IA Scholar Query: Computational Collapse of Quantum State with Application to Oblivious Transfer.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 03 Aug 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Constant Variables: An Artist-led Curatorial Methodology
https://scholar.archive.org/work/zbyyb3dkojbopcf7jsonto7jzq
In this exegesis I argue for an artist-led curatorial methodology focussed on adapting to the constant variables of artist and context to generate exhibitions that are sensitive and responsive to the artworks they present. I reflect on my experience of curating exhibitions with three artists from Aoteaora New Zealand, Emma Fitts (Pākehā), Shannon Te Ao (Ngāti Tūwharetoa, Ngāti Wairangi, Te Pāpaka-a-Māui) and Ruth Buchanan (Te Ātiawa, Taranaki), who were each working with archives. This exegesis articulates my curatorial methodology as being flexible and responsive to an artist's practice, which I define as artist-led curating.Melanie Oliverwork_zbyyb3dkojbopcf7jsonto7jzqWed, 03 Aug 2022 00:00:00 GMTDynamic deformables
https://scholar.archive.org/work/ail7xnlyuzeblargndqwropb3e
Simulating dynamic deformation has been an integral component of Pixar's storytelling since Boo's shirt in Monsters, Inc. (2001). Recently, several key transformations have been applied to Pixar's core simulator Fizt that improve its speed, robustness, and generality. Starting with Coco (2017), improved collision detection and response were incorporated into the cloth solver, then with Cars 3 (2017) 3D solids were introduced, and in Onward (2020) clothing is allowed to interact with a character's body with two-way coupling. The 3D solids are based on a fast, compact, and powerful new formulation that we have published over the last few years at SIGGRAPH. Under this formulation, the construction and eigendecomposition of the force gradient, long considered the most onerous part of the implementation, becomes fast and simple. We provide a detailed, self-contained, and unified treatment here that is not available in the technical papers. We also provide, for the first time, open-source C++ implementations of many of the described algorithms. This new formulation is only a starting point for creating a simulator that is up challenges of a production environment. One challenge is performance: we discuss our current best practices for accelerating system assembly and solver performance. Another challenge that requires considerable attention is robust collision detection and response. Much has been written about collision detection approaches such as proximity-queries, continuous collisions and global intersection analysis. We discuss our strategies for using these techniques, which provides us with valuable information that is needed to handle challenging scenarios.Theodore Kim, David Eberlework_ail7xnlyuzeblargndqwropb3eTue, 02 Aug 2022 00:00:00 GMTQuantum Computing: Lecture Notes
https://scholar.archive.org/work/2pcfo6u7jzg25alp6mv6fq3w2y
This is a set of lecture notes suitable for a Master's course on quantum computation and information from the perspective of theoretical computer science. The first version was written in 2011, with many extensions and improvements in subsequent years. The first 10 chapters cover the circuit model and the main quantum algorithms (Deutsch-Jozsa, Simon, Shor, Hidden Subgroup Problem, Grover, quantum walks, Hamiltonian simulation and HHL). They are followed by 3 chapters about complexity, 4 chapters about distributed ("Alice and Bob") settings, a chapter about quantum machine learning, and a final chapter about quantum error correction. Appendices A and B give a brief introduction to the required linear algebra and some other mathematical and computer science background. All chapters come with exercises, with some hints provided in Appendix C.Ronald de Wolfwork_2pcfo6u7jzg25alp6mv6fq3w2yTue, 02 Aug 2022 00:00:00 GMTQuantum machine learning for chemistry and physics
https://scholar.archive.org/work/ts35ancqmvay5fhyqya6degva4
Machine learning (ML) has emerged as a formidable force for identifying hidden but pertinent patterns within a given data set with the objective of subsequent generation of automated predictive behavior. In recent years, it is safe to conclude that ML and its close cousin, deep learning (DL), have ushered in unprecedented developments in all areas of physical sciences, especially chemistry. Not only classical variants of ML, even those trainable on near-term quantum hardwares have been developed with promising outcomes. Such algorithms have revolutionized materials design and performance of photovoltaics, electronic structure calculations of ground and excited states of correlated matter, computation of force-fields and potential energy surfaces informing chemical reaction dynamics, reactivity inspired rational strategies of drug designing and even classification of phases of matter with accurate identification of emergent criticality. In this review we shall explicate a subset of such topics and delineate the contributions made by both classical and quantum computing enhanced machine learning algorithms over the past few years. We shall not only present a brief overview of the well-known techniques but also highlight their learning strategies using statistical physical insight. The objective of the review is not only to foster exposition of the aforesaid techniques but also to empower and promote cross-pollination among future research in all areas of chemistry which can benefit from ML and in turn can potentially accelerate the growth of such algorithms.Manas Sajjan, Junxu Li, Raja Selvarajan, Shree Hari Sureshbabu, Sumit Suresh Kale, Rishabh Gupta, Vinit Singh, Sabre Kaiswork_ts35ancqmvay5fhyqya6degva4Mon, 18 Jul 2022 00:00:00 GMTA Constant Lower Bound for Any Quantum Protocol for Secure Function Evaluation
https://scholar.archive.org/work/fupuvszy4zgqvdnlgrnh3znl4a
Secure function evaluation is a two-party cryptographic primitive where Bob computes a function of Alice's and his respective inputs, and both hope to keep their inputs private from the other party. It has been proven that perfect (or near perfect) security is impossible, even for quantum protocols. We generalize this no-go result by exhibiting a constant lower bound on the cheating probabilities for any quantum protocol for secure function evaluation, and present many applications from oblivious transfer to the millionaire's problem. Constant lower bounds are of practical interest since they imply the impossibility to arbitrarily amplify the security of quantum protocols by any means.Sarah A. Osborn, Jamie Sikora, François Le Gall, Tomoyuki Morimaework_fupuvszy4zgqvdnlgrnh3znl4aMon, 04 Jul 2022 00:00:00 GMTSuccinct Classical Verification of Quantum Computation
https://scholar.archive.org/work/olh2roppmreoxcrajic6t2t3fm
We construct a classically verifiable succinct interactive argument for quantum computation (BQP) with communication complexity and verifier runtime that are poly-logarithmic in the runtime of the BQP computation (and polynomial in the security parameter). Our protocol is secure assuming the post-quantum security of indistinguishability obfuscation (iO) and Learning with Errors (LWE). This is the first succinct argument for quantum computation in the plain model; prior work (Chia-Chung-Yamakawa, TCC '20) requires both a long common reference string and non-black-box use of a hash function modeled as a random oracle. At a technical level, we revisit the framework for constructing classically verifiable quantum computation (Mahadev, FOCS '18). We give a self-contained, modular proof of security for Mahadev's protocol, which we believe is of independent interest. Our proof readily generalizes to a setting in which the verifier's first message (which consists of many public keys) is compressed. Next, we formalize this notion of compressed public keys; we view the object as a generalization of constrained/programmable PRFs and instantiate it based on indistinguishability obfuscation. Finally, we compile the above protocol into a fully succinct argument using a (sufficiently composable) succinct argument of knowledge for NP. Using our framework, we achieve several additional results, including - Succinct arguments for QMA (given multiple copies of the witness), - Succinct non-interactive arguments for BQP (or QMA) in the quantum random oracle model, and - Succinct batch arguments for BQP (or QMA) assuming post-quantum LWE (without iO).James Bartusek, Yael Tauman Kalai, Alex Lombardi, Fermi Ma, Giulio Malavolta, Vinod Vaikuntanathan, Thomas Vidick, Lisa Yangwork_olh2roppmreoxcrajic6t2t3fmWed, 29 Jun 2022 00:00:00 GMTDelocalized and Dynamical Catalytic Randomness and Information Flow
https://scholar.archive.org/work/wukz5tjberbehou53wnkftccwq
We generalize the theory of catalytic quantum randomness to delocalized and dynamical settings. First, we expand the resource theory of randomness (RTR) by calculating the amount of entropy catalytically extractable from a correlated or dynamical randomness source. In doing so, we show that no entropy can be catalytically extracted when one cannot implement local projective measurement on randomness source without altering its state. The RTR, as an archetype of the 'concave' resource theory, is complementary to the convex resource theories in which the amount of randomness required to erase the resource is a resource measure. As an application, we prove that quantum operation cannot be hidden in correlation between two parties without using randomness, which is the dynamical generalization of the no-hiding theorem. Second, we study the physical properties of information flow. Popularized quotes like "information is physical" or "it from bit" suggest the matter-like picture of information that can travel with the definite direction while leaving detectable traces on its region of departure. To examine the validity of this picture, we focus on that catalysis of randomness models directional flow of information with the distinguished source and recipient. We show that classical information can always spread from its source without altering its source or its surrounding context, like an immaterial entity, while quantum information cannot. We suggest an approach to formal definition of semantic quantum information and claim that utilizing semantic information is equivalent to using a partially depleted information source. By doing so, we unify the utilization of semantic and non-semantic quantum information and conclude that one can always extract more information from an incompletely depleted classical randomness source, but it is not possible for quantum randomness sources.Seok Hyung Lie, Hyunseok Jeongwork_wukz5tjberbehou53wnkftccwqThu, 23 Jun 2022 00:00:00 GMTMulticore Quantum Computing
https://scholar.archive.org/work/voifsg4u6zhyxgdqjzazovxvky
Any architecture for practical quantum computing must be scalable. An attractive approach is to create multiple cores, computing regions of fixed size that are well-spaced but interlinked with communication channels. This exploded architecture can relax the demands associated with a single monolithic device: the complexity of control, cooling and power infrastructure as well as the difficulties of cross-talk suppression and near-perfect component yield. Here we explore interlinked multicore architectures through analytic and numerical modelling. While elements of our analysis are relevant to diverse platforms, our focus is on semiconductor electron spin systems in which numerous cores may exist on a single chip. We model shuttling and microwave-based interlinks and estimate the achievable fidelities, finding values that are encouraging but markedly inferior to intra-core operations. We therefore introduce optimsed entanglement purification to enable high-fidelity communication, finding that 99.5% is a very realistic goal. We then assess the prospects for quantum advantage using such devices in the NISQ-era and beyond: we simulate recently proposed exponentially-powerful error mitigation schemes in the multicore environment and conclude that these techniques impressively suppress imperfections in both the inter- and intra-core operations.Hamza Jnane, Brennan Undseth, Zhenyu Cai, Simon C Benjamin, Bálint Koczorwork_voifsg4u6zhyxgdqjzazovxvkyWed, 08 Jun 2022 00:00:00 GMTAnatomy of single-field inflationary models for primordial black holes
https://scholar.archive.org/work/5rpo7cwigngfpnn5efsmsuhnle
We construct an analytically solvable simplified model that captures the essential features for primordial black hole (PBH) production in most models of single-field inflation. The construction makes use of the Wands duality between the constant-roll (or slow-roll) and the preceding ultra-slow-roll phases and can be realized by a simple inflaton potential of two joined parabolas. Within this framework, it is possible to formulate explicit inflationary scenarios consistent with the CMB observations and copious production of PBHs of arbitrary mass. We quantify the variability of the shape of the peak in the curvature power spectrum in different inflationary scenarios and discuss its implications for probing PBHs with scalar-induced gravitational wave backgrounds. We find that the COBE/Firas μ-distortion constraints exclude the production of PBHs heavier than 10^4 M_⊙ in single-field inflation.Alexandros Karam, Niko Koivunen, Eemeli Tomberg, Ville Vaskonen, Hardi Veermäework_5rpo7cwigngfpnn5efsmsuhnleTue, 07 Jun 2022 00:00:00 GMTDeniable Encryption in a Quantum World
https://scholar.archive.org/work/ox6u5jqywren5l27rczinql3y4
(Sender-)Deniable encryption provides a very strong privacy guarantee: a sender who is coerced by an attacker into "opening" their ciphertext after-the-fact is able to generate "fake" local random choices that are consistent with any plaintext of their choice. The only known fully-efficient constructions of public-key deniable encryption rely on indistinguishability obfuscation (iO) (which currently can only be based on sub-exponential hardness assumptions). In this work, we study (sender-)deniable encryption in a setting where the encryption procedure is a quantum algorithm, but the ciphertext is classical. First, we propose a quantum analog of the classical definition in this setting. We give a fully efficient construction satisfying this definition, assuming the quantum hardness of the Learning with Errors (LWE) problem. Second, we show that quantum computation unlocks a fundamentally stronger form of deniable encryption, which we call perfect unexplainability. The primitive at the heart of unexplainability is a quantum computation for which there is provably no efficient way, such as exhibiting the "history of the computation", to establish that the output was indeed the result of the computation. We give a construction which is secure in the random oracle model, assuming the quantum hardness of LWE. Crucially, this notion implies a form of protection against coercion "before-the-fact", a property that is impossible to achieve classically.Andrea Coladangelo, Shafi Goldwasser, Umesh Vaziraniwork_ox6u5jqywren5l27rczinql3y4Fri, 03 Jun 2022 00:00:00 GMTOn the Controllability of Artificial Intelligence: An Analysis of Limitations
https://scholar.archive.org/work/ih35iy2h7vag3grsgmzwzfr46y
The invention of artificial general intelligence is predicted to cause a shift in the trajectory of human civilization. In order to reap the benefits and avoid the pitfalls of such a powerful technology it is important to be able to control it. However, the possibility of controlling artificial general intelligence and its more advanced version, superintelligence, has not been formally established. In this paper, we present arguments as well as supporting evidence from multiple domains indicating that advanced AI cannot be fully controlled. The consequences of uncontrollability of AI are discussed with respect to the future of humanity and research on AI, and AI safety and security.Roman V. Yampolskiywork_ih35iy2h7vag3grsgmzwzfr46yWed, 25 May 2022 00:00:00 GMTEmergent tracer dynamics in constrained quantum systems
https://scholar.archive.org/work/pho4gt2745gxngliynjvalhdam
We show how the tracer motion of tagged, distinguishable particles can effectively describe transport in various homogeneous quantum many-body systems with constraints. We consider systems of spinful particles on a one-dimensional lattice subjected to constrained spin interactions, such that some or even all multipole moments of the effective spin pattern formed by the particles are conserved. On the one hand, when all moments - and thus the entire spin pattern - are conserved, dynamical spin correlations reduce to tracer motion identically, generically yielding a subdiffusive dynamical exponent z=4. This provides a common framework to understand the dynamics of several constrained lattice models, including models with XNOR or tJ_z - constraints. We consider random unitary circuit dynamics with such a conserved spin pattern and use the tracer picture to obtain exact expressions for their late-time dynamical correlations. Our results can also be extended to integrable quantum many-body systems that feature a conserved spin pattern but whose dynamics is insensitive to the pattern, which includes for example the folded XXZ spin chain. On the other hand, when only a finite number of moments of the pattern are conserved, the dynamics is described by a convolution of the internal hydrodynamics of the spin pattern with a tracer distribution function. As a consequence, we find that the tracer universality is robust in generic systems if at least the quadrupole moment of the pattern remains conserved. In cases where only total magnetization and dipole moment of the pattern are constant, we uncover an intriguing coexistence of two processes with equal dynamical exponent but different scaling functions, which we relate to phase coexistence at a first order transition.Johannes Feldmeier, William Witczak-Krempa, Michael Knapwork_pho4gt2745gxngliynjvalhdamMon, 16 May 2022 00:00:00 GMTQuantum Universally Composable Oblivious Linear Evaluation
https://scholar.archive.org/work/6y2oingfevempedev5p4xvro5a
Oblivious linear evaluation is a generalization of oblivious transfer, whereby two distrustful parties obliviously compute a linear function, f (x) = ax + b, i.e., each one provides their inputs that remain unknown to the other, in order to compute the output f (x) that becomes known to only one of them. From both a structural and a security point-of-view, oblivious linear evaluation is fundamental for arithmetic-based secure multi-party computation protocols. In the classical case it is known that oblivious linear evaluation can be generated based on oblivious transfer, and quantum counterparts of these protocols can, in principle, be constructed as straightforward extensions based on quantum oblivious transfer. Here, we present the first, to the best of our knowledge, quantum protocol for oblivious linear evaluation that, furthermore, does not rely on quantum oblivious transfer. We start by presenting a semi-honest protocol and then we extend it to the malicious setting employing a commit-and-open strategy. Our protocol uses high-dimensional quantum states to obliviously compute the linear function, f (x), on Galois Fields of prime dimension or prime-power dimension. These constructions utilize the existence of a complete set of mutually unbiased bases in prime-power dimension Hilbert spaces and their linear behaviour upon the Heisenberg-Weyl operators. We also generalize our protocol to achieve vector oblivious linear evaluation, where several instances of oblivious linear evaluation are generated, thus making the protocol more efficient. We prove the protocols to have static security in the framework of quantum universal composability.Manuel B. Santos, Paulo Mateus, Chrysoula Vlachouwork_6y2oingfevempedev5p4xvro5aFri, 29 Apr 2022 00:00:00 GMTSPIKE: Secure and Private Investigation of the Kidney Exchange problem
https://scholar.archive.org/work/7a56fd33mjhw7cskocovjz3vae
The kidney exchange problem (KEP) addresses the matching of patients in need for a replacement organ with compatible living donors. Ideally many medical institutions should participate in a matching program to increase the chance for successful matches. However, to fulfill legal requirements current systems use complicated policy-based data protection mechanisms that effectively exclude smaller medical facilities to participate. Employing secure multi-party computation (MPC) techniques provides a technical way to satisfy data protection requirements for highly sensitive personal health information while simultaneously reducing the regulatory burdens. Results: We have designed, implemented, and benchmarked SPIKE, a secure MPC-based privacy-preserving KEP which computes a solution by finding matching donor-recipient pairs in a graph structure. SPIKE matches 40 pairs in cycles of length 2 in less than 4 minutes and outperforms the previous state-of-the-art protocol by a factor of 400x in runtime while providing medically more robust solutions. Conclusions: We show how to solve the KEP in a robust and privacy-preserving manner achieving practical performance. The usage of MPC techniques fulfills many data protection requirements on a technical level, allowing smaller health care providers to directly participate in a kidney exchange with reduced legal processes.Timm Birka, Kay Hamacher, Tobias Kussel, Helen Möllering, Thomas Schneiderwork_7a56fd33mjhw7cskocovjz3vaeThu, 21 Apr 2022 00:00:00 GMTSimulating fermionic systems on classical and quantum computing devices
https://scholar.archive.org/work/ddu3szbvtzgntb2tyyo2vj5ena
This thesis presents a theoretical study of topics related to the simulation of quantum mechanical systems on classical and quantum computers. A large part of this work focuses on strongly interacting fermionic systems, more precisely, the behavior of electrons in presence of strong magnetic fields. We show how the energy spectrum of a Hamiltonian describing the fractional quantum Hall effect can be computed on a quantum computer and derive a closed form for the Hamiltonian coefficients in second quantization. We then discuss a mean-field method and a multi-reference state approach that allow for an efficient classical computation and an efficient initial state preparation on a quantum computer. The second part of the thesis presents a detailed description on how long-range interacting fermionic systems can be simulated on classical computers using a variational method, introduce an Ansatz which could potentially simplify numerical simulations and give an explicit quantum circuit that shows how the variational state can be used as an initial state and how it can implemented on a quantum computer. In the last part, two novel protocols are presented that generate a variety of prominent many-body operators from two-body interactions and show how these protocols improve over previous construction schemes for a number of important examples. iv Zusammenfassung Diese Arbeit behandelt verschiedene zentrale Probleme theoretischer Natur, welche im Rahmen der Simulation quantenmechanischer Systeme auf klassischen und Quantencomputern auftreten. Ein Großteil dieser Arbeit beschäftigt sich mit stark wechselwirkendenden fermionischen Systemen, genauer gesagt, dem Verhalten von Elektronen innerhalb eines starken Magnetfelds. Es wird dargelegt, wie das Energiespektrum des Quanten-Hall-Effekt-Hamiltonoperators auf einem Quantencomputer berechnet werden kann, und es werden geschlossene Ausdrücke für dessen Hamilton-Koeffizienten in zweiter Quantisierung hergeleitet. Anschließend werden sowohl ein Molekularfeld-als auch ein Multi-Referenz-Ansatz diskutiert, welche eine effiziente Berechnung auf klassischen Rechnern zulassen sowie eine effiziente Implementierung auf Quantencomputern ermöglichen. Der zweite Teil dieser Arbeit erläutert, wie man langreichweitige, wechselwirkende fermionische Systeme mit Hilfe einer neuen Variationsmethode, welche über die Molekularfeldnäherung hinaus geht, auf einem klassischen Computer simulieren kann. Es wird darüber hinaus ein alternativer Ansatz vorgestellt, der Teile dieser Variationsmethode vereinfachen könnte, und gezeigt, wie sich der Ansatz auf einem Quantencomputer realisieren lässt. Im letzten Teil werden zwei neue Methoden vorgestellt, welche es ermöglichen, eine Reihe wichtiger Vielteilchen-Operatoren aus Zweiteilchen-Wechselwirkungen zu erzeugen. Beide Methoden werden durch eine Vielzahl an wichtigen Beispielen veranschaulicht. v 1 A classical (quantum) algorithm is a step-by-step instruction on how to solve a given problem with operations that can run on a classical (quantum) computer. 2 The runtime is measured by the number of elementary operations used by the respective quantum or classical algorithm. For the former, this can be measured in terms of the quantum circuit model, which is just a specific sequence of elementary quantum operations applied to a number of qubits (a qubit is the quantum analogue to a classical bit). All of this and more is detailed in Sections 1.5 and 1.6. 3 Some of the most prominent classical methods include density functional theory (DFT), which exploits the electron density distribution rather than the many electron wave function using a variety of approximations [19] , but fails at describing strongly interacting systems. Another approach based on the wave function representation is the quantum Monte Carlo (QMC) method, but its efficient implementation suffers from the infamous fermionic sign problem, that leads to an exponential increase in the error of the simulation with system size [20] . Another classical algorithm used to find approximate ground states to the many-body problem is density matrix renormalization group (DMRG) [21] , which very successfully describes one-dimensional systems, but has trouble building up enough entanglement to describe most strongly correlated two-and three-dimensional systems. More on the chemistry side, full configuration quantum Monte Carlo (FCIQMC) is an approach based on QMC, that deals with the One can combine Eqs. (1.2.13) and (1.2.16) and obtain the electronic structure Hamiltonian H = T + V . In doing so, we have quietly neglected the fact that matter consists not only of electrons, but also of nuclei. The nuclei masses are however three orders of magnitudes larger than the masses of the electrons and one can assume the electrons to move within a field of fixed nuclei within good approximation, which is known as the Born-Oppenheimer approximation [45, 46] . A precise non-relativistic treatment of matter would include electron-nucleon, nucleon-nucleon, electron-electron interaction as well as single-body electron and nucleon terms. 9 Note that this definition slightly deviates from the definition we use in Chapters 2 and 3. (1.3.10) By comparing the right-hand sides of Eqs. (1.3.9) and (1.3.10), one realizes that equality requires γ to be composed of anti-commuting variables to obtain non-trivial solutions. Fermionic coherent states For fermionic fields, the only physically realizable eigenstate of the fermionic annihilation operator is the vacuum state. Other eigenstates can be constructed only in a formal way and are merely introduced as a means to do analytical computations. One can show that the unitary displacement operator Functions of Grassmann variables f (γ) which do commute with a Grassmann number are called even, those that anti-commute are called odd functions. 12 We will consider a physical density operator ρ which is a positive Hermitian operator of unit trace, i.o.w. ρ must fulfill The expectation value of a fermionic operator X w.r.t. a normalized quantum state ρ is given by X ρ = tr(ρX). i 2 2Nso p,q=1 θp(Γm) pq θq (1.3.54) for some real and anti-symmetric (i.e. skew-symmetric) (2N so × N so )-matrix Γ m , which is called the correlation matrix. 13 Wick's theorem will be discussed in detail in Appendix 3.B. 14 A basic example for Eq. (1.3.56) and p = 2 is given by 16 The time evolution of a density operator ρ is described by the von-Neumann equation For pure states, the von-Neumann equation is equivalent to the Schrödinger equation. A fault-tolerant quantum computer This thesis considers an idealized quantum computer, arguably the most frustrating assumption for anyone who is trying to run an actual experiment. An idealized quantum computer performs state initialization, gates and measurements without any errors or losses and is perfectly isolated from the environment. While this seems to be the somewhat most unrealistic assumption one can make, it turns out that using quantum error-correction one can not only protect stored and transmitted quantum states, but even protect quantum states which dynamically undergo a quantum computation. This is the content of the following theorem, which we state due to its significance for quantum computing. 5. One has to be able to read out the state of a qubit (in e.g. the computational basis) at the end or even in between the computation. Lemma 1.6.2 (Oblivious amplitude amplification). Let W (V ) be a unitary matrix which acts on n + m (n) qubits ant let θ ∈ (0, π/2). For any |ψ , we let W |0 m |ψ = sin(θ) |0 m V |ψ + cos(θ) |Φ ⊥ , (1.6.13) 34 Where efficiently implementable here again refers to its respective quantum circuit scaling at most polynomially in circuit size and depth (time) with system size. 35 When V is unitary, p can be interpreted as a probability, however, if V is not unitary, p can be larger than 1. V = e −iHt/m = e −i j U j /m .Michael Kaicher, Universität Des Saarlandeswork_ddu3szbvtzgntb2tyyo2vj5enaThu, 14 Apr 2022 00:00:00 GMTDagstuhl Reports, Volume 11, Issue 10, October 2021, Complete Issue
https://scholar.archive.org/work/3w5nqw2gangnrkuqgfzp32cw4u
Dagstuhl Reports, Volume 11, Issue 10, October 2021, Complete Issuework_3w5nqw2gangnrkuqgfzp32cw4uMon, 11 Apr 2022 00:00:00 GMTFiat-Shamir for Proofs Lacks a Proof Even in the Presence of Shared Entanglement
https://scholar.archive.org/work/jztthakf7rbz5lvfrtvj7ytlpy
We explore the cryptographic power of arbitrary shared physical resources. The most general such resource is access to a fresh entangled quantum state at the outset of each protocol execution. We call this the Common Reference Quantum State (CRQS) model, in analogy to the well-known Common Reference String (CRS). The CRQS model is a natural generalization of the CRS model but appears to be more powerful: in the two-party setting, a CRQS can sometimes exhibit properties associated with a Random Oracle queried once by measuring a maximally entangled state in one of many mutually unbiased bases. We formalize this notion as a Weak One-Time Random Oracle (WOTRO), where we only ask of the m-bit output to have some randomness when conditioned on the n-bit input. We show that WOTRO with n - m ∈ω( n) is black-box impossible in the CRQS model, meaning that no protocol can have its security black-box reduced to a cryptographic game. We define a (inefficient) quantum adversary against any WOTRO protocol that can be efficiently simulated in polynomial time, ruling out any reduction to a secure game that only makes black-box queries to the adversary. On the other hand, we introduce a non-game quantum assumption for hash functions that implies WOTRO in the CRQ$ model (where the CRQS consists only of EPR pairs). We first build a statistically secure WOTRO protocol where m = n, then hash the output. The impossibility of WOTRO has the following consequences. First, we show the black-box impossibility of a quantum Fiat-Shamir transform, extending the impossibility result of Bitansky et al. (TCC '13) to the CRQS model. Second, we show a black-box impossibility result for a strenghtened version of quantum lightning (Zhandry, Eurocrypt '19) where quantum bolts have an additional parameter that cannot be changed without generating new bolts.Frédéric Dupuis, Philippe Lamontagne, Louis Salvailwork_jztthakf7rbz5lvfrtvj7ytlpyTue, 05 Apr 2022 00:00:00 GMTAn Introduction to Quantum Computing for Statisticians and Data Scientists
https://scholar.archive.org/work/sm2v5mh6pnc6tgepm7ing2ljg4
Quantum computers promise to surpass the most powerful classical supercomputers when it comes to solving many critically important practical problems, such as pharmaceutical and fertilizer design, supply chain and traffic optimization, or optimization for machine learning tasks. Because quantum computers function fundamentally differently from classical computers, the emergence of quantum computing technology will lead to a new evolutionary branch of statistical and data analytics methodologies. This review provides an introduction to quantum computing designed to be accessible to statisticians and data scientists, aiming to equip them with an overarching framework of quantum computing, the basic language and building blocks of quantum algorithms, and an overview of existing quantum applications in statistics and data analysis. Our goal is to enable statisticians and data scientists to follow quantum computing literature relevant to their fields, to collaborate with quantum algorithm designers, and, ultimately, to bring forth the next generation of statistical and data analytics tools.Anna Lopatnikova, Minh-Ngoc Tran, Scott A. Sissonwork_sm2v5mh6pnc6tgepm7ing2ljg4Sun, 03 Apr 2022 00:00:00 GMTSampling statistical distributions in physics: a machine learning approach
https://scholar.archive.org/work/7zfus7pysndkvnebdkf35or33u
This thesis presents work which uses Machine Learning techniques in a variety of sampling situations which appear in physics. In the first Chapter some background on Machine Learning will be presented which will lay the foundations required for the later Chapters. Next we will look at how a specific Machine Learning model, the Restricted Boltzmann Machine, can be trained to approximate a target distribution from data which has already been sampled from the target distribution. We estimate observables on states sampled from trained models and compare them to observables estimated directly from the training data. We present a technique for estimating the likelihood function of the model using annealed importance sampling. Finally we present a closed form expression for extracting the N-point interactions which the model learns from the data directly from the parameters of the model, a result which is useful for a range of fields which study binary data. In the next Chapter we investigate a different generative model, the normalizing flow, and investigate its efficacy of generating configurations for a lattice scalar field theory. An initial study which quantifies how the cost of training this model scales with the system size is performed. Whilst the cost of training our models is significantly less than those reported in the proof of principle study which first presented using these models for this purpose [1], we discuss how there is still an exponential scaling of the training cost with the system size which must be overcome in order for these models to be practically useful. Finally we investigate inverse problems from a Bayesian perspective. With this framework, we are faced with the task of sampling from the posterior distributions in model space given the data. An approach for sampling in model space presented by the NNPDF collaboration is examined within this formal framework. We present some statistical estimators which can be used to validate a methodology which produces a sample of models. These estimato [...]Michael Wilson, University Of Edinburgh, Luigi Del Debbio, Richard Ball, Roman Zwicky, Roger Horsleywork_7zfus7pysndkvnebdkf35or33uFri, 18 Mar 2022 00:00:00 GMTA constant lower bound for any quantum protocol for secure function evaluation
https://scholar.archive.org/work/xv2a3k2ulvfhxp5u5jgavhe4zy
Secure function evaluation is a two-party cryptographic primitive where Bob computes a function of Alice's and his respective inputs, and both hope to keep their inputs private from the other party. It has been proven that perfect (or near perfect) security is impossible, even for quantum protocols. We generalize this no-go result by exhibiting a constant lower bound on the cheating probabilities for any quantum protocol for secure function evaluation, and present many applications from oblivious transfer to the millionaire's problem. Constant lower bounds are of practical interest since they imply the impossibility to arbitrarily amplify the security of quantum protocols by any means.Sarah Osborn, Jamie Sikorawork_xv2a3k2ulvfhxp5u5jgavhe4zyTue, 15 Mar 2022 00:00:00 GMT