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Quantum state-agnostic work extraction (almost) without dissipation

Josep Lumbreras, Ruo Cheng Huang, Yanglin Hu, Mile Gu, Marco Tomamichel

TL;DR

Here, the core challenge is designing interactions to optimally balance two competing goals: charging of the battery optimally using the qubit in hand, and acquiring more information by qubit to improve energy harvesting in subsequent rounds.

Abstract

We investigate work extraction protocols designed to transfer the maximum possible energy to a battery using sequential access to $N$ copies of an unknown pure qubit state. The core challenge is designing interactions to optimally balance two competing goals: charging of the battery optimally using the qubit in hand, and acquiring more information by qubit to improve energy harvesting in subsequent rounds. Here, we leverage exploration-exploitation trade-off in reinforcement learning to develop adaptive strategies achieving energy dissipation that scales only poly-logarithmically in $N$. This represents an exponential improvement over current protocols based on full state tomography.

Quantum state-agnostic work extraction (almost) without dissipation

TL;DR

Here, the core challenge is designing interactions to optimally balance two competing goals: charging of the battery optimally using the qubit in hand, and acquiring more information by qubit to improve energy harvesting in subsequent rounds.

Abstract

We investigate work extraction protocols designed to transfer the maximum possible energy to a battery using sequential access to copies of an unknown pure qubit state. The core challenge is designing interactions to optimally balance two competing goals: charging of the battery optimally using the qubit in hand, and acquiring more information by qubit to improve energy harvesting in subsequent rounds. Here, we leverage exploration-exploitation trade-off in reinforcement learning to develop adaptive strategies achieving energy dissipation that scales only poly-logarithmically in . This represents an exponential improvement over current protocols based on full state tomography.
Paper Structure (8 sections, 8 theorems, 107 equations, 2 figures, 4 algorithms)

This paper contains 8 sections, 8 theorems, 107 equations, 2 figures, 4 algorithms.

Table of Contents

  1. Learning pure quantum states (almost) without regret
  2. -work extraction protocol
  3. Work distribution
  4. Extracted work for different inputs
  5. Cumulative dissipation
  6. Non-degenerate Hamiltonian
  7. Jaynes-Cummings work extraction protocol
  8. Cost of measurement and erasure

Key Result

Theorem 1

Fix $K^*\in\mathbb{N}$, $t= \lceil 24\ln \left( K^* / \delta \right) \rceil$ for some $\delta > 0$ and time horizon $N = 4t K^*$. Then we have that the quantum state tomography Algorithm alg:linucb_vn_var over an unknown state $\ket{\psi}$ achieves with probability at least $1-\delta$ the regret Eq. for some universal constant $C_1 > 0$. Also for all $k\in\{1,\ldots,N\}$ the selected 2-outcome POV

Figures (2)

  • Figure 1: Sketch of the sequential work extraction protocol with a thermal reservoir. At each time step $k \in [N]$, the agent receives a copy of an unknown qubit state $\psi$ and performs a thermal operation involving the reservoir and a battery. A measurement in the battery system is carried out to determine the extracted work $\Delta W_k$, which is then used as feedback to improve the extraction strategy in subsequent rounds.
  • Figure 2: Illustration of the repetitions of the thermal operation in the full system $ABR$, where arrows represent Bloch vectors of states, showing that the system qubit becomes more and more mixed as the process goes. The energy gaps $\{\nu_{k,i}\}_i$ of successive reservoir Hamiltonian forms a strictly decreasing sequence, making the successive thermal states more mixed. At each step, we take a new qubit from the reservoir and swap the system qubit with the reservoir qubit, the energy from reservoir will flow into the battery. At the end of the process, the qubit in system $A$ is the thermal state.

Theorems & Definitions (11)

  • Theorem 1: lumbreras24pure
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • proof
  • Theorem 5
  • proof
  • Theorem 6: Theorem 2.34 in Flammia2024quantumchisquared
  • Theorem 7
  • proof
  • ...and 1 more