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On the Super-exponential Quantum Speedup of Equivariant Quantum Machine Learning Algorithms with SU(dd) Symmetry

Han Zheng, Zimu Li, Junyu Liu, Sergii Strelchuk, Risi KondorJ

ul 18 2022 quant-ph cs.AI cs.LG math-ph math.MP stat.ML arXiv:2207.07250v1

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We introduce a framework of the equivariant convolutional algorithms which is tailored for a number of machine-learning tasks on physical systems with arbitrary SU(dd) symmetries. It allows us to enhance a natural model of quantum computation–permutational quantum computing (PQC) [Quantum Inf. Comput., 10, 470-497 (2010)] –and defines a more powerful model: PQC+. While PQC was shown to be effectively classically simulatable, we exhibit a problem which can be efficiently solved on PQC+ machine, whereas the best known classical algorithms runs in O(n!n2)O(n!n2) time, thus providing strong evidence against PQC+ being classically simulatable. We further discuss practical quantum machine learning algorithms which can be carried out in the paradigm of PQC+.

Generalized possibilistic Theories: the tensor product problem

Eric Buffenoir

Jul 21 2022 quant-ph arXiv:2207.09905v1

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Inspired by the operational quantum logic program, we have the contention that probabilities can be viewed as a derived concept, even in a reconstruction program of Quantum Mechanics. We propose an operational description of physical theories where probabilities are replaced by counterfactual statements belonging to a three-valued (i.e. possibilistic) semantic domain. The space of states and the space of effects are then built as posets put in duality through a Chu 3 space. The convexity requirements on the spaces of states and effects, addressed basically in Generalized Probabilistic Theories, are then replaced by semi-lattice structures on these spaces. The pure states are also easily constructed as completely meet-irreducible elements which generate the whole space of states. The channels (i.e. symmetries) of the theory are then naturally built as Chu morphisms. An axiomatic can then be summarized for what can be called ”Generalized possibilistic Theory” based on this States/Effects Chu space’s category. The problem of bipartite experiment is then addressed as the main skill of this paper. An axiomatic for the tensor product of the space of states is then given and a solution is explicitly constructed. The relations/differences between this tensor product and the tensor product of semi-lattices present in the mathematical literature are then analyzed. This new proposal for the tensor product of semi-lattices can be considered as an interesting byproduct of this work.

Effects of correlated errors on the Quantum Approximate Optimization Algorithm

Joris Kattemölle, Guido Burkard

Jul 22 2022 quant-ph arXiv:2207.10622v1

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The Quantum Approximate Optimization Algorithm (QAOA) has the potential of providing a useful quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) devices. The effects of uncorrelated noise on variational quantum algorithms such as QAOA has been studied intensively. Recent experimental results, however, show that the errors impacting NISQ devices are significantly correlated. We introduce a model for both spatially and temporally (non-Markovian) correlated errors based on classical environmental fluctuators. The model allows for the independent variation of the marginalized spacetime-local error rates and the correlation strength. Using this model, we study the effects of correlated stochastic noise on QAOA. We find evidence that the performance of QAOA improves as the correlation time or correlation length of the noise is increased at fixed local error rates. This shows that noise correlations in itself need not be detrimental for NISQ algorithms such as QAOA.

Quantum vs classical genetic algorithms: A numerical comparison shows faster convergence

Rubén Ibarrondo, Giancarlo Gatti, Mikel Sanz

Jul 20 2022 quant-ph arXiv:2207.09251v1

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Genetic algorithms are heuristic optimization techniques inspired by Darwinian evolution. Quantum computation is a new computational paradigm which exploits quantum resources to speed up information processing tasks. Therefore, it is sensible to explore the potential enhancement in the performance of genetic algorithms by introducing quantum degrees of freedom. Along this line, a modular quantum genetic algorithm has recently been proposed, with individuals encoded in independent registers comprising exchangeable quantum subroutines [arXiv:2203.15039], which leads to different variants. Here, we perform a numerical comparison among quantum and classical genetic algorithms, which was missed in previous literature. In order to isolate the effect of the quantum resources in the performance, the classical variants have been selected to resemble the fundamental characteristics of the quantum genetic algorithms. Under these conditions, we encode an optimization problem in a two-qubit Hamiltonian and face the problem of finding its ground state. A numerical analysis based on a sample of 200 random cases shows that some quantum variants outperform all classical ones in convergence speed towards a near-to-optimal result. Additionally, we have considered a diagonal Hamiltonian and the Hamiltonian of the hydrogen molecule to complete the analysis with two relevant use-cases. If this advantage holds for larger systems, quantum genetic algorithms would provide a new tool to address optimization problems with quantum computers.

Learning quantum dissipation by the neural ordinary differential equation

Li Chen, Yadong Wu

Jul 20 2022 quant-ph cond-mat.dis-nn cond-mat.quant-gas cond-mat.str-el arXiv:2207.09056v1

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Quantum dissipation arises from the unavoidable coupling between a quantum system and its surrounding environment, which is known as a major obstacle in the quantum processing of information. Apart from its existence, how to trace the dissipation from observational data is a crucial topic that may stimulate manners to suppress the dissipation. In this paper, we propose to learn the quantum dissipation from dynamical observations using the neural ordinary differential equation, and then demonstrate this method concretely on two open quantum-spin systems — a large spin system and a spin-1/2 chain. We also investigate the learning efficiency of the dataset, which provides useful guidance for data acquisition in experiments. Our work promisingly facilitates effective modeling and decoherence suppression in open quantum systems

Winning Mastermind Overwhelmingly on Quantum Computers

Lvzhou Li, Jingquan Luo, Yongzhen Xu

Jul 20 2022 quant-ph arXiv:2207.09356v1

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From the 1970s up to now, Mastermind, a classic two-player game, has attracted plenty of attention, not only from the public as a popular game, but also from the academic community as a scientific issue. Mastermind with n positions and k colors is formally described as: the codemaker privately chooses a secret s∈[k]ns∈[k]n, and the coderbreaker want to determine ss in as few queries like fs(x)fs(x) as possible to the codemaker, where fs(x)fs(x) indicates how x is close to s. The complexity of a strategy is measured by the number of queries used. In this work we have a systematic study on quantum strategies for playing Mastermind, obtaining a full characterization of the quantum complexity and optimal quantum algorithms in both non-adaptive and adaptive settings. (i) The quantum complexity is proved to be Θ(k)Θ(k) in the non-adaptive setting. Two non-adaptive quantum algorithms are constructed for Mastermind with nn positions and kk colors that returns the secret with certainty: one with O(klogk)O(klog⁡k)-complexity and the other with O(k)O(k)-complexity. In addition, an algorithm with O(1)O(1) queries is constructed for the case k=2k=2. The algorithm-design skills in the three algorithms have substantial differences, and may be helpful for solving other problems. (ii) The quantum complexity is proved to be Θ(k−−√)Θ(k) in the adaptive setting. An optimal adaptive quantum algorithm is constructed that uses O(k−−√)O(k) queries and returns the secret with certainty. Our results show that the codebreaker wins greatly more on quantum computers than on classical computers. In the non-adaptive setting, when k≤nk≤n the classical complexity is Θ(nlogkmax{log(n/k),1})Θ(nlog⁡kmax{log⁡(n/k),1}), and when k>nk>n the current best classical algorithm has complexity O(klogk)O(klog⁡k). In the adaptive setting, the classical complexity is Θ(nlogklogn+kn)Θ(nlog⁡klog⁡n+kn).

Teaching Qubits to Sing: Mission Impossible?

Eduardo Reck Miranda, Brian N. Siegelwax

Jul 19 2022 quant-ph cs.AI arXiv:2207.08225v2

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This paper introduces a system that learns to sing new tunes by listening to examples. It extracts sequencing rules from input music and uses these rules to generate new tunes, which are sung by a vocal synthesiser. We developed a method to represent rules for musical composition as quantum circuits. We claim that such musical rules are quantum native: they are naturally encodable in the amplitudes of quantum states. To evaluate a rule to generate a subsequent event, the system builds the respective quantum circuit dynamically and measures it. After a brief discussion about the vocal synthesis methods that we have been experimenting with, the paper introduces our novel generative music method through a practical example. The paper shows some experiments and concludes with a discussion about harnessing the creative potential of the system.

Machine Learning assisted excess noise suppression for continuous-variable quantum key distribution

Kexin Liang, Geng Chai, Zhengwen Cao, Qing Wang, Lei Wang, Jinye Peng

Jul 22 2022 quant-ph arXiv:2207.10444v1

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Excess noise is a major obstacle to high-performance continuous-variable quantum key distribution (CVQKD), which is mainly derived from the amplitude attenuation and phase fluctuation of quantum signals caused by channel instability. Here, an excess noise suppression scheme based on equalization is proposed. In this scheme, the distorted signals can be corrected through equalization assisted by a neural network and pilot tone, relieving the pressure on the post-processing and eliminating the hardware cost. For a free-space channel with more intense fluctuation, a classification algorithm is added to classify the received variables, and then the distinctive equalization correction for different classes is carried out. The experimental results show that the scheme can suppress the excess noise to a lower level, and has a significant performance improvement. Moreover, the scheme also enables the system to cope with strong turbulence. It breaks the bottleneck of long-distance quantum communication and lays a foundation for the large-scale application of CVQKD.

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