistry simulations and machine learning.

Chad Rigetti was Technical Lead for 3-D quantum computing at IBM Research. He has been building prototype quantum processors for 12+ years. At Yale, he developed the first all-microwave control methods for superconducting qubits, and at IBM built qubits with world-record performance.

3. John Martinis leads the quantum computing research group at the University of California, Santa Barbara He was hired by Google in June 2014 after persuading the company that his team’s technology could mature rapidly with the right support. Google’s project estimates that Martinis’s group can make a quantum annealer with 100 qubits as soon as 2017.

The coherence time of Martinis/Google’s qubits, or the length of time they can maintain a superposition, is tens of microseconds—about 10,000 times the figure for those on D-Wave’s chip.

Using the 49th most powerful computer in the world, the US National Energy Research Scientific Computing Center’s Edison, Google simulated the behaviour of quantum circuits on larger and larger grids of qubits, up to a 6 × 7 grid of 42 qubits.

Computing these grids grows exponentially in memory requirements as grids get bigger – a 6 × 4 grid needs just 268 megabytes, while the 6 × 7 grid requires 70 terabytes. A 48-qubit grid would have required 2.252 petabytes of memory, nearly double that of the most powerful computer in the world.

This is the problem Google hopes to solve with a 50 qubit quantum computer. Scalable quantum computers will see improvements of thousands of times or more per year in speed. Thus quantum computing will achieve dominance over classical computers and then never give up that dominance.

After that, the plan is to grow the number of qubits the computer can handle. “It’s absolutely progress to building a fully scalable machine,” Ian Walmsley at the University of Oxford said.

4. IBM is also developing more stable superconducting quantum qubits.

**Quantum computing applications**

D-Wave has begun to work with Investment managers on the related problem of designing portfolios. In order to generate the maximum returns for a given risk profile, a fund manager needs to not only choose among the thousands of available securities, but also minimize transaction costs by achieving the most optimal portfolio in the minimum number of trades.

In each case, D-Wave’s quantum systems allow us to swallow complexity whole, rather than using shortcuts that reduce efficiency. Jeremy Hilton, Senior Vice President, Systems, at D-Wave says “Complex processes are all around us. By using quantum computing to operate them more effectively, we can make just about everything we do run more smoothly.”

Scientists at Harvard have found that quantum computers will allow us to map proteins much as we do genes today. D-Wave has also formed a partnership with DNA-SEQ to use its quantum computers to explore how to analyze entire genomes to create more effective therapies.

Mapping the human genome was a triumph of technology as much as it was an achievement in biology. It was, essentially, more powerful computers that allowed us to map human DNA . However, if we are to advance further, quantum systems will likely be a big part of the answer.

Rigetti cites the Haber-Bosch process, used to manufacture ammonia for fertilizer production, which has been estimated to consume 2 percent of the world’s energy. Devising a more efficient catalyst for the reaction could be extremely valuable.

Rigetti aims to ultimately set up a kind of quantum-powered cloud computing service, where customers pay to run problems on the company’s superconducting chips.

Quantum computing can provide a major acceleration to the improvement and capabilities in machine learning.

Quantum computing will help in all areas where complexity and large search domains are slowing progress. This includes finding new materials and making systems more efficient.

SOURCES- Forbes, Rigetti, Dwave Systems, IBM, Technology review, google