Niraj Kumar | LIP6 - Équipe QI

Graph neural network initialisation of quantum approximate optimisation

Sat, 01 Jan 2022 00:00:00 +0000

Approximate combinatorial optimisation has emerged as one of the most promising application areas for quantum computers, particularly those in the near term. In this work, we focus on the quantum approximate optimisation algorithm (QAOA) for solving the Max-Cut problem. Specifically, we address two problems in the QAOA, how to select initial parameters, and how to subsequently train the parameters to find an optimal solution. For the former, we propose graph neural networks (GNNs) as an initialisation routine for the QAOA parameters, adding to the literature on warm-starting techniques. We show the GNN approach generalises across not only graph instances, but also to increasing graph sizes, a feature not available to other warm-starting techniques. For training the QAOA, we test several optimisers for the MaxCut problem. These include quantum aware/agnostic optimisers proposed in literature and we also incorporate machine learning techniques such as reinforcement and meta-learning. With the incorporation of these initialisation and optimisation toolkits, we demonstrate how the QAOA can be trained as an end-to-end differentiable pipeline.

On the connection between quantum pseudorandomness and quantum hardware assumptions

Sat, 01 Jan 2022 00:00:00 +0000

This paper, for the first time, addresses the questions related to the connections between quantum pseudorandomness and quantum hardware assumptions, specifically quantum physical unclonable functions (qPUFs). Our results show that efficient pseudorandom quantum states (PRS) are sufficient to construct the challenge set for universally unforgeable qPUFs, improving the previous existing constructions based on the Haar-random states. We also show that both the qPUFs and the quantum pseudorandom unitaries (PRUs) can be constructed from each other, providing new ways to obtain PRS from the hardware assumptions. Moreover, we provide a sufficient condition (in terms of the diamond norm) that a set of unitaries should have to be a PRU in order to construct a universally unforgeable qPUF, giving yet another novel insight into the properties of the PRUs. Later, as an application of our results, we show that the efficiency of an existing qPUF-based client–server identification protocol can be improved without losing the security requirements of the protocol.

Efficient Construction of Quantum Physical Unclonable Functions with Unitary t-designs

Sat, 27 Nov 2021 00:00:00 +0000

Quantum physical unclonable functions, or QPUFs, are rapidly emerging as theoretical hardware solutions to provide secure cryptographic functionalities such as key-exchange, message authentication, entity identification among others. Recent works have shown that in order to provide provable security of these solutions against any quantum polynomial time adversary, QPUFs are required to be a unitary sampled uniformly randomly from the Haar measure. This however is known to require an exponential amount of resources. In this work, we propose an efficient construction of these devices using unitary t-designs, called QPUF_t. Along the way, we modify the existing security definitions of QPUFs to include efficient constructions and showcase that QPUF_t still retains the provable security guarantees against a bounded quantum polynomial adversary with t-query access to the device. This also provides the first use case of unitary t-design construction for arbitrary t, as opposed to previous applications of t-designs where usually a few (relatively low) values of t are known to be useful for performing some task. We study the noise-resilience of QPUF_t against specific types of noise, unitary noise, and show that some resilience can be achieved particularly when the error rates affecting individual qubits become smaller as the system size increases. To make the noise-resilience more realistic and meaningful, we conclude that some notion of error mitigation or correction should be introduced.

Optimal quantum-programmable projective measurements with coherent states

Fri, 01 Oct 2021 00:00:00 +0000

We consider a device which can be programed using coherent states of light to approximate a given projective measurement on an input coherent state. We provide and discuss three practical implementations of this programmable projective measurement device with linear optics, involving only balanced beam splitters and single photon threshold detectors. The three schemes optimally approximate any projective measurement onto a program coherent state. We further extend these to the case where there are no assumptions on the input state. In this setting, we show that our scheme enables an efficient verification of an unbounded untrusted source with only local coherent states, balanced beam splitters, and threshold detectors. Exploiting the link between programmable measurements and generalized swap test, we show as a direct application that our schemes provide an asymptotically quadratic improvement in existing quantum fingerprinting protocol to approximate the Euclidean distance between two unit vectors.

Experimental demonstration of quantum advantage for NP verification with limited information

Mon, 08 Feb 2021 00:00:00 +0000

In recent years, many computational tasks have been proposed as candidates for showing a quantum computational advantage, that is an advantage in the time needed to perform the task using a quantum instead of a classical machine. Nevertheless, practical demonstrations of such an advantage remain particularly challenging because of the difficulty in bringing together all necessary theoretical and experimental ingredients. Here, we show an experimental demonstration of a quantum computational advantage in a prover-verifier interactive setting, where the computational task consists in the verification of an NP-complete problem by a verifier who only gets limited information about the proof sent by an untrusted prover in the form of a series of unentangled quantum states. We provide a simple linear optical implementation that can perform this verification task efficiently (within a few seconds), while we also provide strong evidence that, fixing the size of the proof, a classical computer would take much longer time (assuming only that it takes exponential time to solve an NP-complete problem). While our computational advantage concerns a specific task in a scenario of mostly theoretical interest, it brings us a step closer to potential useful applications, such as server-client quantum computing.

Client-Server Identification Protocols with Quantum PUF

Tue, 05 Jan 2021 00:00:00 +0000

Recently, major progress has been made towards the realisation of the quantum internet to enable a broad range of applications that would be out of reach for classical internet. Most of these applications such as delegated quantum computation require running a secure identification protocol between a low-resource and a high-resource party to provide secure communication. Physical Unclonable Functions (PUFs) have been shown as resource-efficient hardware solutions for providing secure identification schemes in both classical and quantum settings. In this work, we propose two identification protocols based on quantum PUFs (qPUFs) as defined by Arapinis et al. In the first protocol, the low-resource party wishes to prove its identity to the high-resource party and in the second protocol, it is vice versa. Unlike existing identification protocols based on Quantum Read-out PUFs which rely on the security against a specific family of attacks, our protocols provide provable exponential security against any Quantum Polynomial-Time (QPT) adversary with resource-efficient parties. We provide a comprehensive comparison between the two proposed protocols in terms of resources such as quantum memory and computing ability required in both parties as well as the communication overhead between them. A stand-out feature of our second protocol is secure identification of a high-resource party by running a purely classical verification algorithm. This is achieved by delegating quantum operations to the high-resource party and utilising the resulting classical outcomes for identification.

Variational Quantum Cloning: Improving Practicality for Quantum Cryptanalysis

Tue, 05 Jan 2021 00:00:00 +0000

Cryptanalysis on standard quantum cryptographic systems generally involves finding optimal adversarial attack strategies on the underlying protocols. The core principle of modelling quantum attacks in many cases reduces to the adversary’s ability to clone unknown quantum states which facilitates the extraction of some meaningful secret information. Explicit optimal attack strategies typically require high computational resources due to large circuit depths or, in many cases, are unknown. In this work, we propose variational quantum cloning (VQC), a quantum machine learning based cryptanalysis algorithm which allows an adversary to obtain optimal (approximate) cloning strategies with short depth quantum circuits, trained using hybrid classical-quantum techniques. The algorithm contains operationally meaningful cost functions with theoretical guarantees, quantum circuit structure learning and gradient descent based optimisation. Our approach enables the end-to-end discovery of hardware efficient quantum circuits to clone specific families of quantum states, which in turn leads to an improvement in cloning fidelites when implemented on quantum hardware: the Rigetti Aspen chip. Finally, we connect these results to quantum cryptographic primitives, in particular quantum coin flipping. We derive attacks on two protocols as examples, based on quantum cloning and facilitated by VQC. As a result, our algorithm can improve near term attacks on these protocols, using approximate quantum cloning as a resource.

Quantum versus Classical Generative Modelling in Finance

Tue, 15 Dec 2020 00:00:00 +0000

Finding a concrete use case for quantum computers in the near term is still an open question, with machine learning typically touted as one of the first fields which will be impacted by quantum technologies. In this work, we investigate and compare the capabilities of quantum versus classical models for the task of generative modelling in machine learning. We use a real world financial dataset consisting of correlated currency pairs and compare two models in their ability to learn the resulting distribution - a restricted Boltzmann machine, and a quantum circuit Born machine. We provide extensive numerical results indicating that the simulated Born machine always at least matches the performance of the Boltzmann machine in this task, and demonstrates superior performance as the model scales. We perform experiments on both simulated and physical quantum chips using the Rigetti forest platform, and also are able to partially train the largest instance to date of a quantum circuit Born machine on quantum hardware. Finally, by studying the entanglement capacity of the training Born machines, we find that entanglement typically plays a role in the problem instances which demonstrate an advantage over the Boltzmann machine.

Experimental demonstration of quantum advantage for one-way communication complexity surpassing best-known classical protocol

Tue, 01 Jan 2019 00:00:00 +0000

Demonstrating a quantum advantage with currently available experimental systems is of utmost importance in quantum information science. While this remains elusive for quantum computation, the field of communication complexity offers the possibility to already explore and showcase this advantage for useful tasks. Here, we define such a task, the Sampling Matching problem, which is inspired by the Hidden Matching problem and features an exponential gap between quantum and classical protocols in the one-way communication model. Our problem allows by its conception a photonic implementation based on encoding in the phase of coherent states of light, the use of a fixed size linear optic circuit, and single-photon detection. This enables us to demonstrate in a proof-of-principle experiment an advantage in the transmitted information resource over the best known classical protocol, something impossible to reach for the original Hidden Matching problem. Our demonstration has implications in quantum verification and cryptographic settings.

Design, analysis and implementation of advanced quantum communication protocols

Wed, 05 Dec 2018 00:00:00 +0000

Abstract :
In this thesis we focus on designing protocols for quantum information processing tasks that can be implemented with current photonic technologies. We start by providing the first example of a communication model and a distributed task for which there exists a realistic quantum protocol asymptotically more efficient than any classical protocol, both in terms of communication and information resources. To this end, we extend the recently proposed coherent state mapping for quantum communication protocols, study the use of coherent state fingerprints over multiple channels and show their role in the design of an efficient quantum protocol for estimating the Euclidean distance between two real vectors within a constant factor. In the second part of the thesis, we propose a new problem in one-way communication model, Sampling Matching problem, for which there exists an exponential gap between a realistic quantum protocol and any randomized classical protocol within bounded error. We implement this problem using attenuated coherent states and linear optics, and show an advantage in using quantum resources from very low input sizes to the problem. This new proposal is a far simplified alternative to the previous problems in one-way communication model due to it requiring O(1) linear optical elements for implementation. This facilitates the implementation of the quantum protocol for arbitrarily large input sizes. Then we introduce a private-key quantum money-scheme with the verification protocol based on the Sampling Matching scheme. We look at the scheme when the Bank prepares notes as single photon superposition states. The features of our scheme include single-round classical interaction with the Bank, linear note re-usability, robustness against experimental imperfection, and an unconditional security against an adversary trying to forge the Bank note. We then follow up this work by proposing a practical quantum money-scheme when the Bank prepares notes as attenuated coherent states. This is an experimentally motivated framework which utilises the advantage offered by the Sampling Matching verification protocol that it requires only O(1) linear optical elements for implementation. Finally we introduce a programmable device whose input states control the the measure- ment operation. In particular, our device is the generalised Sylvester-Hadamard operation to discriminate two unknown coherent states in the setting of a single copy of one state (test state), and M −1 copies of the other state (reference state). Our distinguishing scheme involves M linear optics components (50/50 beam splitters), and M −1 single photon thresh- old detectors. We show that our setting strictly improves the soundness in discriminating two coherent states compared to the setting when one is provided only a single copy of the two states.