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.
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.
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
Dynamic circuits, which incorporate mid-circuit measurements and classically controlled operations, extend the expressive power of quantum programs and are central to applications such as quantum error correction, state preparation, and distributed quantum algorithms. However, their classical simulation is challenging due to the exponential growth of execution branches induced by mid-circuit measurements. In this work, we develop a tensor network approach for simulating dynamic circuits by extending a DMRG-based method for quantum circuit simulation to support dynamic circuit operations. To address the exponential proliferation of execution branches, we introduce and compare two strategies: a single-path stochastic approach that samples individual measurement outcomes, and a multi-path approach that maintains an ensemble of branches. We benchmark these methods on standard dynamic circuits, including the teleportation protocol and GHZ state preparation, as well as on random dynamic circuits. Our analysis explores the trade-offs between simulation accuracy and computational efficiency. These results provide a practical and scalable framework for the classical simulation of dynamic circuits.
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±0.02, surpassing the entanglement-certification threshold F>0.5 that the baseline dynamic-circuit implementation fails to reach (0.39±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≈0.2 across the largest sizes studied. Altogether, these results bring low-depth dynamic-circuit primitives within practical reach on present-day hardware.
Dynamic quantum circuits combine mid-circuit measurement with classical feed-forward, enabling circuit constructions with reduced entangling-gate depth. Here, we investigate their use in Quantum Imaginary Time Evolution (QITE), where circuit depth and parameter growth limit practical implementations of ground-state preparation. For dense classical optimization Hamiltonians, we introduce a reduced-parameter QITE ansatz that restricts entanglement generation via a small set of control qubits, enabling each QITE layer to be implemented with constant two-qubit gate depth using fan-out-based dynamic circuits. In noiseless simulations of exact cover and set partitioning instances, the reduced ansatz yields a higher success probability than standard QITE approaches. We implement unitary, dynamic fan-out, and semi-classical adaptive variants on IBM superconducting hardware. The semi-classical variant performs favorably to the unitary implementation, while the fully dynamic construction exposes the trade-offs between entangling-depth reduction and measurement and feed-forward overhead associated to dynamic circuit implementations. Using a fidelity threshold of 0.5 relative to the noiseless QITE ansatz, we show that dynamic fan-out based QITE would outperform unitary implementations on current devices when the measurement and two-qubit gate errors are reduced by 65% and the feedback latency is halved.
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.
In this work, we show how dynamic circuit compilation methods can transform a densely connected circuit into an ancilla-mediated, sparsely connected dynamic circuit that includes mid-circuit measurement and feedforward operations. This sparse connectivity is better suited to current quantum hardware, which often has limited qubit connectivity. Compared to compilation methods focused on unitary circuits, our method can reduce both circuit depth and the additional CNOTs required to execute non-adjacent qubit interactions.