密度行列を使用してノイズのある量子システムをシミュレートする必要があるのはなぜですか?


1

ノイズのある量子システムをシミュレートするのになぜ密度行列を使用する必要があるのですか?

QEC回路は、通常の場合と同様に一部の量子ゲートに含まれていることがわかりました。つまり、状態ベクトルを使用してシミュレーションを行うこともできますが、すべてのシミュレータは密度行列を使用してノイズモデルを実現できるだけです。それで私を助けますか?

3

Noise effects introduce classical uncertainty in what the underlying state is. A mixed state is a statistical ensemble of several quantum states $|\psi_i\rangle$ (not necessarily orthogonal), with respective probabilities $p_i$.

With the state vector you can represent pure states, not mixed ones. Instead, with the density operator you can represent both pure and mixed states.

Noise models are always defined in terms of density operators.


2

You do not need to use the density matrix approach. However, as the most general representation of a quantum state, doing so has several advantages. You can simulate noise using just statevectors using probabilistic approaches, eg wavefunction monte-carlo, that converge to the density matrix results in the limit of many repetitions. Along this same thread of thought, it is important to note that the density matrix approach is not what the system is actually doing. Rather, it is the average of what the system does if the experiment is repeated many (formally infinitely many) times. In contrast, the statevector based methods should well approximate a single realization of the experiment.