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arXiv:2201.04665 · Physical Review Research

Error-robust quantum signal processing using Rydberg atoms

Sina Zeytinoǧlu, Sho Sugiura

Published Jan 3, 2024• 3 citations
arXivHTMLPDF

Abstract

Rydberg atom arrays have recently emerged as one of the most promising platforms for quantum simulation and quantum information processing. However, as is the case for other experimental platforms, the longer-term success of the Rydberg atom arrays in implementing quantum algorithms depends crucially on their robustness to gate-induced errors. Here we show that, for an idealized biased-error model based on Rydberg atom dynamics, the implementation of quantum signal processing (QSP) protocols can be made error robust, in the sense that the asymptotic scaling of the gate-induced error probability is slower than that of gate complexity. Moreover, our numerical results that use experimentally accessible parameters indicate that QSP iterates made out of more than 100 gates can be implemented with constant error probability. To showcase our approach, we provide a concrete blueprint to implement QSP-based near-optimal Hamiltonian simulation on the Rydberg atom platform. The proposed protocol substantially improves both the scaling and the overhead of gate-induced errors in comparison to those protocols that implement a fourth-order product formula. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.013003

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Rydberg atom arrays have recently emerged as one of the most promising platforms for quantum simulation and quantum information processing. However, as is the case for other experimental platforms, the longer-term success of the Rydberg atom arrays in implementing quantum algorithms depends crucially on their robustness to gate-induced errors. Here we show that, for an idealized biased-error model based on Rydberg atom dynamics, the implementation of quantum signal processing (QSP) protocols can be made error robust, in the sense that the asymptotic scaling of the gate-induced error probability is slower than that of gate complexity. Moreover, our numerical results that use experimentally accessible parameters indicate that QSP iterates made out of more than 100 gates can be implemented with constant error probability. To showcase our approach, we provide a concrete blueprint to implement QSP-based near-optimal Hamiltonian simulation on the Rydberg atom platform. The proposed protocol substantially improves both the scaling and the overhead of gate-induced errors in comparison to those protocols that implement a fourth-order product formula. Published by the American Physical Society 2024
The utility of near-term quantum computers and simulators is likely to rely upon software-hardware codesign, with error-aware algorithms and protocols optimized for the platforms they are run on. Here, we show how knowledge of noise in a system can be exploited to improve the design of gate-based quantum simulation algorithms. We demonstrate this codesign in the context of a trapped ion quantum simulation of the dynamics of a Heisenberg spin model. Specifically, we derive a theoretical noise model describing unitary gate errors due to heating of the ions' collective motion, finding that the temporal correlations in the noise induce an optimal gate depth. We then illustrate how tailored feedforward control, best applied at this optimum, can be used to partially mitigate unitary gate errors and improve the simulation outcome. Our results provide a practical guide to the codesign of gate-based quantum simulation algorithms. Published by the American Physical Society 2024
Quantum error correction (QEC) requires the execution of deep quantum circuits with large numbers of physical qubits to protect information against errors. Designing protocols that can reduce gate and space-time overheads of QEC is therefore crucial to enable more efficient QEC in near-term experiments. Multiqubit gates offer a natural path toward fast and low-depth stabilizer measurement circuits. However, they typically introduce high-weight correlated errors that can degrade the circuit-level distance, leading to slower scalings of the logical error probabilities. In this Letter, we show how to realize fast and efficient surface code stabilizer readout using only two singly controlled z gates acting simultaneously on two target qubits, i.e., two CZ_{2} gates-instead of four cz. We show that this scheme is fault tolerant and provide a blueprint for implementation in Rydberg atom arrays. We derive the time-optimal pulses implementing the gates and perform extensive QEC numerical simulations with Rydberg decay errors. Compared to the standard protocol using four cz gates, our scheme is faster, uses fewer gates, and crucially maintains fault tolerance with comparable logical error probabilities. Fault-tolerant generalizations of this scheme to biased and erasure-dominant noise models, as well as to other QEC codes such as quantum Low-Density Parity-Check codes, are also discussed.
Despite rapid advances in quantum hardware, noise remains a central obstacle to deploying quantum algorithms on near-term devices. In particular, random coherent errors that accumulate during circuit execution constitute a dominant and fundamentally challenging noise source. We introduce a noise-resilient framework for Quantum Signal Processing (QSP) that mitigates such coherent errors without increasing circuit depth or ancillary qubit requirements. Our approach uses ensembles of noisy QSP circuits combined with measurement-level averaging to suppress random phase errors in Z rotations. Building on this framework, we develop robust QSP algorithms for implementing polynomial functions of Hermitian matrices and for estimating observables, with applications to Hamiltonian simulation, quantum linear systems, and ground-state preparation. We analyze the trade-off between approximation error and hardware noise, which is essential for practical implementation under the stringent depth and coherence constraints of current quantum hardware. Our results establish a practical pathway for integrating error mitigation seamlessly into algorithmic design, advancing the development of robust quantum computing, and enabling the discovery of scientific applications with near- and mid-term quantum devices.
Neutral-atom arrays have recently emerged as a promising platform for quantum information processing.One important remaining roadblock for the large-scale application of these systems is the ability to perform error-corrected quantum operations.To entangle the qubits in these systems, atoms are typically excited to Rydberg states, which could decay or give rise to various correlated errors that cannot be addressed directly through traditional methods of fault-tolerant quantum computation.In this work, we provide the first complete characterization of these sources of error in a neutral-atom quantum computer and propose hardware-efficient, fault-tolerant quantum computation schemes that mitigate them.Notably, we develop a novel and distinctly efficient method to address the most important errors associated with the decay of atomic qubits to states outside of the computational subspace.These advances allow us to significantly reduce the resource cost for fault-tolerant quantum computation compared to existing, general-purpose schemes.Our protocols can be implemented in the near term using state-of-the-art neutral-atom platforms with qubits encoded in both alkali and alkaline-earth atoms.
Quantum logic gates are the essential components of quantum computation and have broad practical applications, especially for the multiple-qubit logic gates. Compared with appliying a series of single- and two-qubit gates, constrcuting quantum computation with multiple-qubit logic gates can be more efficient and high-fidelity. As a three-qubit logic gate, Deutsch gate enables the realization of any feasible quantum computations. Based on neutral atoms, we present a scheme of super-robust Deutsch gate via optimal control technique. Utilizing the Rydberg blockade effect of neutral atoms, we design an implementable D ( β ) based on the three-step program. One of the notable advantages of this function is that β can be achieved arbitrarily between 0 and π with the operation of target atom. In addition, we give an analytical solution agreed very well with numerical simulations for the residual blocking effect between next-neighbor atoms that affects the performance quality of Deutsch gate. The fidelity of our proposed scheme is demonstrated by numerical simulation of the master equation based on the full Hamiltonian, and the robustness of our scheme with control errors is also illustrated. Our proposal offers an alternative promising scheme for fault-tolerant quantum computation. Published by the American Physical Society 2024
Abstract Quantum signal processing (QSP) is a powerful toolbox for the design of quantum algorithms and can lead to asymptotically optimal computational costs. Its realization on noisy quantum computers without fault tolerance, however, is challenging because it requires a deep quantum circuit in general. We propose a strategy to run an entire QSP protocol on noisy quantum hardware by carefully reducing overhead costs at each step. To illustrate the approach, we consider the application of Hamiltonian simulation for which QSP implements a polynomial approximation of the time evolution operator. We test the protocol by running the algorithm on the Quantinuum H1-1 trapped-ion quantum computer powered by Honeywell. In particular, we compute the time dependence of bipartite entanglement entropies for Ising spin chains and find good agreements with exact numerical simulations. To make the best use of the device, we determine optimal experimental parameters by using a simplified error model for the hardware and numerically studying the trade-off between Hamiltonian simulation time, polynomial degree, and total accuracy. Our results are the first step in the experimental realization of QSP-based quantum algorithms.