When we talk about quantum computers, we usually mean fault-tolerant devices. These will be able to run Shor's algorithm for factoring, as well as all the other algorithms that have been developed over the years. But the power comes at a cost: to solve a factoring problem that is not feasible for a classical computer, we will require millions of qubits. This ...
This is a greatly debated topic, and I'm not sure there is an answer to your question at the current time. However, the IEEE (Institute of Electrical and Electronics Engineers) has proposed PAR 7131 - Standard for Quantum Computing Performance Metrics & Performance Benchmarking:
The purpose of this project is to provide a standardized set of
While number of qubits should be part of such a metric, as you say, it's far from everything.
However, comparing two different completely different devices (e.g. superconducting and linear optics) is not the most straightforward task1.
Asking about coherence and gate times is equivalent to asking about fidelity and gate times1. Gates being harder ...
IBM is promoting their quantum volume (see also this) idea to quantify the power of a gate model machine with a single number. Before IBM, there was an attempt from Rigetti to define a total quantum factor.
There are a lot of interesting applications that use similar technology. A lot of labs that work towards quantum computing also publish papers with these applications.
Here are some:
All-optical computation. Personally, I think this has more potential than quantum computing, as it has already been shown to be useful for quickly processing neural networks ...
Cirq uses numpy's pseudo random number generator to pick measurement results, e.g. here is code from XmonStepper.simulate_measurement:
def simulate_measurement(self, index: int) -> bool:
prob_one = np.sum(self._pool.map(_one_prob_per_shard, args))
result = bool(np.random.random() <= prob_one)
I think the answer depends on why you are comparing them. Things like the quantum volume, are perhaps better suited to defining progress in the development of devices rather than fully informing end users.
For example, you are buying a new laptop, you probably use more than just a single number when comparing them. The same should be true for quantum ...
Perform and checking basic quantum-mechanic experiments
Before the IBM and alibaba quantum cloud computers, you would need an expensive lab to do simple CHSH or GHZ experiments. Of course the qubits in the IBM computer are not loophole free but many institutes and also collegeschools could not have better experiment facilities purchased within their physics ...
Have a look at these for quantum machine learning:
Supervised learning with quantum computers by Schuld and Petruccione (2018)
An introduction to quantum machine learning by the same authors of the textbook above
Quantum machine learning published in Nature 2017 by some experts in the field: Wittek, Rebentrost, Lloyd, et al
Video presentations by Dr. Schuld ...
Here is the best circuit I've found. It uses 14 CNOTs.
Note that this circuit is not using a linear layout! It is placed on the grid like this:
Where 'A' is an ancilla initialized in the |0> state and '0','1','2','3' are the qubits making up the register (with '0' being the least significant bit).
I verified this circuit in Quirk ...
Thinking about the theoretical capabilities of quantum computers has led to important insights on the theory of classical computers.
One example is the proof that the (classical) complexity class PP is closed under intersection. While there was already a purely classical proof due to Beigel, Reingold, and Spielman, there exists a simpler proof that uses ...
Since quantum machine learning with NISQ hardware is such a relatively new field, it is still very highly research driven, and a lot of the potential is still being determined.
To make these new research implementations more accessible, we've begun building implementations over at https://pennylane.ai/qml. Interesting ones include:
Quantum Generative ...
Executing a NISQ-device in a manner that asymptotically outperforms a classical computer invalidates the Extended Church-Turing Thesis (ECT).
Voluminous tomes written about the (non-extended) Church-Turing Thesis, with implications for branches of philosophy such as the philosophy of mind.
The fact that the ECT was not only falsifiable but also is likely ...
You can participate in and contribute to open-source Qiskit.
You can write tools to work with Qiskit and/or other development kits, e.g., my qis_job which makes it easy to run a .qasm file right away.
You can write your own toys! See my quantum_yiqing.
For completely arbitrary coefficients you are out of luck. A simple counting argument says that because:
1) The coefficients are continuous parameters
2) gates implement discrete operations
There is no finite circuit to prepare the vast majority of states. However, if you're okay with an arbitrarily good approximation to your state, then it can be ...
I am not an expert but I read a few papers and here is what I have found. Similarly to NN, people found strategies to avoid this issue with the gradients.
Basically, for some problems, you can use ansatzes that are inspired by the physics of the problem itself. For example, in quantum chemistry, people use something called unitary coupled clusters. See ...