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arXiv:2205.00125 · IEEE International Conference on Quantum Computing and Engineering (QCE)

Quantum Telecloning on NISQ Computers

Elijah Pelofske, Andreas Bärtschi, Bryan Garcia, Boris Kiefer, Stephan Eidenbenz

Published Sep 1, 2022• 7 citations
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Abstract

Due to the no-cloning theorem, generating perfect quantum clones of an arbitrary unknown quantum state is not possible, however approximate quantum clones can be constructed. Quantum telecloning is a protocol that originates from a combination of quantum teleportation and quantum cloning. Here we present 1 → 2 and 1 → 3 quantum telecloning circuits, with and without ancilla, that are theoretically optimal (meaning the clones have the highest fidelity allowed by quantum mechanics), universal (meaning the clone fidelity is independent of the state being cloned), and symmetric (meaning the clones all have the same fidelity). We implement these circuits on gate model IBMQ and Quantinuum NISQ hardware and quantify the clone fidelities using parallel single qubit state tomography. Quantum telecloning using mid-circuit measurement with classical feed-forward control (i.e. real time if statements) is demonstrated on the Quantinuum H1-2 device. Two alternative implementations of quantum telecloning, deferred measurement and post selection, are demonstrated on ibmq_montreal, where mid-circuit measurements with real time if statements are not available. Our results show that NISQ devices can achieve near-optimal quantum telecloning fidelity; for example the Quantinuum H1-2 device running the telecloning circuits without ancilla achieved a mean clone fidelity of 0.824 with standard deviation of 0.024 for two clone circuits and 0.765 with standard deviation of 0.022 for three clone circuits. The theoretical fidelity limits are $0.8\bar 3$ for two clones and $0.\bar 7$ for three clones. This demonstrates the viability of performing experimental analysis of quantum information networks and quantum cryptography protocols on NISQ computers.

DOI
10.1109/qce53715.2022.00083

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Due to the no-cloning theorem, generating perfect quantum clones of an arbitrary unknown quantum state is not possible, however approximate quantum clones can be constructed. Quantum telecloning is a protocol that originates from a combination of quantum teleportation and quantum cloning. Here we present 1 → 2 and 1 → 3 quantum telecloning circuits, with and without ancilla, that are theoretically optimal (meaning the clones have the highest fidelity allowed by quantum mechanics), universal (meaning the clone fidelity is independent of the state being cloned), and symmetric (meaning the clones all have the same fidelity). We implement these circuits on gate model IBMQ and Quantinuum NISQ hardware and quantify the clone fidelities using parallel single qubit state tomography. Quantum telecloning using mid-circuit measurement with classical feed-forward control (i.e. real time if statements) is demonstrated on the Quantinuum H1-2 device. Two alternative implementations of quantum telecloning, deferred measurement and post selection, are demonstrated on ibmq_montreal, where mid-circuit measurements with real time if statements are not available. Our results show that NISQ devices can achieve near-optimal quantum telecloning fidelity; for example the Quantinuum H1-2 device running the telecloning circuits without ancilla achieved a mean clone fidelity of 0.824 with standard deviation of 0.024 for two clone circuits and 0.765 with standard deviation of 0.022 for three clone circuits. The theoretical fidelity limits are 0.83ˉ0.8\bar 30.83ˉ for two clones and 0.7ˉ0.\bar 70.7ˉ for three clones. This demonstrates the viability of performing experimental analysis of quantum information networks and quantum cryptography protocols on NISQ computers.
Although perfect copying of an unknown quantum state is not possible, approximate cloning is possible in quantum mechanics. Quantum telecloning is a variant of approximate quantum cloning which uses quantum teleportation to allow for the use of classical communication to create physically separate clones of a quantum state. We present results of a of 1 →9 universal, symmetric, optimal quantum telecloning implementation on a cloud accessible quantum computer - the Quantinuum H1-1 device. The H1-1 device allows direct creation of the telecloning protocol due to real time classical if-statements that are conditional on the mid-circuit measurement outcome of a Bell measurement. In this implementation, we also provide an improvement over previous work for the circuit model description of quantum telecloning, which reduces the required gate depth and gate count for an all-to-all connectivity. The demonstration of creating 9 approximate clones on a quantum processor is the largest number of clones that has been generated, telecloning or otherwise.
Quantum information can not be perfectly cloned, but approximate copies of quantum information can be generated. Quantum telecloning combines approximate quantum cloning, more typically referred as quantum cloning, and quantum teleportation. Quantum telecloning allows approximate copies of quantum information to be constructed by separate parties, using the classical results of a Bell measurement made on a prepared quantum telecloning state. Quantum telecloning can be implemented as a circuit on quantum computers using a classical co-processor to compute classical feed forward instructions using if statements based on the results of a mid-circuit Bell measurement in real time. We present universal, symmetric, optimal1→M1 \rightarrow M1→Mtelecloning circuits, and experimentally demonstrate these quantum telecloning circuits forM=2M=2M=2up toM=10M=10M=10, natively executed with real time classical control systems on IBM Quantum superconducting processors, known as dynamic circuits. We perform the cloning procedure on many different message states across the Bloch sphere, on 7 IBM Quantum processors, optionally using the error suppression technique X-X sequence digital dynamical decoupling. Two circuit optimizations are utilized, one which removes ancilla qubits forM=2,3M=2, 3M=2,3, and one which reduces the total number of gates in the circuit but still uses ancilla qubits. Parallel single qubit tomography with MLE density matrix reconstruction is used in order to compute the mixed state density matrices of the clone qubits, and clone quality is measured using quantum fidelity. These results present one of the largest and most comprehensive NISQ computer experimental analyses on (single qubit) quantum telecloning to date. The clone fidelity sharply decreases to 0.5 forM>5M > 5M>5, but forM=2M=2M=2we are able to achieve a mean clone fidelity of up to 0.79 using dynamical decoupling.
Abstract The present work contains two telecloning protocols for obtaining approximately cloned copies of Bell-like states at two distant locations. The first one is a universal telecloning procedure utilizing ancilla qubits while in the second protocol, no ancilla qubit is required. The analysis of fidelity measuring the quality of the cloned copy is presented. Both the protocols are executed on the IBM platform using Aer Simulator as well as on quantum real computers. By comparing the outcomes of these two cases we conclude that both the protocols are robust.
Symmetric N→MN \to MN→M telecloning and remote quantum state inference
Teleporting unknown quantum states between distant nodes of a network is a significant feature of quantum communication. Few studies, however, have been conducted on N→MN \to MN→M telecloning, in which NNN copies of an unknown quantum state are optimally teleported to M≥NM \geq NM≥N receivers. Previous work requires global POVMs on all copies and auxiliaries; here, we show that symmetric N→MN \to MN→M telecloning can be probabilistically performed using only sequential (or parallel) Bell state measurements (BSMs), allowing the copies to be spatially separated. When successful, the fidelity of each receiver's reduced state saturates the bound imposed by the no-cloning theorem, with the probability of success being independent of MMM. In the case of an `unsuccessful' BSM, we show that the teleportation fidelity is likely to remain high, with the measurement outcome also providing information about the closest Pauli eigenbasis to the unknown state being telecloned. In this sense, each receiver can remotely infer the unknown quantum state with a level of confidence that scales with the number of copies, even if the fidelity of their own reduced state is sub-optimal. We additionally analyze the required resources to ensure the classical-communication fidelity bound is surpassed, both in terms of two-qubit inseparability and varying classes of multipartite entanglement. Surprisingly, we uncover that, at a given iteration of the protocol, pairwise entanglement is not always necessary to increase the teleportation fidelity and is never required to beat the classical bound for N≥2N \geq 2N≥2.
Telecloning -- the combination of quantum teleportation and cloning -- offers a powerful mechanism to disseminate unknown quantum states to multiple spatially separated recipients with optimal fidelity. Despite its conceptual importance for quantum networks, an experimental demonstration of symmetric qubit quantum telecloning remains elusive, particularly due to the challenges of generating multipartite entangled resource states and implementing stable multi-photon interference across distributed nodes. Here, we realize the optimal 1 to 2 symmetric quantum telecloning using a scalable silicon photonic platform. We implement a six-photon protocol using two independent, fiber-linked photonic chips: one generating a heralded input state and the other preparing a four-photon entangled resource state. By performing an interchip Bell-state measurement, we successfully distribute the input state into two optimal clones at remote nodes. We observe an interchip cloning fidelity of 78.45 ±\pm± 1.39%, exceeding the classical limit of 2/3 by 8 standard deviations. Our results demonstrate the robust generation and manipulation of complex multi-photon states between integrated chips, providing a foundational building block for large-scale multi-party quantum networks.
This chapter begins by providing proofs of no-cloning and no-broadcasting theorems. No-cloning theorem makes it possible to detect any eavesdropper on a quantum communication channel. The chapter presents the features of some of the quantum cloning machines. In spite of the no-cloning theorem, it is quite possible to construct a quantum cloning machine which copies an unknown state approximately. A probabilistic cloning machine has been proposed which can succeed only with a probability. When it succeeds it will give a perfect copy. This probabilistic quantum cloning is much useful in studying the B92 quantum key distribution protocol which involves only two non-orthogonal states and we can try to clone it with the largest probability. A telecloning scheme combines cloning with teleportation. A quantum telecloning system for two-level system in which one input is sent to M-receivers has been proposed. The no-hiding theorem is found to have applications in black hole evaporation, quantum teleportation and private quantum channels.