Quantum Computation

Of the many and varied applications of quantum information theory, perhaps the most fascinating is the sub-field of quantum computation. In this sub-field, computational algorithms are designed which utilise the resources available in quantum systems in order to compute solutions to computational problems with, in some cases, exponentially fewer resources than any known classical algorithm. While the fact of quantum computational speedup is almost beyond doubt, the source of quantum speedup is still a matter of debate. In this paper I (...) argue that entanglement is a necessary component for any explanation of quantum speedup and I address some purported counter-examples that some claim show that the contrary is true. In particular, I address Cleve et al.'s solution to Deutsch's problem, Biham et al.'s mixed-state version of the Deutsch-Jozsa algorithm, and Knill & Laflamme's deterministic quantum computation with one qubit model of quantum computation. I argue that these examples do not demonstrate that entanglement is unnecessary for the explanation of quantum speedup, but that they rather illuminate and clarify the role that entanglement does play. (shrink)

Quantum computers are hypothetical quantum information processing (QIP) devices that allow one to store, manipulate, and extract information while harnessing quantum physics to solve various computational problems and do so putatively more efficiently than any known classical counterpart. Despite many ‘proofs of concept’ (Aharonov and Ben–Or 1996; Knill and Laflamme 1996; Knill et al. 1996; Knill et al. 1998) the key obstacle in realizing these powerful machines remains their scalability and susceptibility to noise: almost three decades after their conceptions, experimentalists (...) still struggle to maintain useful quantum coherence in QIP devices with more than a pair of qubits (e.g., Blatt and Wineland 2008). This slow progress has prompted debates on the feasibility of quantum computers, yet the quantum information community has dismissed the skepticism as “ideology” (Aaronson 2004), claiming that the obstacles are merely technological (Kaye et al. 2007, 240). In a recent paper (Hagar 2009) I’ve argued that such a skepticism with respect to the feasibility of quantum computers need not be deemed ideological at all, and that the aforementioned ‘proofs of concept’ are physically suspect. Using analogies from the foundations of classical statistical mechanics (SM), I’ve also argued that instead of active error correction, the appropriate framework for debating the feasibility of large–scale, fault–tolerant and computationally superior quantum computers should be the project of error avoidance: rather than trying to constantly ‘cool down’ the QIP device and prevent its thermalization, one should try to locate those regions in the device’s state space which are thermodynamically ‘abnormal’, i.e., those regions in the device’s state space which resist thermalization regardless of external noise. This paper is intended as a further contribution to the debate on the feasibility of large–scale, fault–tolerant and computationally superior quantum computers. Relying again on analogies from the foundations of classical SM, it suggests a skeptical conjecture and frames it in the ‘passive’, error avoidance, context.. (shrink)

The potential for scalable quantum computing depends on the viability of fault tolerance and quantum error correction, by which the entropy of environmental noise is removed during a quantum computation to maintain the physical reversibility of the computer’s logical qubits. However, the theory underlying quantum error correction applies a linguistic double standard to the words “noise” and “measurement” by treating environmental interactions during a quantum computation as inherently reversible, and environmental interactions at the end of a quantum computation as irreversible (...) measurements. Specifically, quantum error correction theory models noise as interactions that are uncorrelated or that result in correlations that decay in space and/or time, thus embedding no permanent information to the environment. I challenge this assumption both on logical grounds and by discussing a hypothetical quantum computer based on “position qubits.” The technological difficulties of producing a useful scalable position-qubit quantum computer parallel the overwhelming difficulties in performing a double-slit interference experiment on an object comprising a million to a billion fermions. (shrink)

This work-in-progress paper consists of four points which relate to the foundations and physical realization of quantum computing. The first point is that the qubit cannot be taken as the basic unit for quantum computing, because not every superposition of bit-strings of length n can be factored into a string of n-qubits. The second point is that the “No-cloning” theorem does not apply to the copying of one quantum register into another register, because the mathematical representation of this copying is (...) the identity operator, which is manifestly linear. The third point is that quantum parallelism is not destroyed only by environmental decoherence. There are two other forms of decoherence, which we call measurement decoherence and internal decoherence, that can also destroy quantum parallelism. The fourth point is that processing the contents of a quantum register “one qubit at a time” destroys entanglement. (shrink)

The ecology of fear has become a common rhetoric in efforts to support climate mitigation. The thesis of the collapse is an extreme version, asserting the inevitable collapse of the world. Fear, then, becomes the ultimate emotion for spurring action. In this article, drawing on the work of the pragmatist John Dewey, we show that fear is an ambiguous emotion. Dewey stressed the quality of an emotion. Following his reasoning, this article draws a distinction between intense and moderate fear. Intense (...) fear annihilates action, while moderate fear fulfils the conditions for an emotion of quality, which enables action. For this reason, the thesis of the collapse must be rejected, while an ecology of fear, drawing on moderate fear, may be maintained. (shrink)

Climate change threatens humanity more than anything else. If we talk of nationalism, we ought therefore consider its pros and cons in light of the climate emergency. Anatol Lieven believes that civic nationalism along the lines of Chaim Gans, David Miller, and Yuli Tamir helps combat global warming. He thinks that when nationalists recognize that climate change is just as threatening to the survival of their nation-state as wars, they will make the sacrifices necessary to avert the threat. In this (...) view, the military has an important role, and migration will have to be restricted. In this paper, I show that this solution is at best highly risky, and more probably unsound. However difficult it will be to realize, addressing climate change must be based on international cooperation, normatively grounded in human rights. I show how international law rather than civic nationalism gives us examples of how to go forward. (shrink)

Quantum computing is of high interest because it promises to perform at least some kinds of computations much faster than classical computers. Arute et al. 2019 (informally, “the Google Quantum Team”) report the results of experiments that purport to demonstrate “quantum supremacy” – the claim that the performance of some quantum computers is better than that of classical computers on some problems. Do these results close the debate over quantum supremacy? We argue that they do not. In the following, we (...) provide an overview of the Google Quantum Team’s experiments, then identify some open questions in the quest to demonstrate quantum supremacy. (shrink)

Climate change mitigation has become a paradigm case both for externalities in general and for the game-theoretic model of the Tragedy of the Commons in particular. This situation is worrying, as we have reasons to suspect that some models in the social sciences are apt to be performative to the extent that they can become self-fulfilling prophecies. Framing climate change mitigation as a hardly solvable coordination problem may force us into a worse situation, by changing real-world behaviour to fit our (...) model, rather than the other way around. But while this problem of the performativity of the ToC has been noted in a recent paper in this journal by Matthew Kopec, his proposed strategies for dealing with their self-fulfilling nature fall short of providing an adequate solution. Instead of relying on the idea that modelling assumptions are always strictly speaking false, this paper shows that the problem may be better framed as a problem of underdetermination between competing explanations. Our goal here is to provide a framework for choosing between this set of competing models that allows us to avoid a ‘Russian Roulette’-like situation in which we gamble with existential risk. (shrink)

There is a growing movement in online social networks and within some governments to deny the long-established scientific consensus regarding climate change. Scientific research has shown that a series of climatic events in Latin America, and especially in Brazil, are being exacerbated by global warming. These events have had a profound impact on populations. Disruptions to Brazilian rainfall patterns with their devastating environmental and economic effects on agriculture have been directly linked with Amazonian deforestation. Furthermore, the Bolsonaro government, with its (...) erratic environmental policies and ardent followers, has promoted misinformation about climate change and conservation of the Amazon. It is necessary to simultaneously inform society about scientific misunderstandings regarding the environment and the way these misunderstandings are amplified via the internet and social networks. (shrink)

One is occasionally reminded of Foucault's proclamation in a 1970 interview that "perhaps, one day this century will be known as Deleuzian." Less often is one compelled to update and restart with a supplementary counter-proclamation of the mathematician, David Lindley: "the twenty-first century would be a Bayesian era..." The verb tenses of both are conspicuous. // To critically attend to what is today often feared and demonized, but also revered, deployed, and commonly referred to as algorithm(s), one cannot avoid the (...) mathematical and philosophical legacies of probability. // But attending to these probabilistic or Bayesian legacies must include an undeniable theological legacy in which they remain entangled. // We are not, today, discovering quirky theological metaphors in contemporary technics. It's the other way around. The technologies are mere metaphors of past theologies. (shrink)

This is an extended essay review of Tanya and Jeffrey Bub’s Totally Random: Why Nobody Understands Quantum Mechanics: A serious comic on entanglement. We review the philosophical aspects of the book, provide suggestions for instructors on how to use the book in a class setting, and evaluate the authors’ artistic choices in the context of comics theory. Although Totally Random does not defend any particular interpretation of quantum mechanics, we find that, in its mode of presentation, Totally Random is a (...) beautiful expression and illustration of the information-theoretic interpretation and its value. (shrink)

The superposition of magical thinking, quantum entanglement, and self-referential recursion explains the relationship between human and machine intelligence (universal intelligence).

Natural argument is represented as the limit, to which an infinite Turing process converges. A Turing machine, in which the bits are substituted with qubits, is introduced. That quantum Turing machine can recognize two complementary natural arguments in any data. That ability of natural argument is interpreted as an intellect featuring any quantum computer. The property is valid only within a quantum computer: To utilize it, the observer should be sited inside it. Being outside it, the observer would obtain quite (...) different result depending on the degree of the entanglement of the quantum computer and observer. All extraordinary properties of a quantum computer are due to involving a converging infinite computational process contenting necessarily both a continuous advancing calculation and a leap to the limit. Three types of quantum computation can be distinguished according to whether the series is a finite one, an infinite rational or irrational number. -/- . (shrink)

Any computer can create a model of reality. The hypothesis that quantum computer can generate such a model designated as quantum, which coincides with the modeled reality, is discussed. Its reasons are the theorems about the absence of “hidden variables” in quantum mechanics. The quantum modeling requires the axiom of choice. The following conclusions are deduced from the hypothesis. A quantum model unlike a classical model can coincide with reality. Reality can be interpreted as a quantum computer. The physical processes (...) represent computations of the quantum computer. Quantum information is the real fundament of the world. The conception of quantum computer unifies physics and mathematics and thus the material and the ideal world. Quantum computer is a non-Turing machine in principle. Any quantum computing can be interpreted as an infinite classical computational process of a Turing machine. Quantum computer introduces the notion of “actually infinite computational process”. The discussed hypothesis is consistent with all quantum mechanics. The conclusions address a form of neo-Pythagoreanism: Unifying the mathematical and physical, quantum computer is situated in an intermediate domain of their mutual transformation. (shrink)

Two strategies to infinity are equally relevant for it is as universal and thus complete as open and thus incomplete. Quantum mechanics is forced to introduce infinity implicitly by Hilbert space, on which is founded its formalism. One can demonstrate that essential properties of quantum information, entanglement, and quantum computer originate directly from infinity once it is involved in quantum mechanics. Thus, thеse phenomena can be elucidated as both complete and incomplete, after which choice is the border between them. A (...) special kind of invariance to the axiom of choice shared by quantum mechanics is discussed to be involved that border between the completeness and incompleteness of infinity in a consistent way. The so-called paradox of Albert Einstein, Boris Podolsky, and Nathan Rosen is interpreted entirely in the same terms only of set theory. Quantum computer can demonstrate especially clearly the privilege of the internal position, or “observer”, or “user” to infinity implied by Henkin’s proposition as the only consistent ones as to infinity. (shrink)

Any logic is represented as a certain collection of well-orderings admitting or not some algebraic structure such as a generalized lattice. Then universal logic should refer to the class of all subclasses of all well-orderings. One can construct a mapping between Hilbert space and the class of all logics. Thus there exists a correspondence between universal logic and the world if the latter is considered a collection of wave functions, as which the points in Hilbert space can be interpreted. The (...) correspondence can be further extended to the foundation of mathematics by set theory and arithmetic, and thus to all mathematics. (shrink)

Pattern recognition is represented as the limit, to which an infinite Turing process converges. A Turing machine, in which the bits are substituted with qubits, is introduced. That quantum Turing machine can recognize two complementary patterns in any data. That ability of universal pattern recognition is interpreted as an intellect featuring any quantum computer. The property is valid only within a quantum computer: To utilize it, the observer should be sited inside it. Being outside it, the observer would obtain quite (...) different result depending on the degree of the entanglement of the quantum computer and observer. All extraordinary properties of a quantum computer are due to involving a converging infinite computational process contenting necessarily both a continuous advancing calculation and a leap to the limit. Three types of quantum computation can be distinguished according to whether the series is a finite one, an infinite rational or irrational number. (shrink)

In the past four decades, the notion of quantum polynomial-time computability has been mathematically modeled by quantum Turing machines as well as quantum circuits. This paper seeks the third model, which is a quantum analogue of the schematic definition of recursive functions. For quantum functions mapping finite-dimensional Hilbert spaces to themselves, we present such a schematic definition, composed of a small set of initial quantum functions and a few construction rules that dictate how to build a new quantum function from (...) the existing ones. We prove that our schematic definition precisely characterizes all functions that can be computable with high success probabilities on well-formed quantum Turing machines in polynomial time, or equivalently uniform families of polynomial-size quantum circuits. Our new, schematic definition is quite simple and intuitive and, more importantly, it avoids the cumbersome introduction of the well-formedness condition imposed on a quantum Turing machine model as well as of the uniformity condition necessary for a quantum circuit model. Our new approach can further open a door to the descriptional complexity of quantum functions, to the theory of higher-type quantum functionals, to the development of new first-order theories for quantum computing, and to the designing of programming languages for real-life quantum computer. (shrink)

A recent paper from Brun et al. has argued that access to a closed timelike curve would allow for the possibility of perfectly distinguishing nonorthogonal quantum states. This result can be used to develop a protocol for instantaneous nonlocal signaling. Several commenters have argued that nonlocal signaling must fail in this and in similar cases, often citing consistency with relativity as the justification. I argue that this objection fails to rule out nonlocal signaling in the presence of a CTC. I (...) argue that the reason these authors are motivated to exclude the prediction of nonlocal signaling is because the No Signaling principle is considered to a fundamental part of the formulation of the quantum information approach. I draw out the relationship between nonlocal signaling, quantum information, and relativity, and argue that the principle theory formulation of quantum mechanics, which is at the foundation of the quantum information approach, is in tension with foundational assumptions of Deutsch’s D-CTC model, on which this protocol is based. (shrink)

Combining physics, mathematics and computer science, quantum computing and its sister discipline of quantum information have developed in the past few decades from visionary ideas to two of the most fascinating areas of quantum theory. General interest and excitement in quantum computing was initially triggered by Peter Shor (1994) who showed how a quantum algorithm could exponentially “speed-up” classical computation and factor large numbers into primes far more efficiently than any (known) classical algorithm. Shor’s algorithm was soon followed by several (...) other algorithms that aimed to solve combinatorial and algebraic problems, and in the years since theoretical study of quantum systems serving as computational devices has achieved tremendous progress. Common belief has it that the implementation of Shor’s algorithm on a large scale quantum computer would have devastating consequences for current cryptography protocols which rely on the premise that all known classical worst-case algorithms for factoring take time exponential in the length of their input (see, e.g., Preskill 2005). Consequently, experimentalists around the world are engaged in attempts to tackle the technological difficulties that prevent the realisation of a large scale quantum computer. But regardless whether these technological problems can be overcome (Unruh 1995; Ekert and Jozsa 1996; Haroche and Raimond 1996), it is noteworthy that no proof exists yet for the general superiority of quantum computers over their classical counterparts. -/- The philosophical interest in quantum computing is manifold. From a social-historical perspective, quantum computing is a domain where experimentalists find themselves ahead of their fellow theorists. Indeed, quantum mysteries such as entanglement and nonlocality were historically considered a philosophical quibble, until physicists discovered that these mysteries might be harnessed to devise new efficient algorithms. But while the technology for harnessing the power of 50–100 qubits (the basic unit of information in the quantum computer) is now within reach (Preskill 2018), only a handful of quantum algorithms exist, and the question of whether these can truly outperform any conceivable classical alternative is still open. From a more philosophical perspective, advances in quantum computing may yield foundational benefits. For example, it may turn out that the technological capabilities that allow us to isolate quantum systems by shielding them from the effects of decoherence for a period of time long enough to manipulate them will also allow us to make progress in some fundamental problems in the foundations of quantum theory itself. Indeed, the development and the implementation of efficient quantum algorithms may help us understand better the border between classical and quantum physics (Cuffaro 2017, 2018a; cf. Pitowsky 1994, 100), and perhaps even illuminate fundamental concepts such as measurement and causality. Finally, the idea that abstract mathematical concepts such as computability and complexity may not only be translated into physics, but also re-written by physics bears directly on the autonomous character of computer science and the status of its theoretical entities—the so-called “computational kinds”. As such it is also relevant to the long-standing philosophical debate on the relationship between mathematics and the physical world. (shrink)

Computing, today more than ever before, is a multi-faceted discipline which collates several methodologies, areas of interest, and approaches: mathematics, engineering, programming, and applications. Given its enormous impact on everyday life, it is essential that its debated origins are understood, and that its different foundations are explained. On the Foundations of Computing offers a comprehensive and critical overview of the birth and evolution of computing, and it presents some of the most important technical results and philosophical problems of the discipline, (...) combining both historical and systematic analyses. -/- The debates this text surveys are among the latest and most urgent ones: the crisis of foundations in mathematics and the birth of the decision problem, the nature of algorithms, the debates on computational artefacts and malfunctioning, and the analysis of computational experiments. By covering these topics, On the Foundations of Computing provides a much-needed resource to contextualize these foundational issues. -/- For practitioners, researchers, and students alike, a historical and philosophical approach such as what this volume offers becomes essential to understand the past of the discipline and to figure out the challenges of its future. (shrink)

Computational complexity theory is a branch of computer science dedicated to classifying computational problems in terms of their difficulty. While computability theory tells us what we can compute in principle, complexity theory informs us regarding our practical limits. In this chapter I argue that the science of \emph{quantum computing} illuminates complexity theory by emphasising that its fundamental concepts are not model-independent, but that this does not, as some suggest, force us to radically revise the foundations of the theory. For model-independence (...) never has been essential to those foundations. The fundamental aim of complexity theory is to describe what is achievable in practice under various models of computation for our various practical purposes. Reflecting on quantum computing illuminates complexity theory by reminding us of this, too often under-emphasised, fact. (shrink)

I argue that our judgements regarding the locally causal models that are compatible with a given constraint implicitly depend, in part, on the context of inquiry. It follows from this that certain quantum no-go theorems, which are particularly striking in the traditional foundational context, have no force when the context switches to a discussion of the physical systems we are capable of building with the aim of classically reproducing quantum statistics. I close with a general discussion of the possible implications (...) of this for our understanding of the limits of classical description, and for our understanding of the fundamental aim of physical investigation. _1_ Introduction _2_ No-Go Results _2.1_ The CHSH inequality _2.2_ The GHZ equality _3_ Classically Simulating Quantum Statistics _3.1_ GHZ statistics _3.2_ Singlet statistics _4_ What Is a Classical Computer Simulation? _5_ Comparing the All-or-Nothing GHZ with Statistical equalities _6_ General Discussion _7_ Conclusion. (shrink)

Although computation and the science of physical systems would appear to be unrelated, there are a number of ways in which computational and physical concepts can be brought together in ways that illuminate both. This volume examines fundamental questions which connect scholars from both disciplines: is the universe a computer? Can a universal computing machine simulate every physical process? What is the source of the computational power of quantum computers? Are computational approaches to solving physical problems and paradoxes always fruitful? (...) Contributors from multiple perspectives reflecting the diversity of thought regarding these interconnections address many of the most important developments and debates within this exciting area of research. Both a reference to the state of the art and a valuable and accessible entry to interdisciplinary work, the volume will interest researchers and students working in physics, computer science, and philosophy of science and mathematics. (shrink)

According to the Gottesman–Knill theorem, quantum algorithms that utilize only the operations belonging to a certain restricted set are efficiently simulable classically. Since some of the operations in this set generate entangled states, it is commonly concluded that entanglement is insufficient to enable quantum computers to outperform classical computers. I argue in this article that this conclusion is misleading. First, the statement of the theorem is, on reflection, already evident when we consider Bell’s and related inequalities in the context of (...) a discussion of computational machines. This, in turn, helps us to understand that the appropriate conclusion to draw from the Gottesman–Knill theorem is not that entanglement is insufficient to enable a quantum performance advantage, but rather that if we limit ourselves to the operations referred to in the Gottesman–Knill theorem, we will not have used the resources provided by an entangled quantum system to their full potential. (shrink)

David Bohm, in his "causal theory", made the correct Hegelian synthesis of Einstein's thesis that there is a "there" there, and Bohr's antithesis of "thinglessness" (Nick Herbert’s term). Einstein was a materialist and Bohr was an idealist. Bohm showed that quantum reality has both. This is “physical dualism” (my term). Physical dualism may be a low energy approximation to a deeper monism of cosmic consciousness called "the super-implicate order" (Bohm and Hiley’s term), “pregeometry” (Wheeler’s term), “substratum” (Dirac’s term), “funda-MENTAL space” (...) (Hameroff’s term), “Chi” (Chinese medicine & Falun Gong) etc., but for our immediate pragmatic purpose of constructing naturally conscious nano-computers and of virtually reverse engineering alleged reports of propellantless UFO propulsion (French Intelligence Report, 1999 [email protected] Vol. 5, No. 11, Part 1 -- August 1, 1999 & NIDS report "Best UFO Cases - Europe", I. Von Ludwiger) to the stars and beyond, physical dualism will work. (shrink)

This article tells the story of Ed Fredkin, a pilot, programmer, engineer, hardware designer and entrepreneur, whose work inside and outside academia has influenced major developments in computer science and in the foundations of theoretical physics for the past fifty years.

A primary goal of quantum computer science is to find an explanation for the fact that quantum computers are more powerful than classical computers. In this paper I argue that to answer this question is to compare algorithmic processes of various kinds and to describe the possibility spaces associated with these processes. By doing this, we explain how it is possible for one process to outperform its rival. Further, in this and similar examples little is gained in subsequently asking a (...) how-actually question. Once one has explained how-possibly, there is little left to do. (shrink)

We propose a new interpretation of objective deterministic chances in statistical physics based on physical computational complexity. This notion applies to a single physical system (be it an experimental set--up in the lab, or a subsystem of the universe), and quantifies (1) the difficulty to realize a physical state given another, (2) the 'distance' (in terms of physical resources) from a physical state to another, and (3) the size of the set of time--complexity functions that are compatible with the physical (...) resources required to reach a physical state from another. (shrink)

A formal model of metaphor is introduced. It models metaphor, first, as an interaction of “frames” according to the frame semantics, and then, as a wave function in Hilbert space. The practical way for a probability distribution and a corresponding wave function to be assigned to a given metaphor in a given language is considered. A series of formal definitions is deduced from this for: “representation”, “reality”, “language”, “ontology”, etc. All are based on Hilbert space. A few statements about a (...) quantum computer are implied: The sodefined reality is inherent and internal to it. It can report a result only “metaphorically”. It will demolish transmitting the result “literally”, i.e. absolutely exactly. A new and different formal definition of metaphor is introduced as a few entangled wave functions corresponding to different “signs” in different language formally defined as above. The change of frames as the change from the one to the other formal definition of metaphor is interpreted as a formal definition of thought. Four areas of cognition are unified as different but isomorphic interpretations of the mathematical model based on Hilbert space. These are: quantum mechanics, frame semantics, formal semantics by means of quantum computer, and the theory of metaphor in linguistics. (shrink)

Open peer commentary on the article “Info-computational Constructivism and Cognition” by Gordana Dodig-Crnkovic. Upshot: Dodig-Crnkovic’s “info-computational constructivism” (IC), as an essential part of a constructivist approach, needs integration with the logical, mathematical and physical evidence coming from quantum field theory (QFT) as the fundamental physics of the emergence of “complex systems” in all realms of natural sciences.

In The Philosophy of Information, Luciano Floridi presents an ontological theory of Being qua Being, which he calls “Informational Structural Realism”, a theory which applies, he says, to every possible world. He identifies primordial information (“dedomena”) as the foundation of any structure in any possible world. The present essay examines Floridi’s defense of that theory, as well as his refutation of “Digital Ontology” (which some people might confuse with his own). Then, using Floridi’s ontology as a starting point, the present (...) essay adds quantum features to dedomena, yielding an ontological theory for our own universe, Quantum Informational Structural Realism, which provides a metaphysical interpretation of key quantum phenomena, and diminishes the “weirdness” or “spookiness” of quantum mechanics. (shrink)

The foundations of quantum mechanics are attracting new and significant interest in the scientific community due to the recent striking experimental and technical progress in the fields of quantum computation, quantum teleportation and quantum information processing. However, at a more fundamental level the understanding and manipulation of these novel phenomena require not only new laboratory techniques but also new understanding, development and interpretation of the formalism of quantum mechanics itself, a mathematical structure whose connection to what happens in physical reality (...) continues to present puzzles and engender debate.The present issue of Foundations of Physics considers, from physical, philosophical and logical perspectives, a range of problems: these range from the meaning of quantum identity and individuality, through probability and complementarity, to decoherence and gauge theories.The idea of preparing this special issue was conceived in connection with the Workshop .. (shrink)

Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and intermediate-scale systems are on the horizon, capable of calculating numeric results or simulating physical systems far beyond what humans can do by hand. However, to be commercially viable, they must surpass what our wildly successful, highly advanced classical computers can already do. At the same time, those classical (...) computers continue to advance, but those advances are now constrained by thermodynamics, and will soon be limited by the discrete nature of atomic matter and ultimately quantum effects. Technological advances benefit both quantum and classical machinery, altering the competitive landscape. Can we build quantum computing systems that out-compute classical systems capable of some \(10^{30}\) logic gates per month? This article will discuss the interplay in these competing and cooperating technological trends. (shrink)

Takes students and researchers on a tour through some of the deepest ideas of maths, computer science and physics.

The aim of this dissertation is to clarify the debate over the explanation of quantum speedup and to submit, for the reader's consideration, a tentative resolution to it. In particular, I argue, in this dissertation, that the physical explanation for quantum speedup is precisely the fact that the phenomenon of quantum entanglement enables a quantum computer to fully exploit the representational capacity of Hilbert space. This is impossible for classical systems, joint states of which must always be representable as product (...) states. I begin the dissertation by considering, in Chapter 2, the most popular of the candidate physical explanations for quantum speedup: the many worlds explanation of quantum computation. I argue that, although it is inspired by the neo-Everettian interpretation of quantum mechanics, unlike the latter it does not have the conceptual resources required to overcome objections such as the so-called `preferred basis objection'. I further argue that the many worlds explanation, at best, can serve as a good description of the physical process which takes place in so-called network-based computation, but that it is incompatible with other models of computation such as cluster state quantum computing. I next consider, in Chapter 3, a common component of most other candidate explanations of quantum speedup: quantum entanglement. I investigate whether entanglement can be said to be a necessary component of any explanation for quantum speedup, and I consider two major purported counter-examples to this claim. I argue that neither of these, in fact, show that entanglement is unnecessary for speedup, and that, on the contrary, we should conclude that it is. In Chapters 4 and 5 I then ask whether entanglement can be said to be sufficient as well. In Chapter 4 I argue that despite a result that seems to indicate the contrary, entanglement, considered as a resource, can be seen as sufficient to enable quantum speedup. Finally, in Chapter 5 I argue that entanglement is sufficient to explain quantum speedup as well. (shrink)

Shi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. The basic algebraic properties of this system have been studied in Dalla Chiara et al. (Foundations of Physics 39(6):559–572, 2009), where we have introduced the notion of Shi-Aharonov quantum computational structure. In this paper we propose an algebraic abstraction from the Hilbert-space quantum computational structures, by introducing the notion of Toffoli-Hadamard algebra. From an intuitive point of (...) view, such abstract algebras represent a natural quantum generalization of both classical and fuzzy-like structures. (shrink)

Quantum probability theory offers a viable alternative to classical probability, although there are some ambiguities inherent in transferring the quantum formalism to a less determined realm. A number of physicists are now looking at the applicability of quantum ideas to the assessment of physics learning, an area particularly suited to quantum probability ideas.