A major difficulty in quantum rewinding is the fact that measurement is destructive: extracting information from a quantum state irreversibly changes it. This is especially problematic in the context of zero-knowledge simulation, where preserving the adversary's state is essential. In this work, we develop new techniques for quantum rewinding in the context of extraction and zero-knowledge simulation: (1) We show how to extract information from a quantum adversary by rewinding it without disturbing its internal state. We use this technique to prove that important interactive protocols, such as the Goldreich-Micali-Wigderson protocol for graph non-isomorphism and the Feige-Shamir protocol for NP, are zero-knowledge against quantum adversaries. (2) We prove that the Goldreich-Kahan protocol for NP is post-quantum zero knowledge using a simulator that can be seen as a natural quantum extension of the classical simulator. Our results achieve (constant-round) black-box zero-knowledge with negligible simulation error, appearing to contradict a recent impossibility result due to Chia-Chung-Liu-Yamakawa (FOCS 2021). This brings us to our final contribution: (3) We introduce coherent-runtime expected quantum polynomial time, a computational model that (a) captures all of our zero-knowledge simulators, (b) cannot break any polynomial hardness assumptions, and (c) is not subject to the CCLY impossibility. In light of our positive results and the CCLY negative results, we propose coherent-runtime simulation to be the right quantum analogue of classical expected polynomial-time simulation.
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Various fields of science face a reproducibility crisis. For quantum software engineering as an emerging field, it is therefore imminent to focus on proper reproducibility engineering from the start. Yet the provision of reproduction packages is almost universally lacking. Actionable advice on how to build such packages is rare, particularly unfortunate in a field with many contributions from researchers with backgrounds outside computer science. In this article, we argue how to rectify this deficiency by proposing a 1-2-3~approach to reproducibility engineering for quantum software experiments: Using a meta-generation mechanism, we generate DOI-safe, long-term functioning and dependency-free reproduction packages. They are designed to satisfy the requirements of professional and learned societies solely on the basis of project-specific research artefacts (source code, measurement and configuration data), and require little temporal investment by researchers. Our scheme ascertains long-term traceability even when the quantum processor itself is no longer accessible. By drastically lowering the technical bar, we foster the proliferation of reproduction packages in quantum software experiments and ease the inclusion of non-CS researchers entering the field.
Quantum computers have the unique ability to operate relatively quickly in high-dimensional spaces -- this is sought to give them a competitive advantage over classical computers. In this work, we propose a novel quantum machine learning model called the Quantum Discriminator, which leverages the ability of quantum computers to operate in the high-dimensional spaces. The quantum discriminator is trained using a quantum-classical hybrid algorithm in O(N logN) time, and inferencing is performed on a universal quantum computer in linear time. The quantum discriminator takes as input the binary features extracted from a given datum along with a prediction qubit initialized to the zero state and outputs the predicted label. We analyze its performance on the Iris data set and show that the quantum discriminator can attain 99% accuracy in simulation.
We study private classical communication over quantum multiple-access channels. For an arbitrary number of transmitters, we derive a regularized expression of the capacity region. In the case of degradable channels, we establish a single-letter expression for the best achievable sum-rate and prove that this quantity also corresponds to the best achievable sum-rate for quantum communication over degradable quantum multiple-access channels. In our achievability result, we decouple the reliability and privacy constraints, which are handled via source coding with quantum side information and universal hashing, respectively. Hence, we also establish that the multi-user coding problem under consideration can be handled solely via point-to-point coding techniques. As a by-product of independent interest, we derive a distributed leftover hash lemma against quantum side information that ensures privacy in our achievability result.
Enabling additive manufacturing to employ a wide range of novel, functional materials can be a major boost to this technology. However, making such materials printable requires painstaking trial-and-error by an expert operator, as they typically tend to exhibit peculiar rheological or hysteresis properties. Even in the case of successfully finding the process parameters, there is no guarantee of print-to-print consistency due to material differences between batches. These challenges make closed-loop feedback an attractive option where the process parameters are adjusted on-the-fly. There are several challenges for designing an efficient controller: the deposition parameters are complex and highly coupled, artifacts occur after long time horizons, simulating the deposition is computationally costly, and learning on hardware is intractable. In this work, we demonstrate the feasibility of learning a closed-loop control policy for additive manufacturing using reinforcement learning. We show that approximate, but efficient, numerical simulation is sufficient as long as it allows learning the behavioral patterns of deposition that translate to real-world experiences. In combination with reinforcement learning, our model can be used to discover control policies that outperform baseline controllers. Furthermore, the recovered policies have a minimal sim-to-real gap. We showcase this by applying our control policy in-vivo on a single-layer, direct ink writing printer.
We study vulnerability of a uniformly distributed random graph to an attack by an adversary who aims for a global change of the distribution while being able to make only a local change in the graph. We call a graph property $A$ anti-stochastic if the probability that a random graph $G$ satisfies $A$ is small but, with high probability, there is a small perturbation transforming $G$ into a graph satisfying $A$. While for labeled graphs such properties are easy to obtain from binary covering codes, the existence of anti-stochastic properties for unlabeled graphs is not so evident. If an admissible perturbation is either the addition or the deletion of one edge, we exhibit an anti-stochastic property that is satisfied by a random unlabeled graph of order $n$ with probability $(2+o(1))/n^2$, which is as small as possible. We also express another anti-stochastic property in terms of the degree sequence of a graph. This property has probability $(2+o(1))/(n\ln n)$, which is optimal up to factor of 2.
Human-centered systems of systems such as social networks, Internet of Things, or healthcare systems are growingly becoming major facets of modern life. Realistic models of human behavior in such systems play a significant role in their accurate modeling and prediction. Yet, human behavior under uncertainty often violates the predictions by the conventional probabilistic models. Recently, quantum-like decision theories have shown a considerable potential to explain the contradictions in human behavior by applying quantum probability. But providing a quantum-like decision theory that could predict, rather than describe the current, state of human behavior is still one of the unsolved challenges. The main novelty of our approach is introducing an entangled Bayesian network inspired by the entanglement concept in quantum information theory, in which each human is a part of the entire society. Accordingly, society's effect on the dynamic evolution of the decision-making process, which is less often considered in decision theories, is modeled by the entanglement measures. The proposed predictive entangled quantum-like Bayesian network (PEQBN) is evaluated on 22 experimental tasks. Results confirm that PEQBN provides more realistic predictions of human decisions under uncertainty, when compared with classical Bayesian networks and three recent quantum-like approaches.
Kernel matrices, which arise from discretizing a kernel function $k(x,x')$, have a variety of applications in mathematics and engineering. Classically, the celebrated fast multipole method was designed to perform matrix multiplication on kernel matrices of dimension $N$ in time almost linear in $N$ by using techniques later generalized into the linear algebraic framework of hierarchical matrices. In light of this success, we propose a quantum algorithm for efficiently performing matrix operations on hierarchical matrices by implementing a quantum block-encoding of the hierarchical matrix structure. When applied to many kernel matrices, our quantum algorithm can solve quantum linear systems of dimension $N$ in time $O(\kappa \operatorname{polylog}(\frac{N}{\varepsilon}))$, where $\kappa$ and $\varepsilon$ are the condition number and error bound of the matrix operation. This runtime is exponentially faster than any existing quantum algorithms for implementing dense kernel matrices. Finally, we discuss possible applications of our methodology in solving integral equations or accelerating computations in N-body problems.
Identification over quantum broadcast channels is considered. As opposed to the information transmission task, the decoder only identifies whether a message of his choosing was sent or not. This relaxation allows for a double-exponential code size. An achievable identification region is derived for a quantum broadcast channel, and full characterization for the class of classical-quantum broadcast channels. The results are demonstrated for a depolarizing broadcast channel. Furthermore, the identification capacity region of the single-mode pure-loss bosonic broadcast channel is obtained as a consequence. In contrast to the single-user case, the capacity region for identification can be significantly larger than for transmission.
Two-player (antagonistic) games on (possibly stochastic) graphs are a prevalent model in theoretical computer science, notably as a framework for reactive synthesis. Optimal strategies may require randomisation when dealing with inherently probabilistic goals, balancing multiple objectives, or in contexts of partial information. There is no unique way to define randomised strategies. For instance, one can use so-called mixed strategies or behavioural ones. In the most general settings, these two classes do not share the same expressiveness. A seminal result in game theory - Kuhn's theorem - asserts their equivalence in games of perfect recall. This result crucially relies on the possibility for strategies to use infinite memory, i.e., unlimited knowledge of all the past of a play. However, computer systems are finite in practice. Hence it is pertinent to restrict our attention to finite-memory strategies, defined as automata with outputs. Randomisation can be implemented in these in different ways: the initialisation, outputs or transitions can be randomised or deterministic respectively. Depending on which aspects are randomised, the expressiveness of the corresponding class of finite-memory strategies differs. In this work, we study two-player turn-based stochastic games and provide a complete taxonomy of the classes of finite-memory strategies obtained by varying which of the three aforementioned components are randomised. Our taxonomy holds both in settings of perfect and imperfect information.
Quantum machine learning is expected to be one of the first potential general-purpose applications of near-term quantum devices. A major recent breakthrough in classical machine learning is the notion of generative adversarial training, where the gradients of a discriminator model are used to train a separate generative model. In this work and a companion paper, we extend adversarial training to the quantum domain and show how to construct generative adversarial networks using quantum circuits. Furthermore, we also show how to compute gradients -- a key element in generative adversarial network training -- using another quantum circuit. We give an example of a simple practical circuit ansatz to parametrize quantum machine learning models and perform a simple numerical experiment to demonstrate that quantum generative adversarial networks can be trained successfully.
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