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arXiv:2308.13065 · PRX Quantum

Efficient Long-Range Entanglement Using Dynamic Circuits

Elisa Bäumer, Vinay Tripathi, Derek S. Wang, Patrick Rall, Edward H. Chen, Swarnadeep Majumder, Alireza Seif, Zlatko Minev

Published Aug 22, 2024• 110 citations
arXivHTMLPDF

Abstract

Quantum simulation traditionally relies on unitary dynamics, inherently imposing efficiency constraints on the generation of intricate entangled states. In principle, these limitations can be superseded by nonunitary, dynamic circuits. These circuits exploit measurements alongside conditional feed-forward operations, providing a promising approach for long-range entangling gates, higher effective connectivity of near-term hardware, and more efficient state preparations. Here, we explore the utility of shallow dynamic circuits for creating long-range entanglement on large-scale quantum devices. Specifically, we study two tasks: controlled- gate teleportation between up to 101 qubits by feeding forward 99 midcircuit measurement outcomes, and the preparation of Greenberger–Horne–Zeilinger states with genuine entanglement. In the former, we observe that dynamic circuits can outperform their unitary counterparts. In the latter, by tallying instructions of compiled quantum circuits, we provide an error budget detailing the obstacles that must be addressed to unlock the full potential of dynamic circuits. Looking forward, we expect dynamic circuits to be useful for generating long-range entanglement in the near term on large-scale quantum devices. Published by the American Physical Society 2024

DOI
10.1103/prxquantum.5.030339

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Quantum simulation traditionally relies on unitary dynamics, inherently imposing efficiency constraints on the generation of intricate entangled states. In principle, these limitations can be superseded by nonunitary, dynamic circuits. These circuits exploit measurements alongside conditional feed-forward operations, providing a promising approach for long-range entangling gates, higher effective connectivity of near-term hardware, and more efficient state preparations. Here, we explore the utility of shallow dynamic circuits for creating long-range entanglement on large-scale quantum devices. Specifically, we study two tasks: controlled- gate teleportation between up to 101 qubits by feeding forward 99 midcircuit measurement outcomes, and the preparation of Greenberger–Horne–Zeilinger states with genuine entanglement. In the former, we observe that dynamic circuits can outperform their unitary counterparts. In the latter, by tallying instructions of compiled quantum circuits, we provide an error budget detailing the obstacles that must be addressed to unlock the full potential of dynamic circuits. Looking forward, we expect dynamic circuits to be useful for generating long-range entanglement in the near term on large-scale quantum devices. Published by the American Physical Society 2024
In many domains, quantum computing has demonstrated its superiority over classical computing, and it continues to expand. It has demonstrated exponential speedups compared to the classic approach in certain problems. Nevertheless, scalability and noisy environments remain challenges for quantum hardware. In contrast to the unitary dynamics that characterise quantum circuits, recent research has introduced dynamic circuits with non-unitary dynamics. Dynamic circuits include mid-circuit measurement and conditional feed-forward operations. Our proposal involves using dynamic circuits to achieve reduced circuit depth, which in turn significantly decreases error rates by integrating error-correcting feed-forward operations within the circuit. Long-Range Teleportation enables the expansion of teleportation protocols to accommodate intricate quantum states spanning multiple qubits. We have employed Dynamic circuits to ensure an optimal circuit depth and showcase the efficacy of dynamic circuits in facilitating reliable teleportation with an increasing number of qubits. Our findings highlight the benefits of using dynamic circuits to optimize the compilation time of the multi qubit quantum teleportation protocol.
Dynamic circuits, which augment unitary operations with mid-circuit measurements and classical feedforward, can generate long-range entanglement in constant depth, enabling low-depth primitives ranging from nontrivial state preparation to many-qubit entangling gates. Escaping the light-cone constraints of unitary circuits, however, comes at a cost: these primitives typically require a number of mid-circuit measurements that scales with system size and that, together with feedforward latency, can introduce errors that degrade the long-range entanglement they rely on. Here, we alleviate this tension by showing that many such primitives, when cast into a common framework, admit an error-detection scheme that trades infidelity for postselection overhead with no additional ancillas. Our framework thus unifies and upgrades a broad class of primitives including fan-out gates, multi-qubit Pauli rotations, the preparation of W and higher-weight Dicke states, and certain non-normal matrix product states. We also introduce a reduced-depth, error-detected implementation of the Hadamard test, extending the use cases of dynamic circuits to a key algorithmic primitive. Finally, we establish the practical utility of our scheme through experiments on a superconducting quantum processor. We demonstrate the error-detected preparation of a long-range entangled Bell pair spanning a 100-qubit chain with fidelity F=0.59±0.02F=0.59\pm0.02F=0.59±0.02, surpassing the entanglement-certification threshold F>0.5F>0.5F>0.5 that the baseline dynamic-circuit implementation fails to reach (0.39±0.010.39\pm0.010.39±0.01). Separately, we demonstrate constant-depth preparation of W states of up to 20 qubits by consuming GHZ states of up to 40 qubits, finding absolute fidelity improvements of ΔF≈0.2ΔF\approx 0.2ΔF≈0.2 across the largest sizes studied. Altogether, these results bring low-depth dynamic-circuit primitives within practical reach on present-day hardware.
In dynamic quantum circuits, classical information from midcircuit measurements is fed forward during circuit execution. This emerging capability of quantum computers confers numerous advantages that can enable more efficient and powerful protocols by drastically reducing the resource requirements for certain core algorithmic primitives. In particular, in the case of the n-qubit quantum Fourier transform followed immediately by measurement, the scaling of resource requirements is reduced from O(n^{2}) two-qubit gates in an all-to-all connectivity in the standard unitary formulation to O(n) midcircuit measurements in its dynamic counterpart without any connectivity constraints. Here, we demonstrate the advantage of dynamic quantum circuits for the quantum Fourier transform on IBM's superconducting quantum hardware with certified process fidelities of >50% on up to 16 qubits and >1% on up to 37 qubits, exceeding previous reports across all quantum computing platforms. These results are enabled by our contribution of an efficient method for certifying the process fidelity, as well as of a dynamical decoupling protocol for error suppression during midcircuit measurements and feed forward within a dynamic quantum circuit that we call "feed-forward-compensated dynamical decoupling." Our results demonstrate the advantages of leveraging dynamic circuits in optimizing the compilation of quantum algorithms.
Near-term quantum computers often have connectivity constraints, i.e. restrictions, on which pairs of qubits in the device can interact. Optimally mapping a quantum circuit to a hardware topology under these constraints is a difficult task. While numerous approaches have been proposed to optimize qubit routing, the resulting gate count and depth overheads of the compiled circuits remain high due to the short-range coupling of qubits in many near-term devices. Resource states, such as Bell or Einstein-Podolsky-Rosen (EPR) pairs, can be used to mediate operations that facilitate long-range interactions between qubits. In this work, we studied some of the practical trade-offs involved in using resource states for qubit routing. We developed a method that leverages an existing state-of-the-art compiler to optimize the routing of circuits with both standard gates and EPR mediated remote controlled-NOT gates. This was then used to compile different benchmark circuits for a square grid topology, where a fraction of the qubits are used to store EPR pairs. We demonstrate that EPR-mediated operations can substantially reduce the total number of gates and depths of compiled circuits when used with an appropriate optimizing compiler that accounts for practical overheads. Our results highlight the relevance of developing efficient compilation tools that can integrate EPR-mediated operations.
Quantum circuit compilation is a crucial step in realizing quantum algorithms on near-term quantum hardware. Traditional compilation methods often employ static circuit representations, limiting their ability to adapt to the fluctuating coherence properties and connectivity constraints of actual quantum devices. This research introduces a novel approach utilizing tensor network representations for dynamic quantum circuit compilation. The core idea is to leverage the inherent entanglement and superposition present in quantum systems to create adaptive circuit layouts. Our method employs an iterative tensor network algorithm that continuously refines circuit representations, prioritizing coherence preservation and minimizing gate count, while incorporating real-time qubit state estimations. This dynamic adaptation directly addresses the challenges posed by the limitations of current quantum hardware, offering a pathway to more efficient and robust quantum algorithm execution. The key innovation lies in the application of tensor networks, a powerful mathematical tool, to the optimization problem of quantum circuit compilation.
The resource overhead required to achieve net computational benefits from quantum error correction (QEC) limits its utility while current systems remain constrained in size, despite exceptional progress in experimental demonstrations. In this paper, we demonstrate that the strategic application of QEC primitives without logical encoding can yield significant advantages on superconducting processors—relative to any alternative error-reduction strategy—while only requiring a modest overhead. We first present a novel protocol for implementing long-range gates that relies on a unitarily prepared Greenberger-Horne-Zeilinger (GHZ) state as well as a unitary disentangling step; the protocol natively introduces an error-detection process using the disentangled qubits as flags. We demonstrate that it achieves state-of-the-art gate fidelities of over 85% across up to 40 lattice sites, significantly and consistently outperforming the best alternative measurement-based protocol without introducing any additional ancilla qubits. We then apply sparse stabilizer measurements to generate large GHZ states by detecting bit-flip and amplitude-damping errors. Employing this technique in combination with deterministic error suppression, we generate a 75-qubit GHZ state exhibiting genuine multipartite entanglement, the largest reported to date. The generation requires no more than 9 ancilla qubits and the fraction of samples discarded due to errors grows no higher than 78%, far lower than previous discard fractions required for tests using comparable numbers of fully encoded qubits. This work in total represents compelling evidence that adopting QEC primitives on current-generation devices can deliver substantial net benefits.