Month: May 2023

Time-Varying Quantum Channel Simulation via Programmable Quantum Computers using Online Learning

A quantum computer can be programmed to carry out a given functionality in different ways, including the direct engineering of pulse sequences, the design of parametric quantum circuits via quantum machine learning (QML) [1], the use of adaptive measurements on cluster states, and the optimization of a program state operating on a fixed quantum processor. A fundamental result derived in [2] states there is no universal programmable quantum processor that operates with finite-dimensional program states. Since a quantum processor is universal if it can implement any quantum operation, this conclusion implies that the exact simulation of an arbitrary quantum channel on a single programmable quantum processor is impossible. This, in turn, highlights the importance of developing tools for the optimization of quantum programs. Reference [3] addressed the problem of approximately simulating a given quantum channel using a finite-dimensional program state.


Fig. 1: Fig. 1. Time-varying quantum channel ε^t (top) and its simulation ε_(π^t ) via a programmable quantum processor Q controlled by the time-varying program state π^t (bottom).


In our recent work, presented at IEEE ITW 2023, we study the more challenging setting illustrated in Fig. 1, in which the channel to be simulated varies over time. We adopt a worst-case formulation in which the channel variation is arbitrary and chosen by “nature” in a possibly adversarial way. To study this setting, we propose to adopt the framework of online convex optimization [4], which provides tools to track the optimal solution of time-varying convex problems. We specifically develop and analyze an online mirror descent algorithm over the space of positive definite matrices, yielding a matrix exponentiated gradient descent (MEGD) [5]. We prove that the regret of MEGD with respect to an optimized fixed program state is sublinear in time.



Fig. 2: Generalized teleportation processor as a programmable processor Q
operating on one input qubit (n=1) and on a two-qubit program state π

We conduct experiments by adopting the generalized teleportation processor (GTP), shown in Fig. 2, as the programmable quantum processor. GTP can simulate exactly the class of teleportation-covariant channels, modeling Pauli and erasure channels, and is operated here in an adversarial setting with time varying dephasing channels. Fig.3 plots the normalized regret as a function of time T. We observe that, MEGD is able to obtain a normalized regret that decreases sublinearly with T, hence approaching the performance of the reference program that would have been optimal in hindsight.


Fig. 3: Normalized regret as a function of time T for MEGD when simulating a time-varying dephasing channel with dephasing probabilities drawn independently and uniformly at each time in the interval [0.2,p_max) (setting p_max=0.2 models a constant channel).

[1] O. Simeone, “An introduction to quantum machine learning for engineers”,
Foundations and Trends in Signal Processing, vol. 16, no. 1-2, pp. 1–223, 2022.

[2] M. A. Nielsen and I. L. Chuang, “Programmable quantum gate arrays”, Phys. Rev. Lett., vol. 79, pp. 321–324, Jul 1997.

[3] L. Banchi, J. Pereira, S. Lloyd, and S. Pirandola, “Convex optimization of programmable quantum computers”, npj Quantum Information, vol. 6, no. 1, pp. 1–10, 2020.

[4] F. Orabona, “A modern introduction to online learning”, CoRR, vol. abs/1912.13213, 2019.

[5] K. Tsuda, G. Ratsch, and M. K. Warmuth, “Matrix exponentiated gradient updates for on-line learning and Bregman projection”, Journal of Machine Learning Research, vol. 6, no. 34, pp. 995–1018, 2005.

Distributed Quantum Entanglement Distillation via Quantum Machine Learning

Quantum networking, and with it the quantum Internet, rely on the management and exploitation of entanglement. In fact, entangled qubits enable fundamental quantum communication primitives such as teleportation and superdense coding. Practical sources of entangled qubits, such as single-photon detection, are imperfect, producing mixed states with reduced fidelity as compared to ideal, fully entangled, Bell pairs. In order to enhance the fidelity of entangled qubits available at distributed parties, entanglement distillation protocols leverage local operations and classical communication (LOCC). While existing solutions, such as DEJMPS protocol [1] and LOCCNet [2], assume ideal classical communications, we study the case in which communications between the parties holding imperfectly entangled qubits are noisy. As illustrated in Fig. 1, to address this more challenging scenario, we propose the use of quantum machine learning (QML) [3] via parameterized quantum circuits (PQCs).


Fig. 1: Entanglement distillation at two quantum-enabled devices (Alice and Bob) aided by a noisy classical communication channel to a third party (Charlie).


Noise Aware-LOCCNet (NA-LOCCNet)

In our recent work, accepted for presentation at IEEE ICASSP 2023, we introduce NA-LOCCNet, as shown in Fig. 2, which improves average output fidelity while accounting for the channel errors.


Fig. 2: Proposed Noise Aware-LOCCNet (NA-LOCCNet) circuit for distilling two S states.



Fig.3 plots average output fidelity as a function of bit-flip probability of noisy channel for a given input fidelity, whereas Fig. 4 plots the same quantity as a function of input fidelity for a given bit flip probability of noisy channel. In both the figures NA-LOCCNet performs far better than the state of the art protocols.


Fig. 3: Average output fidelity as a function of the bit flip probability p of the noisy classical channels from Alice and Bob to Charlie for input fidelity F = 0.6.


Fig. 4: Average output fidelity, conditioned on a successful distillation, as a function of the input fidelity F for bit flip probability p = 0.25 on the noisy classical channels from Alice and Bob to Charlie. The black dashed line corresponds to the reference performance of a scheme that simply outputs the input state.


In our another recent work, published in Entropy, we have extended the NA-LOCCNet framework to the problem of quantum state discrimination.


[1] D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels”, Phys. Rev. Lett., vol. 77, pp. 2818– 2821, Sep 1996.

[2] X. Zhao, B. Zhao, Z. Wang, Z. Song, and X. Wang, “Practical distributed quantum information processing with LOCCNet,” Quantum Information, vol. 7, no. 1, pp. 1–7, 2021.

[3] O. Simeone, “An introduction to quantum machine learning for engineers”,
Foundations and Trends in Signal Processing, vol. 16, no. 1-2, pp. 1–223, 2022.