Unified Architecture for Quantum Lookup Tables

Quantum access to arbitrary classical data encoded in unitary black-box oracles underlies interesting data-intensive quantum algorithms, such as machine learning or electronic structure simulation. The feasibility of these applications depends crucially on gate-efficient implementations of these oracles, which are commonly some reversible versions of the boolean circuit for a classical lookup table. We present a general parameterized architecture for quantum circuits implementing a lookup table that encompasses all prior work in realizing a continuum of optimal tradeoffs between qubits, non-Clifford gates, and error resilience, up to logarithmic factors. Our architecture assumes only local 2D connectivity, yet recovers results that previously required all-to-all connectivity, particularly, with the appropriate parameters, poly-logarithmic error scaling. We also identify novel regimes, such as simultaneous sublinear scaling in all parameters. These results enable tailoring implementations of the commonly used lookup table primitive to any given quantum device with constrained resources.

💡 Research Summary

The paper addresses a fundamental building block for many quantum algorithms—quantum access to classical data, formally known as a quantum lookup table (QLT). A QLT implements a unitary Oₓ that maps a superposition of address registers |i⟩|0⟩ to |i, xᵢ⟩, where xᵢ are classical bits or words. The authors observe that the cost of such oracles dominates the overall resource budget of algorithms in quantum chemistry, machine learning, and other data‑intensive domains, especially in the fault‑tolerant regime where logical non‑Clifford (T) gates are expensive.

The core contribution is a unified, parameterized circuit architecture that subsumes all previously known QLT constructions—fan‑out QRAM, bucket‑brigade QRAM, QROM, SELECT‑SWAP, and recent variants. Two tunable parameters, λ∈