Cloud quantum computing on AWS

Some thoughts on Amazon's quantum computing offerings available via AWS, based on a quantum computing workshop I recently attended:

The AWS-Braket library conveniently provides access to three different hardware backends (DWave, Rigetti, IonQ), which each has its own strengths and limitations. 

You can also run two different cloud quantum simulators (SV1 and TN1). SV1 is a state vector simulator (so it runs circuits without any approximation), and can apparently handle up to 24 qubits, which is about double what can be easily done on a standard personal computer. TN1 uses tensor networks to more efficiently simulate certain larger circuits, but it doesn't always work.

Presently the AWS-Braket library only handles circuits defined using the gate model of quantum computation, so there is no ability to control the individual pulses used to implement the gates on the hardware, which are required to perform analog quantum simulation or implement specialised pulse sequences in order to improve the performance of specific circuits. Amazon plans to include this functionality in a later release.

The hardware: the DWave devices have 5760 and 2000 "qubits" (however with limited connectivity, and restricted to quantum annealing), the Rigetti chip has 32 qubits arranged in a quasi-1D geometry, while the IonQ device currently supports 11 qubits, with plans to extend to 32 qubits later this year. This means that one can run circuits that are in principle a real pain to simulate using the best classical computers. However, it's still unclear whether the current levels of device noise and limited qubit connectivity (in the case of the DWave and Rigetti devices) rule out a quantum advantage using these devices.

The catch: running these state-of-the-art devices is expensive! The schedule of prices can be found here: $0.30 per circuit run, plus an additional charge per measurement repetition. How much will this cost the end user? Let's take as a representative example solving the MaxCut problem using the quantum approximate optimization algorithm, taking parameters from a recent proof-of-concept experiment by the Google group. For the simplest implementation of the algorithm, optimization of the two variational parameters to find the optimal solution required ~10 iterations, each comprising 6 energy evaluations with 25,000 shots per energy. Using Rigetti's superconducting chip's fee of $0.00035 per shot, this translates to a total cost of 60*(0.03 + 25000*0.00035) = $527! Larger real world problems will likely require many more iterations in order to converge to good solutions, pushing the price up further. 

Therefore the priority for users of these noisy intermediate-scale quantum computers should be to not merely to use them to solve problems faster existing classical algorithms; it would be more cost-effective to simply throw more classical computing power at them. Instead, focus on problems that will remain too hard to solve even as classical computers continue to improve.