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Comment by JanisErdmanis | Hacker News Reader

There is no enormous work needed to create a time domain solver. Libraries like `QuantumOptics.jl` and analogous on Matlab, Python and Mathematica let's you define the Hamiltonian of an idealized system and solve it. For 16 qubits the matrix size (dimension) is 2^16=65536, can be solved very quickly on a local machine. Furthermore the Hamiltonian matrix is sparse enabling more optimizations.

At the moment state of the art supercomputer can simulate 47 qubits. For 46 the necessary resources are about 4 times smaller. So with handful you meant order of 30 then yes. Only a handful of qubits.

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A supercomputer cannot simulate a realistic noise model of 30-40 qubits. It can simulate stochastic Pauli channel noise, but that’s a toy, and it would be ungodly slow anyway.

A density operator representing a mixed state of n qubits grows as 2^(n^2), or a system with leakage into the second and third excited states grows as 4^(n^2).

For just 4 qubits, this would be a 4 billion complex numbers, so 8 billion floating point numbers.

Even this isn’t a time-domain solution, where you might in practice need to solve the Lindblad master equation.

This is all assuming we have a model for the noise, which in practice is highly non-trivial and very dependent on both the implementation of the qubits as well as their geometrical and material construction, and would take a good deal of science and engineering work to do accurately in a way that it reflects both control dynamics and a specific manufactured sample.

Yes there are solvers on the market in Python and Julia, but they don’t give you realistic noise computations for “free”.

I never had seen the scaling 2^(n^2) before. Can you provide a reference for that?

I am also don't understand the point of simulating noise correctly. If you get the result from computation on some vendor black-box black box quantum computer can you really know with what type of noise you would have obtained the result?

Another skepticism about the hype is that the result of quantum computation is just a matrix product on initial state from predefined gates. It is just linear algebra on large unitary matricies. Nothing quantum about it.

They're talking about propagating a density matrix instead of a state vector. If you're not familiar, a density matrix is an n x n matrix where n is the number of elements in the corresponding state vector, and contains information akin to a probability distribution over state vectors.

However, actual quantum computers propagate state vectors, not density matrices, as far as I know. You'd need to run it a large number of times, or have a large ensemble of identical sets of qbits being propagated with the same algorithm to need a density matrix to describe it, I would have thought. So saying you'd need to simulate a density matrix to simulate a quantum computer confuses me.

I know quantum physics but not quantum computing specifically, so I could be wrong - the grandparent comment sounds like they know what they're talking about otherwise.

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