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arXiv:2406.13405 · IEEE International Conference on Quantum Computing and Engineering (QCE)

Gate Teleportation in Noisy Quantum Networks with the SquidASM Simulator

Valter Uotila

Published Sep 15, 2024• 1 citation
arXivHTMLPDF

Abstract

We implement the gate teleportation algorithm for teleporting arbitrary two-qubit Clifford gates and the Toffoli gate within the context of multi-node quantum networks, utilizing the SquidASM quantum network simulator. We show how a gate teleportation scheme can be used to implement gate cutting, which is an important approach to realize large circuits in distributed quantum computing environments. The correction operations in teleportation are automatically constructed for arbitrary two-qubit Clifford gates. We apply a similar gate teleportation protocol for the Toffoli gate, but the correction operation becomes more complex since the gate is non-Clifford. We present the simulation results for the CNOT, DCNOT, CZ, SWAP, and Toffoli gates. We perform the simulations under varying quantum channel and device noise levels. The simulations provide valuable insights into the robustness and efficacy of the implemented algorithms, and they assist in identifying the critical components within quantum networks where noise primarily affects the execution of applications.

DOI
10.1109/qce60285.2024.10271

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We implement the gate teleportation algorithm for teleporting arbitrary two-qubit Clifford gates and the Toffoli gate within the context of multi-node quantum networks, utilizing the SquidASM quantum network simulator. We show how a gate teleportation scheme can be used to implement gate cutting, which is an important approach to realize large circuits in distributed quantum computing environments. The correction operations in teleportation are automatically constructed for arbitrary two-qubit Clifford gates. We apply a similar gate teleportation protocol for the Toffoli gate, but the correction operation becomes more complex since the gate is non-Clifford. We present the simulation results for the CNOT, DCNOT, CZ, SWAP, and Toffoli gates. We perform the simulations under varying quantum channel and device noise levels. The simulations provide valuable insights into the robustness and efficacy of the implemented algorithms, and they assist in identifying the critical components within quantum networks where noise primarily affects the execution of applications.
ABSTRACT While distributed quantum computation has primarily utilized circuit cutting, it incurs an exponential growth of sub‐circuit sampling and classical post‐processing overhead with an increasing number of cuts. In contrast, entanglement‐based gate teleportation avoids exponential sampling overhead but requires high‐fidelity quantum interconnects. We model noisy remote (teleported) gates between superconducting qubits entangled via noisy microwave‐to‐optical (M2O) transducers over optical links. We incorporate the effect of the transducer noise added () on the Bell pair state preparation circuit and inject noisy Bell pairs into remote CNOT gates. We perform comparative simulation of Greenberger–Horne–Zeilinger (GHZ) states generated between processor modules using remote gates and gate cuts and study the dependence of the Hellinger fidelity on the dominant error parameter for each approach. We identify break‐even points and regimes where noisy remote gates achieve parity with gate‐cuts. In particular, our work suggests that a 10‐fold reduction in the present M2O transducer noise added figures would favor generating multipartite entangled states with remote gates over circuit cutting. Our work informs near‐term quantum interconnect hardware metrics and motivates a network‐aware hybrid quantum‐classical distributed computation approach, where both quantum links and circuit cuts are employed to minimize quantum runtime.
The Toffoli gate is an important universal quantum gate, and will alongside the Clifford gates be available in future fault-tolerant quantum computing hardware. Many quantum algorithms rely on performing arbitrarily small single-qubit rotations for their function, and these rotations may also be used to construct any unitary from a limited (but universal) gate set. How to carry out such rotations is then of significant interest. In this work, we evaluate the performance of a recently proposed single-qubit rotation algorithm using the Clifford plus Toffoli gate set by implementation of a one-shot version on both a real and a simulated quantum computer. We test the algorithm under various simulated noise levels using a per-qubit depolarizing error noise model and examine how the probabilities and process fidelities are affected. We then conduct live runs and find that the results reasonably match the simulated results. We also attempt to model the hardware noise by combining a number of noise models, matching the results to results of the live runs to approximate the hardware noise. Our results suggest that the algorithm will perform well for up to 1 % noise under the noise models we chose. We further posit the use of our algorithm as a benchmark for quantum processing units, given that it has a low complexity that is easy to fine-tune in small steps. We provide details for how to do this.
Quantum gate teleportation enables distant parties to implement nonlocal quantum operations without physically transferring the participating qubits, making it a promising primitive for distributed quantum computing. We introduce a general framework for deterministic quantum gate teleportation based on path superposition, in which the target nonlocal operation is specified through the phase of a preshared maximally entangled resource and a suitable family of path-dependent local unitary operators. The framework establishes general design conditions that guarantee deterministic teleportation after measurement of the control qubits and the application of local correction operations. As representative realizations, we construct teleportation protocols for controlled-NOT (CNOT) and controlled-Z (CZ) gates, demonstrating that different nonlocal operations can be implemented within the same protocol architecture through appropriate choices of the design parameters. We further outline a proof-of-concept photonic realization based on spatial-path and polarization degrees of freedom. The proposed framework identifies path superposition as a versatile resource for quantum gate teleportation and distributed quantum information processing.
Quantum computers offer computational advantages for specific problems over classical systems [8], but today's devices are limited by qubit counts and susceptibility to noise. Distributed quantum computing (DQC) addresses these constraints by interconnecting quantum processors via quantum networks to enable cooperative execution of quantum algorithms [4]. DQC can be realized either through quantum teleportation [3], which transfers qubit states across nodes, or through remote gates [7], which enact quantum operations between spatially separated qubits while preserving their physical allocation. Both approaches depend on pre-shared entanglement, which must be distributed across potentially multi-hop quantum networks via entanglement swapping [11]. In realistic settings, DQC performance is influenced by factors such as entanglement fidelity, quantum memory coherence time, and routing path length, yet the impact of these parameters on computational fidelity remains insufficiently understood. This work investigates these effects through simulation of distributed Grover circuits executed over quantum networks with 1-4 routers, incorporating entanglement swapping, network delays, and varying physical constraints to assess how network-level properties affect circuit-level performance.
Abstract Quantum teleportation as the key strategy for quantum communication requires pure maximally shared entangled states among quantum nodes. In practice, quantum decoherence drastically degrades the shared entanglement during entanglement distribution, which is a serious challenge for the development of quantum networks. However, most of the decoherence control strategies proposed thus far are either resource-intensive or time-consuming. To overcome this obstacle, we enable noise-resistant teleportation through a noisy channel with a limited number of qubits and without applying time-consuming weak measurements. We apply a quantum gate control unit consisting of a controlled NOT gate and a rotation gate after the original teleportation protocol is accomplished. Furthermore, we demonstrate that a teleportation fidelity of unity is attainable when environment-assisted measurement is added to the proposed teleportation protocol via quantum gates. Moreover, we present an entanglement distribution process by employing the designed quantum gate control unit followed by the deterministic standard teleportation protocol to improve teleportation fidelity by establishing improved shared entanglement. Our performance analysis indicates that the proposed teleportation schemes offer a competitive fidelity and success probability compared with the conventional schemes and a recent weak measurement-based teleportation protocol.
Noise is a major challenge in quantum computing, affecting the reliability of quantum protocols. In this work, we analytically study the impact of various noise processes, such as depolarization, bit flip, and phase flip, on the quantum state teleportation protocol. Each noise process is modeled as a quantum channel and is applied individually to all qubits after the corresponding unitary operations to simulate realistic conditions. We evaluate the fidelity between the ideal and noisy teleported states to quantify the effect of noise. Our analysis shows that the fidelity decreases polynomially, in general, as the noise strength increases for all noise types, highlighting the sensitivity of state teleportation to different noise mechanisms. However, in the low noise regime, the fidelity decreases only linearly, indicating the robustness of the teleportation protocol. These results provide insight into error characterization and can inform strategies for noise mitigation in practical quantum computing applications.