Hard Problem Research Articles

Improving the Efficiency of Quantum Circuits for Information Set Decoding

Code-based cryptosystems are a promising option for Post-Quantum Cryptography, as neither classical nor quantum algorithms provide polynomial time solvers for their underlying hard problem. Indeed, to provide sound alternatives to lattice-based cryptosystems, U.S. National Institute of Standards and Technology (NIST) advanced all round 3 code-based cryptosystems to round 4 of its Post-Quantum standardization initiative. We present a complete implementation of a quantum circuit based on the Information Set Decoding (ISD) strategy, the best known one against code-based cryptosystems, providing quantitative measures for the security margin achieved with respect to the quantum-accelerated key recovery on AES, targeting both the current state-of-the-art approach and the NIST estimates. Our work improves the state-of-the-art, reducing the circuit depth by 2 19 to 2 30 for all the parameters of the NIST selected cryptosystems, mainly due to an improved quantum Gauss–Jordan elimination circuit with respect to previous proposals. We show how our Prange’s-based quantum ISD circuit reduces the security margin with respect to its classical counterpart. Finally, we address the concern brought forward in the latest NIST report on the parameters choice for the McEliece cryptosystem, showing that its parameter choice yields a computational effort slightly below the required target level.

Jiddu Krishnamurti and the Problem of Conscience

Jiddu Krishnamurti (1895–1986) remains an enigma for philosophers, historians and lay audiences. Being chosen to be made “World Teacher” by the Theosophical Society (Adyar), Krishnamurti renounced his demi-godhood, in 1929, and went on to become a spiritual teacher. Krishnamurti’s vexed life has increasingly come under scrutiny, in the last three decades, owing to his perceived acts of immoral behavior. This correlates to the growing culture of public denunciations of acts of moral transgressions that we have witnessed particularly over the last decade. Considering the importance of the themes of conscience and morality within Krishnamurti’s “spiritual anarchy,” this paper tries to locate the absent centre of his seemingly decentered philosophy. It draws a comparative trajectory of the centrality of these themes in the lives and works of his philosophical parents, Helena P. Blavatsky and Annie Besant. The paper contends that Krishnamurti’s conception of morality and its role in human suffering needs to be examined, that his philosophy atavistically recapitulates the struggles of Blavatsky and Besant and, ultimately, that his perceived forays into unconscientious realms do not disqualify but reaffirm his crusade against the “still small voice of conscience.”

Certified Dominance and Symmetry Breaking for Combinatorial Optimisation

Symmetry and dominance breaking can be crucial for solving hard combinatorial search and optimisation problems, but the correctness of these techniques sometimes relies on subtle arguments. For this reason, it is desirable to produce efficient, machine-verifiable certificates that solutions have been computed correctly. Building on the cutting planes proof system, we develop a certification method for optimisation problems in which symmetry and dominance breaking is easily expressible. Our experimental evaluation demonstrates that we can efficiently verify fully general symmetry breaking in Boolean satisfiability (SAT) solving, thus providing, for the first time, a unified method to certify a range of advanced SAT techniques that also includes cardinality and parity (XOR) reasoning. In addition, we apply our method to maximum clique solving and constraint programming as a proof of concept that the approach applies to a wider range of combinatorial problems.

Co-lexicographically Ordering Automata and Regular Languages - Part I

The states of a finite-state automaton 𝒩 can be identified with collections of words in the prefix closure of the regular language accepted by 𝒩. But words can be ordered, and among the many possible orders a very natural one is the co-lexicographic order. Such naturalness stems from the fact that it suggests a transfer of the order from words to the automaton’s states. This suggestion is, in fact, concrete and in a number of articles automata admitting a total co-lexicographic ( co-lex for brevity) ordering of states have been proposed and studied. Such class of ordered automata — Wheeler automata — turned out to require just a constant number of bits per transition to be represented and enable regular expression matching queries in constant time per matched character. Unfortunately, not all automata can be totally ordered as previously outlined. In the present work, we lay out a new theory showing that all automata can always be partially ordered, and an intrinsic measure of their complexity can be defined and effectively determined, namely, the minimum width p of one of their admissible co-lex partial orders –dubbed here the automaton’s co-lex width . We first show that this new measure captures at once the complexity of several seemingly-unrelated hard problems on automata. Any NFA of co-lex width p : (i) has an equivalent powerset DFA whose size is exponential in p rather than (as a classic analysis shows) in the NFA’s size; (ii) can be encoded using just Θ(log p ) bits per transition; (iii) admits a linear-space data structure solving regular expression matching queries in time proportional to p 2 per matched character. Some consequences of this new parameterization of automata are that PSPACE-hard problems such as NFA equivalence are FPT in p , and quadratic lower bounds for the regular expression matching problem do not hold for sufficiently small p . Having established that the co-lex width of an automaton is a fundamental complexity measure, we proceed by (i) determining its computational complexity and (ii) extending this notion from automata to regular languages by studying their smallest-width accepting NFAs and DFAs. In this work we focus on the deterministic case and prove that a canonical minimum-width DFA accepting a language ℒ–dubbed the Hasse automaton ℋ of ℒ–can be exhibited. ℋ provides, in a precise sense, the best possible way to (partially) order the states of any DFA accepting ℒ, as long as we want to maintain an operational link with the (co-lexicographic) order of ℒ’s prefixes. Finally, we explore the relationship between two conflicting objectives: minimizing the width and minimizing the number of states of a DFA. In this context, we provide an analogue of the Myhill-Nerode Theorem for co-lexicographically ordered regular languages.

The "Hard Problem of Consciousness" Arises from Human Psychology.

Consciousness presents a "hard problem" to scholars. At stake is how the physical body gives rise to subjective experience. Why consciousness is "hard", however, is uncertain. One possibility is that the challenge arises from ontology-because consciousness is a special property/substance that is irreducible to the physical. Here, I show how the "hard problem" emerges from two intuitive biases that lie deep within human psychology: Essentialism and Dualism. To determine whether a subjective experience is transformative, people judge whether the experience pertains to one's essence, and per Essentialism, one's essence lies within one's body. Psychological states that seem embodied (e.g., "color vision" ∼ eyes) can thus give rise to transformative experience. Per intuitive Dualism, however, the mind is distinct from the body, and epistemic states (knowledge and beliefs) seem particularly ethereal. It follows that conscious perception (e.g., "seeing color") ought to seem more transformative than conscious knowledge (e.g., knowledge of how color vision works). Critically, the transformation arises precisely because the conscious perceptual experience seems readily embodied (rather than distinct from the physical body, as the ontological account suggests). In line with this proposal, five experiments show that, in laypeople's view (a) experience is transformative only when it seems anchored in the human body; (b) gaining a transformative experience effects a bodily change; and (c) the magnitude of the transformation correlates with both (i) the perceived embodiment of that experience, and (ii) with Dualist intuitions, generally. These results cannot solve the ontological question of whether consciousness is distinct from the physical. But they do suggest that the roots of the "hard problem" are partly psychological.

Physical insights from imaginary-time density–density correlation functions

An accurate theoretical description of the dynamic properties of correlated quantum many-body systems, such as the dynamic structure factor S(q, ω), is important in many fields. Unfortunately, highly accurate quantum Monte Carlo methods are usually restricted to the imaginary time domain, and the analytic continuation of the imaginary-time density–density correlation function F(q, τ) to real frequencies is a notoriously hard problem. Here, it is argued that often no such analytic continuation is required because by definition, F(q, τ) contains the same physical information as does S(q, ω), only represented unfamiliarly. Specifically, it is shown how one can directly extract key information such as the temperature or quasi-particle excitation energies from the τ domain, which is highly relevant for equation-of-state measurements of matter under extreme conditions [T. Dornheim et al., Nat. Commun. 13, 7911 (2022)]. As a practical example, ab initio path-integral Monte Carlo results for the uniform electron gas (UEG) are considered, and it is shown that even nontrivial processes such as the roton feature of the UEG at low density [T. Dornheim et al., Commun. Phys. 5, 304 (2022)] are manifested straightforwardly in F(q, τ). A comprehensive overview is given of various useful properties of F(q, τ) and how it relates to the usual dynamic structure factor. In fact, working directly in the τ domain is advantageous for many reasons and opens up multiple avenues for future applications.

Two phase cooperative learning for supervised dimensionality reduction

The simultaneous minimization of the reconstruction and classification error is a hard non convex problem, especially when a non-linear mapping is utilized. To overcome this obstacle, motivated by the widespread success of Cooperative Neural Networks, an innovative supervised dimensionality reduction framework is proposed, based on a cooperative two phase optimization strategy. Specifically, the proposed framework that requires minimal parameter adjustment consists of an autoencoder for dimensionality reduction and a separator network for separability assessment of the embedding. This scheme results in meaningful and discriminable codes, which are optimized for the classification task and are exploitable by any trainable classifier. The experimental results showed that the proposed methodology achieved competitive results against the state-of-the-art competing methods, while being much more efficient in terms of parameter count. Finally, it was empirically justified that the proposed methodology introduces advanced behavioural explainability, while enabling applicability for image generation tasks.

Preparation process and mechanical properties of laser cladding gradient molybdenum coating on copper alloy

Different types of Mo coatings were prepared on the surface of a copper alloy via laser cladding technology in this study to address the problem of low hardness of copper alloy current-carrying friction subsets. Meanwhile, the problems of high reflectivity of copper alloy materials to infrared laser light and mutual insolubility of Cu and Mo were solved by introducing an intermediate layer structure, and the coating process was optimized to obtain a coating with excellent formation. The microstructure, hardness, and interfacial shear bond strength of coatings were tested. Results showed that the Mo coating prepared using a plasma-spheroidized powder had a lower dilution rate and finer and tighter grain growth compared with the Mo coating prepared by crushing agglomerated powder. The coating phase mainly consisted of Mo, Ni3Mo, MoO2, and Cu0.81Ni0.19. The unfused particles present in the plasma-spheroidized powder coating acted as a second hard reinforcing phase, which could significantly increase the hardness of the coating. Three kinds of coatings exhibited strong bond strength, and coatings prepared from different powders fractured in diverse ways. In sum, the plasma-spheroidized Mo coating prepared using the three-way powder feeding method not only had good formation but also possessed the most excellent mechanical properties.

Recognising permuted Demidenko matrices

We solve the recognition problem for permuted Demidenko matrices. This problem is relevant in the context of hard combinatorial optimization problems becoming tractable if the input is a Demidenko matrix. For example the TSP is polynomially solvable for Demidenko distance matrices. In the TSP context we look for a renumbering of the cities resulting in a Demidenko distance matrix, thus in a polynomially solvable case. We can find such a renumbering of n cities in O(n4) time, if it exists.

Branching with a Humean Face

Abstract This paper investigates the prospects of developing a branching modal framework while keeping with the spirit of Humean Supervenience. It is argued that such an approach is bound to face hard problems regarding haecceitism and the notion of recombination. Possible directions for future philosophical developments of branching frameworks are suggested.

Post-Quantum Secure Identity-Based Proxy Blind Signature Scheme on a Lattice.

Blind signatures have been widely applied when privacy preserving is required, and the delegation of blind signature rights and a proxy blind signature (Proxy-BS) become necessary when the signer cannot sign. Existing Proxy-BS schemes are based on traditional cryptographically hard problems, and they cannot resist quantum attacks. Moreover, most current Proxy-BS schemes depend on public key infrastructure (PKI), which leads to high certificate storage and management overhead. To simplify key management and resist quantum attacks, we propose a post-quantum secure identity-based proxy blind signature (ID-Proxy-BS) scheme on a lattice using a matrix cascade technique and lattice cryptosystem. Under the random oracle model (ROM), the security of the proposed scheme is proved. Security shows that the proposed scheme assures security against quantum attacks and satisfies the correctness, blindness, and unforgeability. In addition, we apply the ID-Proxy-BS scheme on a lattice to e-voting and propose a quantum-resistant proxy e-voting system, which is resistant to quantum attacks and achieves the efficiency of e-voting.

User Interest Based Contextual Conversational Recommender System

The Conversational recommender system is for item recommendation during human-machine dialogue, where items can be movies, music, and goods. Scenarios can be intelligent customer service and shopping assistants. The system's goal is to generate high-quality recommendations in short-round interactions. There are two main problems with the system. Firstly, recommending through dialogues is a hard problem as less contextual information is available, resulting in fewer signals for recommendation and less precision for user interest modeling. Secondly, the recommender system considers the absence of interaction between a user and an item as a negative sample. However, this approach can introduce bias in the objectives because non-interaction could potentially be a positive sample. To tackle the previously mentioned concerns, this paper suggests a new model. This model adds an extra knowledge graph to enrich contextual information. Then, this model introduces contrastive learning to separate the distribution between positive and negative samples and improve learning efficiency. This paper further tests the model on the ReDial dataset, and experiments have shown that the method is effective and performs better than previous work.

On Optimum Sequencing of Job Shop Scheduling in Manufacturing Shop

Joh shop scheduling problem (JSSP) is an NP Hard problem. The most obvious real-world application of the JSSP is within manufacturing and machining as the parameter description describes. Companies that are able to optimize their machining schedules are able to reduce production time and cost in order to maximize profits. The aim of the problem is to find the optimum schedule for allocating shared resources over time to complete all n jobs within the problem. In this research we employ probability sequencing and make of comparison of job-shop sequencing rule such as first-come, first-served (FCFS) rule, which can be accomplished only by used of digital simulation. The result shown that using probability sequencing, when the machine is free, a job is selected in accordance with a sequencing rule and is allowed to occupy the machine for a time equal to its predetermined processing time. A job is complete when it has been processed through all centers on its route.

On Optimal Subarchitectures for Quantum Circuit Mapping

Compiling a high-level quantum circuit down to a low-level description that can be executed on state-of-the-art quantum computers is a crucial part of the software stack for quantum computing. One step in compiling a quantum circuit to some device is quantum circuit mapping, where the circuit is transformed such that it complies with the architecture’s limited qubit connectivity. Because the search space in quantum circuit mapping grows exponentially in the number of qubits, it is desirable to consider as few of the device’s physical qubits as possible in the process. Previous work conjectured that it suffices to consider only subarchitectures of a quantum computer composed of as many qubits as used in the circuit. In this work, we refute this conjecture and establish criteria for judging whether considering larger parts of the architecture might yield better solutions to the mapping problem. We show that determining subarchitectures that are of minimal size, i.e., from which no physical qubit can be removed without losing the optimal mapping solution for some quantum circuit, is a very hard problem. Based on a relaxation of the criteria for optimality, we introduce a relaxed consideration that still maintains optimality for practically relevant quantum circuits. Eventually, this results in two methods for computing near-optimal sets of subarchitectures—providing the basis for efficient quantum circuit mapping solutions. We demonstrate the benefits of this novel method for state-of-the-art quantum computers by IBM, Google, and Rigetti.

Approximate NFA universality and related problems motivated by information theory

In coding and information theory, it is desirable to construct maximal codes that can be either variable length codes or error control codes of fixed length. However deciding code maximality boils down to deciding whether a given NFA is universal, and this is a hard problem (including the case of whether the NFA accepts all words of a fixed length). On the other hand, it is acceptable to know whether a code is ‘approximately’ maximal, which then boils down to whether a given NFA is ‘approximately’ universal. Here we introduce the notion of a (1−ε)-universal automaton and present polynomial randomized approximation algorithms to test NFA universality and related hard automata problems, for certain natural probability distributions on the set of words. We also conclude that the randomization aspect is necessary, as approximate universality remains hard for any fixed polynomially computable ε.

Programmable Quantum Simulations of Bosonic Systems with Trapped Ions.

Trapped atomic ion crystals are a leading platform for quantum simulations of spin systems, with programmable and long-range spin-spin interactions mediated by excitations of phonons in the crystal. We describe a complementary approach for quantum simulations of bosonic systems using phonons in trapped-ion crystals, here mediated by excitations of the trapped-ion spins. The scheme enables a high degree of programability across a dense graph of bosonic couplings, utilizing long-lived collective phonon modes in a trapped-ion chain. As such, it is well suited for tackling hard problems such as boson sampling and simulations of long-range bosonic and spin-boson Hamiltonians.

Ising Hamiltonians for Constrained Combinatorial Optimization Problems and the Metropolis‐Hastings Warm‐Starting Algorithm

AbstractQuantum approximate optimization algorithm (QAOA) is a promising variational quantum algorithm for combinatorial optimization problems. However, the implementation of QAOA is limited due to the requirement that the problems be mapped to Ising Hamiltonians and the nonconvex optimization landscapes. Although the Ising Hamiltonians for many NP hard problems have been obtained, a general method to obtain the Ising Hamiltonians for constrained combinatorial optimization problems (CCOPs) has not yet been investigated. In this paper, a general method is introduced to obtain the Ising Hamiltonians for CCOPs and the Metropolis‐Hastings warm‐starting algorithm for QAOA is presented which can provably converge to the global optimal solutions. The effectiveness of this method is demonstrated by tackling the minimum weight vertex cover (MWVC) problem, the minimum vertex cover (MVC) problem, and the maximal independent set problem as examples. The Ising Hamiltonian for the MWVC problem is obtained first time by using this method. The advantages of the Metropolis‐Hastings warm‐starting algorithm presented here is numerically analyzed through solving 30 randomly generated MVC cases with 1‐depth QAOA.

Consciousness and its hard problems: separating the ontological from the evolutionary.

Few of the many theories devised to account for consciousness are explicit about the role they ascribe to evolution, and a significant fraction, by their silence on the subject, treat evolutionary processes as being, in effect, irrelevant. This is a problem for biological realists trying to assess the applicability of competing theories of consciousness to taxa other than our own, and across evolutionary time. Here, as an aid to investigating such questions, a consciousness "machine" is employed as conceptual device for thinking about the different ways ontology and evolution contribute to the emergence of a consciousness composed of distinguishable contents. A key issue is the nature of the evolutionary innovations required for any kind of consciousness to exist, specifically whether this is due to the underappreciated properties of electromagnetic (EM) field effects, as in neurophysical theories, or, for theories where there is no such requirement, including computational and some higher-order theories (here, as a class, algorithmic theories), neural connectivity and the pattern of information flow that connectivity encodes are considered a sufficient explanation for consciousness. In addition, for consciousness to evolve in a non-random way, there must be a link between emerging consciousness and behavior. For the neurophysical case, an EM field-based scenario shows that distinct contents can be produced in the absence of an ability to consciously control action, i.e., without agency. This begs the question of how agency is acquired, which from this analysis would appear to be less of an evolutionary question than a developmental one. Recasting the problem in developmental terms highlights the importance of real-time feedback mechanisms for transferring agency from evolution to the individual, the implication being, for a significant subset of theories, that agency requires a learning process repeated once in each generation. For that subset of theories the question of how an evolved consciousness can exist will then have two components, of accounting for conscious experience as a phenomenon on the one hand, and agency on the other. This reduces one large problem to two, simplifying the task of investigation and providing what may prove an easier route toward their solution.

Deflating the hard problem of consciousness by multiplying explanatory gaps

AbstractRecent philosophy has seen a resurgence of the realist view of sensible qualities such as colour. The view holds that experienced qualities are properties of the objects in the physical environment, not mentally instantiated properties like qualia or merely intentional, illusory ones. Some suggest that this move rids us of the explanatory gap between physical properties and the qualitative features of consciousness. Others say it just relocates the problem of qualities to physical objects in the environment, given that such qualities cannot be derived from the non‐qualitative properties of objects, and it does not resolve the problem of consciousness either. I argue that such an outcome is welcome: if the physical world is full of explanatory gaps, then the mind–body explanatory gap is not so special. Moreover, the explanatory gaps regarding qualities of objects are less puzzling than the brain‐qualia gap. In order to counter the usual worries concerning realism about objective qualities, I introduce ‘imperfect realism’ as an alternative to colour pluralism and complex reductionism, which accommodates realism in the face of widespread perceptual error. I conclude with a discussion of how this ‘multiple‐gaps view’ sits better with a naturalistic framework compared to the Galilean‐Cartesian account of qualities.

Multi-Agent Pathfinding with Predefined Paths: To Wait, or Not to Wait, That Is the Question [Extended Abstract

Multi-agent pathfinding is the task of navigating a set of agents in a shared environment without collisions. Finding an optimal plan is a computationally hard problem, therefore, one may want to sacrifice optimality for faster computation time. In this paper, we present our preliminary work on finding a valid solution using only a predefined path for each agent with the possibility of adding wait actions. This restriction makes some instances unsolvable, however, we show instances where this approach is guaranteed to find a solution.