Heterogeneously error-corrected QRAMs

TL;DR

This work tackles the challenge of scalable fault-tolerant QRAM by proposing a heterogeneous QRAM that uses variable-strength surface-code error correction across the memory tree. By tying code distance to the router level and distributing error protection, the authors derive fidelity bounds that are constant in QRAM size and develop two concrete implementations—Fat Tree inspired and BB-inspired—that reduce qubit overhead while maintaining desirable error scaling. Numerical simulations validate the constant infidelity behavior for the heterogeneous designs and show substantial resource reductions (up to about 5x for moderate sizes) compared with uniformly error-corrected BB QRAM. Compared to alternative fault-tolerant QRAM approaches, the heterogeneous scheme provides a practical path toward data-intensive quantum applications with scalable, fault-tolerant memory.

Abstract

Quantum Random Access Memory (QRAM) holds the promise of enabling several large scale applications of quantum computers. However, designing fault tolerant QRAMs for large scale applications is still an open problem due to the poor error and resource scaling of current architectures. Existing protocols often overlook the need for error correcting QRAMs, which will be required for data-intensive, fault-tolerant applications. However, naively error correcting all qubits used to implement the QRAM is prohibitively resource intensive, quickly becoming infeasible for large applications. To fill this gap, we propose a novel QRAM architecture that leverages variable strength error correction. We strongly error-correct qubits that heavily influence query fidelity, and lightly correct less critical regions of the QRAM. This scheme produces queries with fidelity bounded by a constant for arbitrarily sized QRAMs without requiring improvements in physical hardware. Furthermore, the heterogeneous scheme requires 5x fewer resources (for depth 30 QRAM) and quadratically slower error scaling as compared to a uniformly error corrected Bucket Brigade QRAM. In this work, we present a rigorous analysis of the query fidelity scaling and perform resource analyses of two variations of the heterogeneous architecture using the surface code. We verify our results using numerical simulations and compare our results against several other existing QRAM techniques. Through our results, we quantitatively prove the optimal scaling of the heterogeneous architecture, paving a way for data-intensive and fault tolerant quantum applications.

Figures (9)

• Figure 1: Heterogeneous QRAM architecture.
• Figure 2: Query circuit for FT-Hetero implementation. Each router only needs $O(\text{Poly}(d))$ bus/address routing steps (red) and address setting steps (green), thereby producing optimal query fidelity scaling.
• Figure 3: (a) Query circuit for the BB-Hetero implementation. The circuit is color coded as Red: Set bus qubits, Blue: Set address qubits, Green: Route through even routers (Red colored router nodes) and Yellow: Route through odd routers (Blue colored router nodes). (b) (Top) Sequence of steps of query circuit in (a). Colors refer to the same steps as in (a). (b) (Bottom) Sequence of steps of querying QRAM with $N=256$.
• Figure 4: Numerical simulations of query infidelity as a function of QRAM circuit depth for three architectures: FT-Hetero (sec. \ref{['sec:implementation']}), BB-Hetero, (sec. \ref{['sec:alternative_implementation']}) and the Uniform BB architecture hann2021resilience. We perform simulations for both qutrit (upper row) and qubit implementations (lower row) of the respective architectures.
• Figure 5: Qubit overhead comparisons of uniform BB QRAM with the two heterogeneous implementations: (a) FT-Hetero and (b) BB-Hetero. The code distance for the uniform QRAM is calculated by equating its query infidelity with those of the heterogeneous implementations which is then used to calculate the number of qubits in the QRAM. The plots for the heterogeneous implementations' overheads is based on the resource scalings in Appendix \ref{['apdx:efficeint_resources']}.