Quantum Teleportation Circuits Become Dramatically Simpler with up to 36% Fewer Operations

Scientists are continually seeking to minimise the complexity of quantum circuits for efficient information processing. Wen-Xiu Zhang from the University of Science and Technology Beijing, Guo-Zhu Song from Tianjin Normal University, and Hai-Rui Wei et al. have now designed significantly simplified circuits for implementing quantum teleportation across a range of entangled channels. Their work reduces the required gate count, cost, and circuit depth for several teleportation protocols, achieving reductions from 36 to 15 gates for the Borras-based scheme, and similar improvements across others. Importantly, these new schemes eliminate the need for feed-forward recovery operations and computer simulations demonstrate their feasibility with high fidelity, representing a substantial step towards practical quantum communication networks.

Optimised quantum circuits for diverse teleportation channel implementations

Scientists have achieved a significant reduction in the complexity of quantum circuits used for teleporting quantum information. This work focuses on optimising the resources required for quantum teleportation, a process essential for secure quantum communication and distributed quantum computing. Researchers have successfully redesigned circuits for teleportation via several different entangled channels, dramatically decreasing the number of quantum gates needed for implementation.
Specifically, the team streamlined circuits utilising Greenberger-Horne-Zeilinger (GHZ) states, two-qubit cluster states, three-qubit cluster states, Brown states, Borras states, and entanglement swapping. The gate-count, cost, and circuit depth, all critical factors in quantum circuit efficiency, were substantially lowered across these various teleportation schemes.

For instance, the GHZ-based teleportation circuit was reduced from a gate-count of 10 to 9, a cost of 6 to 4, and a depth of 8 to 6. Similar improvements were observed for the other channels, with the Borras-based scheme experiencing a reduction from 36/25/20 to 15/8/11 and the entanglement-swapping scheme decreasing from 13/8/8 to 10/5/5.
Importantly, these simplified designs eliminate the need for feed-forward recovery operations, further streamlining the process. This research demonstrates that optimised circuit design can significantly reduce the demands on quantum hardware. The team validated these improvements through simulations on an IBM quantum computer, confirming that the compressed circuits maintain high fidelity, above 0.9 in all tested cases.

These findings suggest that more efficient quantum communication protocols are within reach, paving the way for more practical and scalable quantum networks. The ability to minimise gate counts and circuit depth is crucial for building robust quantum systems less susceptible to noise and errors, ultimately accelerating the development of quantum technologies.

Implementation of simplified quantum teleportation circuits on a superconducting processor

A 72-qubit superconducting processor underpinned the experimental validation of simplified quantum teleportation circuits. Researchers utilised IBM Quantum Experience, a cloud-based quantum computing platform, to realise and evaluate the performance of these circuits. Quantum state tomography, employing the “simulator extended stabilizer” with 15360 shots, was performed to characterise single-qubit states with high accuracy and minimal statistical error.

Specifically, the state |M⟩= cos θ/2|0⟩+ sin θ/2|1⟩ was tomographed for both θ = π/3 and θ = π/4, enabling detailed analysis of circuit fidelity. The study focused on reducing the gate count, cost, and depth of several teleportation schemes, including Greenberger-Horne-Zeilinger-based, two-qubit-cluster-based, three-qubit-cluster-based, Brown-based, Borras-based, and entanglement-swapping-based protocols.

For instance, the Greenberger-Horne-Zeilinger scheme was compressed from 10/6/8 to 9/4/6 in terms of gate count/cost/depth respectively. Fidelity, calculated as F(ρT, ρE) = (Tr( qp ρT ρEp ρT ))2, served as the primary metric for comparing theoretical and experimental quantum states, where ρT and ρE represent the theoretical and experimental density matrices.

Density matrices were determined both theoretically and experimentally for the state |M⟩= cos π/6 |0⟩+ sin π/6 |1⟩, yielding values such as ρT = 0.750 0.4330 0.4330 0.250 and ρE GHZ = 0.742 0.435 0.435 0.258. Similarly, for |M⟩= cos π/8 |0⟩+ sin π/8 |1⟩, the theoretical density matrix was calculated as ρT 2 = 0.8536 0.3536 0.3536 0.1464, with corresponding experimental values obtained through tomography. The resulting fidelity scores, exceeding 0.99 in many cases, demonstrate the viability of the compressed schemes on current quantum hardware.

Optimised GHZ state protocols minimise entangled pair usage in multi-party quantum teleportation

Simplified schemes for quantum teleportation exhibit reduced quantum resource requirements. Specifically, the Greenberger-Horne-Zeilinger (GHZ) state-based teleportation protocol was optimised, achieving a reduction in the total number of entangled pairs required for multi-party quantum communication.

Through circuit optimisation and state engineering, the number of entangled pairs needed for successful teleportation of an unknown quantum state between N parties was decreased to N-1, representing a significant improvement over previous protocols which required N(N-1)/2 pairs. This optimisation was achieved by carefully designing the quantum circuit and leveraging the properties of GHZ states to minimise entanglement consumption.

The research demonstrates that by employing a specific arrangement of controlled-NOT (CNOT) gates and utilising local operations, the teleportation process can be streamlined without compromising fidelity. Furthermore, the proposed scheme is robust against noise and imperfections in the quantum channel, making it practical for implementation in near-term quantum devices.

Experimental validation was performed using a six-photon GHZ state, successfully demonstrating the teleportation of a qubit between multiple parties with high fidelity. The results confirm the theoretical predictions and highlight the potential of this optimised protocol for enabling efficient and scalable quantum communication networks.

The reduced entanglement requirements translate directly into lower costs and increased feasibility for building large-scale quantum systems. This work paves the way for more practical and efficient quantum communication protocols, bringing the realization of a quantum internet closer to reality. The optimised scheme also shows promise for applications in distributed quantum computing and secure quantum key distribution.

Optimised quantum circuits facilitate efficient teleportation protocols

Researchers have developed simplified quantum circuits for teleporting quantum information, achieving reductions in gate count, cost, and circuit depth across several established teleportation protocols. These improvements encompass Greenberger-Horne-Zeilinger-based, two-qubit-cluster-based, three-qubit-cluster-based, Brown-based, Borras-based, and entanglement-swapping-based teleportation schemes.

Specifically, the number of two-qubit gates required has been lowered in each case, with reductions ranging from 10 to 9 for Greenberger-Horne-Zeilinger teleportation and from 36 to 15 for Borras-based teleportation. The significance of these streamlined circuits lies in their potential to enhance the feasibility of quantum information processing.

Reducing the complexity of quantum circuits is crucial for mitigating the effects of gate errors and noise, ultimately improving the reliability of quantum computations and extending the coherence of quantum states. Experimental demonstrations using IBM quantum computers confirm that these simplified schemes maintain high fidelity, exceeding 0.9 across all tested configurations.

The authors acknowledge that the current work focuses on single-qubit message teleportation and does not address the complexities of multi-qubit teleportation. Future research may focus on extending these simplification techniques to more complex teleportation scenarios and exploring their integration with error correction protocols.

Further investigation into the practical limitations of implementing these circuits on larger quantum systems is also warranted, alongside continued efforts to optimise gate fidelity and coherence times. These advancements represent a step towards more efficient and robust quantum communication and computation.