Quantum memory efficiency depends on entanglement request patterns
The Sample Complexity of Quantum Entanglement Allocation
Machine Learning
Summary
This paper studies how much past information about quantum bits (qubits) is needed to decide which ones to connect with quantum entanglement. The authors find that the amount of memory required does not always increase with more data—it depends on how the entanglement choices are made. They analyze scenarios with special types of quantum questions and describe limits on prediction errors for different group sizes of qubits. They also explore how noise affects learning and test their findings with experiments on quantum devices and retail data.
What this means in practice
- •For quantum hardware engineers: Optimize allocation of entangled qubits in quantum devices to reduce sample demands for calibration and control.
- •For retail data analysts: Improve purchase basket grouping methods using quantum-inspired learning laws to enhance recommendation quality.
Authors
Nathan Roll
Abstract
How many past requests are needed to decide which qubits should share entanglement? We show that the answer depends on the allocation choices created by the queries: a larger memory can require no more data. The memory stores a classical bit and answers requests through a fixed detector that preserves coherence within each measured sector. For independent commuting $X$- and $Z$-type Pauli queries, we characterize the full attainable prediction-contrast region and construct encodings that preserve the bit at every nonzero vertex. With sharp reports, a $d$-qubit path and groups of at most $k$ qubits have minimax excess error after $m$ requests proportional to $k^{-1}\min\{1,\sqrt{d\log(k+1)/m}\}$, uniformly for $2\leq k<d$. Connected biclique regions can grow without increasing sample demand when depth, region count and connections per region stay bounded. Preparation noise introduces a separate calibration requirement. We derive an exact tradeoff with extra fresh detector calls and transfer the learning law to structured transaction co-location. Population-risk experiments test the statistical predictions. We also compare encodings on a native 15-qubit device and learned partitions on public purchase baskets. The full chain wins on the device; frequency grouping outperforms basket search in the largest-capacity retail setting.