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arXiv:1911.02694 · Physical Review Letters

Small, Highly Accurate Quantum Processor for Intermediate-Depth Quantum Simulations

Nathan Lysne, Kevin W. Kuper, Pablo M. Poggi, Ivan Deutsch, Poul Jessen

Published Jun 9, 2020• 28 citations
arXivHTMLPDF

Abstract

Analog quantum simulation is widely considered a step on the path to fault tolerant quantum computation. With current noisy hardware, the accuracy of an analog simulator will degrade after just a few time steps, especially when simulating complex systems likely to exhibit quantum chaos. Here we describe a quantum simulator based on the combined electron-nuclear spins of individual Cs atoms, and its use to run high fidelity simulations of three different model Hamiltonians for >100 time steps. While not scalable to exponentially large Hilbert spaces, it provides the accuracy and programmability required to explore the interplay between dynamics, imperfections, and accuracy in quantum simulation.

DOI
10.1103/physrevlett.124.230501

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Analog quantum simulation is widely considered a step on the path to fault tolerant quantum computation. With current noisy hardware, the accuracy of an analog simulator will degrade after just a few time steps, especially when simulating complex systems likely to exhibit quantum chaos. Here we describe a quantum simulator based on the combined electron-nuclear spins of individual Cs atoms, and its use to run high fidelity simulations of three different model Hamiltonians for >100 time steps. While not scalable to exponentially large Hilbert spaces, it provides the accuracy and programmability required to explore the interplay between dynamics, imperfections, and accuracy in quantum simulation.
As uncorrected quantum processors grow in sophistication, many are being used for analog quantum simulation (AQS) of novel physics beyond the capabilities of classical devices. However, without the guarantee of bounded errors achieved by digitizing the computation, we do not know when and how much to trust an AQS result in the presence of inevitable imperfections. Here, we present the results of using our exper- iment as a testbed for studying the impact of errors on AQS. We have developed a small but highly-accurate processor over a 16-dimensional Hilbert space comprising the combined electron-nuclear spin of a single 133Cs atom in the electronic ground state. Advances in Eigenvalue-Only (EVO) optimal control enable us to repeatedly (>100) perform arbitrary unitary transformations in this space while maintaining accuracy on the device. We use this capability to simulate model systems known to exhibit features of interest, such as chaos and hypersensitivity (quantum kicked top) and quantum phase transitions (the transverse Ising and Lipkin-Meshkov-Glick mod- els). Experimental simulations show high fidelity of the quantum state and dynamical features in the presence of native imperfections. We discuss these results in the con- text of a new framework for quantifying the average sensitivity of simulator outcomes to errors. These theoretical and experimental results support the idea that AQS of ‘macroscopic’ observables (e.g., total magnetization) can be robust in the presence of errors, while observables tied to a specific quantum state (e.g., the fidelity) are not.
Abstract The immense resource overhead of full quantum error correction (QEC) presents a formidable barrier to achiev- ing fault-tolerant quantum computation. This paper introduces a hybrid analog-digital quantum processor architecture designed as a pragmatic strategy for achieving ”mid-scale fault tolerance” (MSFT). We formally define MSFT as a hardware-level error suppression scheme that achieves a fidelity gain by replacing deep, error-prone digital gate sequences with single, high-fidelity analog evolution blocks. The architecture comprises a programmable digital core for state preparation and measurement, coupled to an analog co-processor that executes computationally intensive Hamiltonian evolutions. This approach reduces the effective logical depth and error accumulation for algorithms like VQE. We validate this claim with statistically robust simulations on standard molecular Hamiltonians (LiH and BeH), demonstrating a significant performance advantage over purely digital systems based on an aggregation of 50 independent simulation trials. The analysis includes scalability and a discussion of the critical digital-analog interface, proposing trapped-ion and neutral-atom systems as viable physical platforms
Abstract Phosphorus atoms in silicon are an outstanding platform for quantum computing as their nuclear spins exhibit coherence time over seconds [1, 2]. By placing multiple phosphorus atoms within a radius of a few nanometers, they couple via the hyperfine interaction to a single, shared electron. Such a nuclear spin register enables multi-qubit control above the fault-tolerant threshold [3] and the execution of small-scale quantum algorithms [4]. To achieve quantum error correction, fast and efficient interconnects have to be implemented between spin registers while maintaining high fidelity across all qubit metrics. Here, we demonstrate such integration with a fully controlled 11-qubit atom processor composed of two multi-nuclear spin registers which are linked via electron exchange interaction. Through the development of scalable calibration and control protocols, we achieve coherent coupling between nuclear spins using a combination of single- and multi-qubit gates with all fidelities ranging from 99.5% to 99.99%. We verify the efficient all-to-all connectivity by preparing both local and non-local Bell states with a record state fidelity beyond 99% and extend entanglement through the generation of Greenberger-Horne-Zeilinger (GHZ) states over all data qubits. By establishing high-fidelity operation across interconnected nuclear-spin registers, we ealise a key milestone towards fault-tolerant quantum computation with atom processors.
Simulation of quantum systems is notoriously challenging for classical computers, while quantum hardware is naturally well-suited for this task. However, the imperfections of contemporary quantum systems pose a considerable challenge in carrying out accurate simulations over long evolution times. Here, we experimentally demonstrate a method for quantum simulations on a small-scale trapped-ion-based quantum simulator. Our method enables quantum simulations of programmable spin-Hamiltonians, using only simple global fields, driving all qubits homogeneously and simultaneously. We measure the evolution of a quantum Ising ring and accurately reconstruct the Hamiltonian parameters, showcasing an accurate and high-fidelity simulation. Our method enables a significant reduction in the required control and depth of quantum simulations, thus generating longer evolution times with higher accuracy.
Abstract The immense resource overhead of full quantum error correction (QEC) presents a formidable barrier to achieving fault-tolerant quantum computation. This paper introduces a hybrid analog-digital quantum processor architecture designed as a pragmatic strategy for achieving "mid-scale fault tolerance" (MSFT). We formally define MSFT as a hardware-level error suppression scheme that achieves a fidelity gain by replacing deep, error-prone digital gate sequences with single, high-fidelity analog evolution blocks. The architecture comprises a programmable digital core for state preparation and measurement, coupled to an analog co-processor that executes computationally intensive Hamiltonian evolutions. This approach reduces the effective logical depth and error accumulation for algorithms like VQE. We validate this claim with statistically robust simulations on standard molecular Hamiltonians (LiH and BeH₂), demonstrating a significant performance advantage over purely digital systems based on an aggregation of 50 independent simulation trials. The analysis includes scalability and a discussion of the critical digital-analog interface, proposing trapped-ion and neutral-atom systems as viable physical platforms.
In recent years, there has been a significant progress in the development of digital quantum processors. The state-of-the-art quantum devices are imperfect, and fully algorithmic fault-tolerant quantum computing is a matter of future. Until technology develops to the state with practical error correction, computational approaches other than the standard digital one can be used to avoid execution of the most noisy quantum operations. We demonstrate how a hybrid digital-analog approach allows simulating dynamics of a transverse-field Ising model without standard two-qubit gates, which are currently one of the most problematic building blocks of quantum circuits. We use qubit-qubit crosstalks (couplings) of IBM superconducting quantum processors to simulate Trotterized dynamics of spin clusters and then we compare the obtained results with the results of conventional digital computation based on two-qubit gates from the universal set. The comparison shows that digital-analog approach significantly outperforms standard digital approach for this simulation problem, despite of the fact that crosstalks in IBM quantum processors are small. We argue that the efficiency of digital-analog quantum computing can be improved with the help of more specialized processors, so that they can be used to efficiently implement other quantum algorithms. This indicates the prospect of a digital-to-analog strategy for near-term noisy intermediate-scale quantum computers.