Symbol

Meaning

$s\in \mathcal{S}$

States.

$a\in \mathcal{A}$

Actions.

$r\in \mathcal{R}$

Results.

q

A transition function which gives the probability of moving from one state to another.

$s_t\mathrm{,}{a}_t\mathrm{,}{r}_t$

State, action, and reward at time step t for one trajectory.

$r\left(s_t\mathrm{,}{a}_t\mathrm{,}{s}_{t+1}\right)$

Reward for taking action $a_t$ at state $s_t$ and moving to the new state $s_{t+1}$ . Sometimes the notation $r\left(s\mathrm{,}a\mathrm{,}{s}^{\prime }\right)$ is used as well.

$\pi$

A reinforcement learning policy, which maps states to actions. ${\pi }_{\theta }\left(\mathrm{.}\right)$ is a policy parameterized by $\theta$ .

$\mathcal{J}\left(\pi \right)$

Cumulative reward for a policy.

$H\in \mathbb{N}$

Horizon which is the length of time a reinforcement policy can do actions.

$\gamma$

Discount factor which discounts future rewards.

$\alpha$

Step size hyperparameter.

$\sigma$

Hyper parameter which controls how much random variance or “jitter” is applied to the Natural Evolutionary Strategy populations.

$p_f$

Final portfolio value.

$R\left(\varphi \right)$

Quantum Rotation gate.

$D\left(\alpha \right)$

Quantum Displacement gate.

$S\left(r\right)$

Quantum Squeezing gate.

$BS\left(\theta \right)$

Quantum Beamsplitter gate that allows for entanglement between two photons.

$K\left(\kappa \right)$

Quantum Kerr gate.