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Register a new userA Path Towards Quantum Advantage in Training Deep Generative Models with Quantum Annealers
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The development of quantum-classical hybrid (QCH) algorithms is critical to achieve state-of-the-art computational models. A QCH variational autoencoder (QVAE) was introduced in Ref. [1] by some of the authors of this paper. QVAE consists of a classical auto-encoding structure realized by traditional deep neural networks to perform inference to, and generation from, a discrete latent space. The latent generative process is formalized as thermal sampling from either a quantum or classical Boltzmann machine (QBM or BM). This setup allows quantum-assisted training of deep generative models by physically simulating the generative process with quantum annealers. In this paper, we have successfully employed D-Wave quantum annealers as Boltzmann samplers to perform quantum-assisted, end-to-end training of QVAE. The hybrid structure of QVAE allows us to deploy current-generation quantum annealers in QCH generative models to achieve competitive performance on datasets such as MNIST. The results presented in this paper suggest that commercially available quantum annealers can be deployed, in conjunction with well-crafted classical deep neutral networks, to achieve competitive results in unsupervised and semisupervised tasks on large-scale datasets. We also provide evidence that our setup is able to exploit large latent-space (Q)BMs, which develop slowly mixing modes. This expressive latent space results in slow and inefficient classical sampling, and paves the way to achieve quantum advantage with quantum annealing in realistic sampling applications.
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We benchmark the quantum processing units of the largest quantum annealers to date, the 5000+ qubit quantum annealer Advantage and its 2000+ qubit predecessor D-Wave 2000Q, using tail assignment and exact cover problems from aircraft scheduling scenarios. The benchmark set contains small, intermediate, and large problems with both sparsely connected and almost fully connected instances. We find that Advantage outperforms D-Wave 2000Q for almost all problems, with a notable increase in success rate and problem size. In particular, Advantage is also able to solve the largest problems with 120 logical qubits that D-Wave 2000Q cannot solve anymore. Furthermore, problems that can still be solved by D-Wave 2000Q are solved faster by Advantage. We find that D-Wave 2000Q can only achieve better success rates for a few very sparsely connected problems.
Despite the pursuit of quantum advantages in various applications, the power of quantum computers in neural network computations has mostly remained unknown, primarily due to a missing link that effectively designs a neural network model suitable for quantum circuit implementation. In this article, we present the co-design framework, namely QuantumFlow, to provide such a missing link. QuantumFlow consists of novel quantum-friendly neural networks (QF-Nets), a mapping tool (QF-Map) to generate the quantum circuit (QF-Circ) for QF-Nets, and an execution engine (QF-FB). We discover that, in order to make full use of the strength of quantum representation, it is best to represent data in a neural network as either random variables or numbers in unitary matrices, such that they can be directly operated by the basic quantum logical gates. Based on these data representations, we propose two quantum friendly neural networks, QF-pNet and QF-hNet in QuantumFlow. QF-pNet using random variables has better flexibility, and can seamlessly connect two layers without measurement with more qbits and logical gates than QF-hNet. On the other hand, QF-hNet with unitary matrices can encode 2^k data into k qbits, and a novel algorithm can guarantee the cost complexity to be O(k^2). Compared to the cost of O(2^k)in classical computing, QF-hNet demonstrates the quantum advantages. Evaluation results show that QF-pNet and QF-hNet can achieve 97.10% and 98.27% accuracy, respectively. Results further show that for input sizes of neural computation grow from 16 to 2,048, the cost reduction of QuantumFlow increased from 2.4x to 64x. Furthermore, on MNIST dataset, QF-hNet can achieve accuracy of 94.09%, while the cost reduction against the classical computer reaches 10.85x. To the best of our knowledge, QuantumFlow is the first work to demonstrate the potential quantum advantage on neural network computation.
The scaling up of quantum hardware is the fundamental challenge ahead in order to realize the disruptive potential of quantum technology in information science. Among the plethora of hardware platforms, photonics stands out by offering a modular approach, where the main challenge is to construct sufficiently high-quality building blocks and develop methods to efficiently interface them. Importantly, the subsequent scaling-up will make full use of the mature integrated photonic technology provided by photonic foundry infrastructure to produce small foot-print quantum processors of immense complexity. A fully coherent and deterministic photon-emitter interface is a key enabler of quantum photonics, and can today be realized with solid-state quantum emitters with specifications reaching the quantitative benchmark referred to as Quantum Advantage. This light-matter interaction primer realizes a range of quantum photonic resources and functionalities, including on-demand single-photon and multi-photon entanglement sources, and photon-photon nonlinear quantum gates. We will present the current state-of-the-art in single-photon quantum hardware and the main photonic building blocks required in order to scale up. Furthermore, we will point out specific promising applications of the hardware building blocks within quantum communication and photonic quantum computing, laying out the road ahead for quantum photonics applications that could offer a genuine quantum advantage.
The application in cryptography of quantum algorithms for prime factorization fostered the interest in quantum computing. However, quantum computers, and particularly quantum annealers, can also be helpful to construct secure cryptographic keys. Indeed, finding robust Boolean functions for cryptography is an important problem in sequence ciphers, block ciphers, and hash functions, among others. Due to the super-exponential size $mathcal{O}(2^{2^n})$ of the associated space, finding $n$-variable Boolean functions with global cryptographic constraints is computationally hard. This problem has already been addressed employing generic low-connected incoherent D-Wave quantum annealers. However, the limited connectivity of the Chimera graph, together with the exponential growth in the complexity of the Boolean function design problem, limit the problem scalability. Here, we propose a special-purpose coherent quantum annealing architecture with three couplers per qubit, designed to optimally encode the bent function design problem. A coherent quantum annealer with this tree-type architecture has the potential to solve the $8$-variable bent function design problem, which is classically unsolved, with only $127$ physical qubits and $126$ couplers. This paves the way to reach useful quantum supremacy within the framework of quantum annealing for cryptographic purposes.
Quantum computer, harnessing quantum superposition to boost a parallel computational power, promises to outperform its classical counterparts and offer an exponentially increased scaling. The term quantum advantage was proposed to mark the key point when people can solve a classically intractable problem by artificially controlling a quantum system in an unprecedented scale, even without error correction or known practical applications. Boson sampling, a problem about quantum evolutions of multi-photons on multimode photonic networks, as well as its variants, has been considered as a promising candidate to reach this milestone. However, the current photonic platforms suffer from the scaling problems, both in photon numbers and circuit modes. Here, we propose a new variant of the problem, timestamp membosonsampling, exploiting the timestamp information of single photons as free resources, and the scaling of the problem can be in principle extended to infinitely large. We experimentally verify the scheme on a self-looped photonic chip inspired by memristor, and obtain multi-photon registrations up to 56-fold in 750,000 modes with a Hilbert space up to $10^{254}$. Our work exhibits an integrated and cost-efficient shortcut stepping into the quantum advantage regime in a photonic system far beyond previous scenarios, and provide a scalable and controllable platform for quantum information processing.
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