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Resilience of Quantum Random Access Memory to Generic Noise

Connor T. Hann, Gideon Lee, S. M. Girvin, Liang Jiang

Published Apr 29, 2021• 56 citations
Publisher

Abstract

Quantum random access memory (QRAM)—memory which stores classical data but allows queries to be performed in superposition—is required for the implementation of numerous quantum algorithms. While naive implementations of QRAM are highly susceptible to decoherence and hence not scalable, it has been argued that the bucket-brigade QRAM architecture [Giovannetti et al., Phys. Rev. Lett. 100, 160501 (2008)] is highly resilient to noise, with the infidelity of a query scaling only logarithmically with the memory size. In prior analyses, however, this favorable scaling followed directly from the use of contrived noise models, thus leaving open the question of whether experimental implementations would actually enjoy the purported scaling advantage. In this work, we study the effects of decoherence on QRAM in full generality. Our main result is a proof that this favorable infidelity scaling holds for arbitrary error channels (including, e.g., depolarizing noise and coherent errors). Our proof identifies the origin of this noise resilience as the limited entanglement among the memory’s components, and it also reveals that significant architectural simplifications can be made while preserving the noise resilience. We verify these results numerically using a novel classical algorithm for the efficient simulation of noisy QRAM circuits. Our findings indicate that QRAM can be implemented with existing hardware in realistically noisy devices, and that high-fidelity queries are possible without quantum error correction. Furthermore, we also prove that the benefits of the bucket-brigade architecture persist when quantum error correction is used, in which case the scheme offers improved hardware efficiency and resilience to logical errors.

DOI
10.6082/027wm-z2x67

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Quantum random access memory (QRAM)—memory which stores classical data but allows queries to be performed in superposition—is required for the implementation of numerous quantum algorithms. While naive implementations of QRAM are highly susceptible to decoherence and hence not scalable, it has been argued that the bucket-brigade QRAM architecture [Giovannetti et al., Phys. Rev. Lett. 100, 160501 (2008)] is highly resilient to noise, with the infidelity of a query scaling only logarithmically with the memory size. In prior analyses, however, this favorable scaling followed directly from the use of contrived noise models, thus leaving open the question of whether experimental implementations would actually enjoy the purported scaling advantage. In this work, we study the effects of decoherence on QRAM in full generality. Our main result is a proof that this favorable infidelity scaling holds for arbitrary error channels (including, e.g., depolarizing noise and coherent errors). Our proof identifies the origin of this noise resilience as the limited entanglement among the memory’s components, and it also reveals that significant architectural simplifications can be made while preserving the noise resilience. We verify these results numerically using a novel classical algorithm for the efficient simulation of noisy QRAM circuits. Our findings indicate that QRAM can be implemented with existing hardware in realistically noisy devices, and that high-fidelity queries are possible without quantum error correction. Furthermore, we also prove that the benefits of the bucket-brigade architecture persist when quantum error correction is used, in which case the scheme offers improved hardware efficiency and resilience to logical errors.
Quantum random access memory (QRAM)-memory which stores classical data but allows queries to be performed in superposition-is required for the implementation of numerous quantum algorithms.While naive implementations of QRAM are highly susceptible to decoherence and hence not scalable, it has been argued that the bucket-brigade QRAM architecture [Giovannetti et al., Phys. Rev. Lett. 100, 160501 (2008)] is highly resilient to noise, with the infidelity of a query scaling only logarithmically with the memory size.In prior analyses, however, this favorable scaling followed directly from the use of contrived noise models, thus leaving open the question of whether experimental implementations would actually enjoy the purported scaling advantage.In this work, we study the effects of decoherence on QRAM in full generality.Our main result is a proof that this favorable infidelity scaling holds for arbitrary error channels (including, e.g., depolarizing noise and coherent errors).Our proof identifies the origin of this noise resilience as the limited entanglement among the memory's components, and it also reveals that significant architectural simplifications can be made while preserving the noise resilience.We verify these results numerically using a novel classical algorithm for the efficient simulation of noisy QRAM circuits.Our findings indicate that QRAM can be implemented with existing hardware in realistically noisy devices, and that high-fidelity queries are possible without quantum error correction.Furthermore, we also prove that the benefits of the bucket-brigade architecture persist when quantum error correction is used, in which case the scheme offers improved hardware efficiency and resilience to logical errors.
Quantum random access memory (QRAM) is required for numerous quantum algorithms and network architectures. Previous work has shown that the ubiquitous bucket-brigade QRAM is highly resilient to arbitrary local incoherent noise channels occurring during the operation of the QRAM [PRX Quantum 2, 020311 (2021)], with query infidelities growing only polylogarithmically with memory width when errors are assumed to only occur on individual routers. We extend this result to a large class of generalized settings that arise in realistic situations, including arbitrary initialization errors, spatially correlated errors, as well as coherent errors, maintaining the polylogarithmic scaling in all instances. Fully quantifying the extent to which QRAM's noise resilience holds may provide a guide for the design of QRAM architectures - for instance, the resilience to initialization errors indicates that a reset protocol between successive queries may not be necessary. In the case of coherent errors, we find an up-to-quadratic increase in the infidelity bound, and therefore discuss generalizations to randomized compiling schemes, which usually are rendered inapplicable in the QRAM setting, to tailor these errors into more favorable stochastic noise.
Quantum random access memory (QRAM) enables efficient classical data access for quantum computers -- a prerequisite for many quantum algorithms to achieve quantum speedup. Despite various proposals, the experimental realization of QRAM remains largely unexplored. Here, we experimentally investigate the circuit-based bucket-brigade QRAM with a superconducting quantum processor. To facilitate the experimental implementation, we introduce a hardware-efficient gate decomposition scheme for quantum routers, which effectively reduces the depth of the QRAM circuit by more than 30% compared to the conventional controlled-SWAP-based implementation. We further propose an error mitigation method to boost the QRAM query fidelity. With these techniques, we are able to experimentally implement the QRAM architectures with two and three layers, achieving query fidelities up to 0.800 ±\pm± 0.026 and 0.604$\pm$0.005, respectively. Additionally, we study the error propagation mechanism and the scalability of our QRAM implementation, providing experimental evidence for the noise resilience nature of the bucket-brigade QRAM architecture. Our results highlight the potential of superconducting quantum processors for realizing a scalable QRAM architecture.
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.
We study the robustness of the bucket brigade quantum random access memory model introduced by Giovannetti et al (2008 Phys. Rev. Lett. 100 160501 ). Due to a result of Regev and Schiff (ICALP '08 733), we show that for a class of error models the error rate per gate in the bucket brigade quantum memory has to be of order (where is the size of the memory) whenever the memory is used as an oracle for the quantum searching problem. We conjecture that this is the case for any realistic error model that will be encountered in practice, and that for algorithms with super-polynomially many oracle queries the error rate must be super-polynomially small, which further motivates the need for quantum error correction. By contrast, for algorithms such as matrix inversion Harrow et al (2009 Phys. Rev. Lett. 103 150502 ) or quantum machine learning Rebentrost et al (2014 Phys. Rev. Lett. 113 130503 ) that only require a polynomial number of queries, the error rate only needs to be polynomially small and quantum error correction may not be required. We introduce a circuit model for the quantum bucket brigade architecture and argue that quantum error correction for the circuit causes the quantum bucket brigade architecture to lose its primary advantage of a small number of 'active' gates, since all components have to be actively error corrected.
Quantum random-access memory (QRAM) enables coherent queries to classical data. However, the O(N)O(N)O(N) qubits required for a memory with N=2nN=2^nN=2n addresses make QRAM appear vulnerable to noise. Though bucket-brigade routing provides intrinsic noise resilience to reduce the error in QRAM, improving the fidelity of QRAM queries is still an important and challenging problem. We introduce a low-overhead protection framework for bucket-brigade QRAM with two complementary components. First, we propose a one-fault-tolerant repeat-until-success logical controlled-SWAP gate using the [[4,2,2]][[4,2,2]][[4,2,2]] code under erasure noise channel. Interleaved erasure checks and local recovery correct every single erasure, so the leading logical failure probability is second order in the physical erasure error rates. Second, we exploit validity constraints of bucket-brigade routing to define local parity checks directly on the router states, without adding extra data qubits to create code redundancy. Under bit-flip noise, minimum-weight perfect matching with noiseless syndrome measurements corrects single interior faults, while open spatial boundaries retain a first-order contribution in the residual bit-flip rate. Monte Carlo simulations confirm quadratic suppression for the protected controlled-SWAP and improved depth scaling for decoded QRAM router-state snapshots. The two codes admit a concatenated realization in which the inner code supplies erasure protection and the outer code optionally corrects interior logical bit flips. Together, these results show how routing constraints and a protected non-Clifford routing gate can improve QRAM reliability under biased and erasure-dominant noise.