A hybrid algorithm framework for small quantum computers with application to finding Hamiltonian cycles

Recent works have shown that quantum computers can polynomially speed up certain SAT-solving algorithms even when the number of available qubits is significantly smaller than the number of variables. Here we generalise this approach. We present a framework for hybrid quantum-classical algorithms which utilise quantum computers significantly smaller than the problem size. Given an arbitrarily small ratio of the quantum computer to the instance size, we achieve polynomial speedups for classical divide-and-conquer algorithms, provided that certain criteria on the time- and space-efficiency are met. We demonstrate how this approach can be used to enhance Eppstein's algorithm for the cubic Hamiltonian cycle problem, and achieve a polynomial speedup for any ratio of the number of qubits to the size of the graph.Comment: 20+2 page

Simple proof of confidentiality for private quantum channels in noisy environments

Complete security proofs for quantum communication protocols can be notoriously involved, which convolutes their verification, and obfuscates the key physical insights the security finally relies on. In such cases, for the majority of the community, the utility of such proofs may be restricted. Here we provide a simple proof of confidentiality for parallel quantum channels established via entanglement distillation based on hashing, in the presence of noise, and a malicious eavesdropper who is restricted only by the laws of quantum mechanics. The direct contribution lies in improving the linear confidentiality levels of recurrence-type entanglement distillation protocols to exponential levels for hashing protocols. The proof directly exploits the security relevant physical properties: measurement-based quantum computation with resource states and the separation of Bell-pairs from an eavesdropper. The proof also holds for situations where Eve has full control over the input states, and obtains all information about the operations and noise applied by the parties. The resulting state after hashing is private, i.e., disentangled from the eavesdropper. Moreover, the noise regimes for entanglement distillation and confidentiality do not coincide: Confidentiality can be guaranteed even in situation where entanglement distillation fails. We extend our results to multiparty situations which are of special interest for secure quantum networks.Comment: 5 + 11 pages, 0 + 4 figures, A. Pirker and M. Zwerger contributed equally to this work, replaced with accepted versio

Long-range big quantum-data transmission

We introduce an alternative type of quantum repeater for long-range quantum communication with improved scaling with the distance. We show that by employing hashing, a deterministic entanglement distillation protocol with one-way communication, one obtains a scalable scheme that allows one to reach arbitrary distances, with constant overhead in resources per repeater station, and ultrahigh rates. In practical terms, we show that also with moderate resources of a few hundred qubits at each repeater station, one can reach intercontinental distances. At the same time, a measurement-based implementation allows one to tolerate high loss, but also operational and memory errors of the order of several percent per qubit. This opens the way for long-distance communication of big quantum data.Comment: revised manuscript including new result

Quantum learning unravels quantum system

A quantum computer has a decisive advantage in analyzing quantum experiment resultsQuantum Matter and Optic

Geometry of quantum observables and thermodynamics of small systems

The concept of ergodicity---the convergence of the temporal averages of observables to their ensemble averages---is the cornerstone of thermodynamics. The transition from a predictable, integrable behavior to ergodicity is one of the most difficult physical phenomena to treat; the celebrated KAM theorem is the prime example. This Letter is founded on the observation that for many classical and quantum observables, the sum of the ensemble variance of the temporal average and the ensemble average of temporal variance remains constant across the integrability-ergodicity transition. We show that this property induces a particular geometry of quantum observables---Frobenius (also known as Hilbert-Schmidt) one---that naturally encodes all the phenomena associated with the emergence of ergodicity: the Eigenstate Thermalization effect, the decrease in the inverse participation ratio, and the disappearance of the integrals of motion. As an application, we use this geometry to solve a known problem of optimization of the set of conserved quantities---regardless of whether it comes from symmetries or from finite-size effects---to be incorporated in an extended thermodynamical theory of integrable, near-integrable, or mesoscopic systems

Quantum-accessible reinforcement learning beyond strictly epochal environments

In recent years, quantum-enhanced machine learning has emerged as a particularly fruitful application of quantum algorithms, covering aspects of supervised, unsupervised and reinforcement learning. Reinforcement learning offers numerous options of how quantum theory can be applied, and is arguably the least explored, from a quantum perspective. Here, an agent explores an environment and tries to find a behavior optimizing some figure of merit. Some of the first approaches investigated settings where this exploration can be sped-up, by considering quantum analogs of classical environments, which can then be queried in superposition. If the environments have a strict periodic structure in time (i.e. are strictly episodic), such environments can be effectively converted to conventional oracles encountered in quantum information. However, in general environments, we obtain scenarios that generalize standard oracle tasks. In this work we consider one such generalization, where the environment is not strictly episodic, which is mapped to an oracle identification setting with a changing oracle. We analyze this case and show that standard amplitude-amplification techniques can, with minor modifications, still be applied to achieve quadratic speed-ups, and that this approach is optimal for certain settings. This results constitutes one of the first generalizations of quantum-accessible reinforcement learning.Comment: 8+9 pages, 2 figure

Three-dimensional Gross-Pitaevskii solitary waves in optical lattices: stabilization using the artificial quartic kinetic energy induced by lattice shaking

In this Letter, we show that a three-dimensional Bose-Einstein solitary wave can become stable if the dispersion law is changed from quadratic to quartic. We suggest a way to realize the quartic dispersion, using shaken optical lattices. Estimates show that the resulting solitary waves can occupy as little as $\sim 1/20$-th of the Brillouin zone in each of the three directions and contain as many as $N = 10^{3}$ atoms, thus representing a \textit{fully mobile} macroscopic three-dimensional object.Comment: 8 pages, 1 figure, accepted in Phys. Lett.

Flow Ambiguity: A Path Towards Classically Driven Blind Quantum Computation

Blind quantum computation protocols allow a user to delegate a computation to a remote quantum computer in such a way that the privacy of their computation is preserved, even from the device implementing the computation. To date, such protocols are only known for settings involving at least two quantum devices: either a user with some quantum capabilities and a remote quantum server or two or more entangled but noncommunicating servers. In this work, we take the first step towards the construction of a blind quantum computing protocol with a completely classical client and single quantum server. Specifically, we show how a classical client can exploit the ambiguity in the flow of information in measurement-based quantum computing to construct a protocol for hiding critical aspects of a computation delegated to a remote quantum computer. This ambiguity arises due to the fact that, for a fixed graph, there exist multiple choices of the input and output vertex sets that result in deterministic measurement patterns consistent with the same fixed total ordering of vertices. This allows a classical user, computing only measurement angles, to drive a measurement-based computation performed on a remote device while hiding critical aspects of the computation.Comment: (v3) 14 pages, 6 figures. expands introduction and definition of flow, corrects typos to increase readability; contains a new figure to illustrate example run of CDBQC protocol; minor changes to match the published version.(v2) 12 pages, 5 figures. Corrects motivation for quantities used in blindness analysi

Application of quantum-inspired generative models to small molecular datasets

Quantum and quantum-inspired machine learning has emerged as a promising and challenging research field due to the increased popularity of quantum computing, especially with near-term devices. Theoretical contributions point toward generative modeling as a promising direction to realize the first examples of real-world quantum advantages from these technologies. A few empirical studies also demonstrate such potential, especially when considering quantum-inspired models based on tensor networks. In this work, we apply tensor-network-based generative models to the problem of molecular discovery. In our approach, we utilize two small molecular datasets: a subset of $4989$ molecules from the QM9 dataset and a small in-house dataset of $516$ validated antioxidants from TotalEnergies. We compare several tensor network models against a generative adversarial network using different sample-based metrics, which reflect their learning performances on each task, and multiobjective performances using $3$ relevant molecular metrics per task. We also combined the output of the models and demonstrate empirically that such a combination can be beneficial, advocating for the unification of classical and quantum(-inspired) generative learning.Comment: First versio