Quantum Logic Research Papers - Academia.edu (original) (raw)

Quantum logic gates require qubits that can interact strongly with each other and with external fields while minimizing unwanted coupling to the decohering environment. Neutral atoms trapped in a far-off resonance optical lattice satisfy... more

Quantum logic gates require qubits that can interact strongly with each other and with external fields while minimizing unwanted coupling to the decohering environment. Neutral atoms trapped in a far-off resonance optical lattice satisfy these criteria. The adjustable parameters of the lattice (e.g., laser polarization, frequency, intensity) allow one to design interactions for which atoms interact strongly via dipole-dipole interactions

In this paper, the problem of constructing an efficient quantum circuit for the implementation of an arbitrary quantum computation is addressed. To this end, a basic block based on the cosine-sine decomposition method is suggested which... more

In this paper, the problem of constructing an efficient quantum circuit for the implementation of an arbitrary quantum computation is addressed. To this end, a basic block based on the cosine-sine decomposition method is suggested which contains lll qubits. In addition, a previously proposed quantum-logic synthesis method based on quantum Shannon decomposition is recursively applied to reach unitary gates over lll qubits. Then, the basic block is used and some optimizations are applied to remove redundant gates. It is shown that the exact value of lll affects the number of one-qubit and CNOT gates in the proposed method. In comparison to the previous synthesis methods, the value of lll is examined consequently to improve either the number of CNOT gates or the total number of gates. The proposed approach is further analyzed by considering the nearest neighbor limitation. According to our evaluation, the number of CNOT gates is increased by at most a factor of frac53\frac{5}{3}frac53 if the nea...

We introduce a probabilistic modal (dynamic-epistemic) quantum logic PLQP for reasoning about quantum algorithms. We illustrate its expressivity by using it to encode the correctness of the well-known quantum search algorithm, as well as... more

We introduce a probabilistic modal (dynamic-epistemic) quantum logic PLQP for reasoning about quantum algorithms. We illustrate its expressivity by using it to encode the correctness of the well-known quantum search algorithm, as well as of a quantum protocol known to solve one of the paradigmatic tasks from classical distributed computing (the leader election problem). We also provide a general method (extending an idea employed in the decidability proof in [12]) for proving the decidability of a range of quantum logics, interpreted on finite-dimensional Hilbert spaces. We give general conditions for the applicability of this method, and in particular we apply it to prove the decidability of PLQP.

Because the qubit probabilities must be preserved at the output of the quantum gate, it is noted that all matrices representing them are unitary, ie U*U=I. An important unitary matrix property is that of full rank. This property implies... more

Because the qubit probabilities must be preserved at the output of the quantum gate, it is noted that all matrices representing them are unitary, ie U*U=I. An important unitary matrix property is that of full rank. This property implies that quantum gate matrix rows and columns are ...

John Stewart Bell (1928-1990), a truly deep and serious thinker, was one of the leading physi-cists of the 20th century. He became famous for his discovery that quantum mechanics implies that nature is nonlocal, ie, that there are... more

John Stewart Bell (1928-1990), a truly deep and serious thinker, was one of the leading physi-cists of the 20th century. He became famous for his discovery that quantum mechanics implies that nature is nonlocal, ie, that there are physical influences between events that ...

This paper reviews some of the literature on the philosophy of quantum mechanics. The publications involved tend to follow similar patterns of first identifying the mysteries, puzzles or paradoxes of the quantum world, and then discussing... more

This paper reviews some of the literature on the philosophy of quantum mechanics. The publications involved tend to follow similar patterns of first identifying the mysteries, puzzles or paradoxes of the quantum world, and then discussing the existing interpretations of these matters, before the authors produce their own interpretations, or side with one of the existing views. The paper will show that all interpretations of quantum mechanics involve elements of apparent weirdness. They suggest that the quantum world, and possibly our macro world, exists or behaves in a way quite contrary to the way we normally imagine they should. The paper will also show how many of the writers on quantum mechanics misunderstand idealism in the macro world as proposed by philosophers such as George Berkeley, David Hume, Immanuel Kant and John Stuart Mill and misunderstand the concept of the observer dependent universe. The paper concludes by examining the similarities between the idealist view of the macro world and the Copenhagen Interpretation of the quantum world and suggests that as the Copenhagen Interpretation provides a view of the quantum world that is consistent with the macro world then the Copenhagen Interpretation should be the preferred view of the quantum world.

Current research in Logic is no longer confined to the traditional study of logical consequence or valid inference. As can be witnessed by the range of topics covered in this special issue, the subject matter of logic encompasses several... more

Current research in Logic is no longer confined to the traditional study of logical consequence or valid inference. As can be witnessed by the range of topics covered in this special issue, the subject matter of logic encompasses several kinds of informational processes ranging from proofs and inferences to dialogues, observations, measurements, communication and computation. What interests us here is its application to quantum physics: how does logic handle informational processes such as observations and measurements of quantum systems? What are the basic logical principles fit to handle and reason about quantum physical processes? These are the central questions in this paper. It is my aim to provide the reader with some food for thought and to give some pointers to the literature that provide an easy access to this field of research. In the next section I give a brief historical sketch of the origin of the quantum logic project. Next I will explain the theory of orthomodular lattices in section 2. Section 3 covers the syntax and semantics of traditional quantum logic. In section 4, I focus on the limits of quantum logic, dealing in particular with the implication problem. This paves the way to section 5 on modal quantum logic. I end with section 6 on dynamic quantum logic, giving the reader a taste of one of the latest new developments in the field.

At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the noncommutativity of quantum observables, which allegedly would... more

At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the noncommutativity of quantum observables, which allegedly would generate a non-distributive lattice of propositions, and from quantum superpositions, which would entail new rules for quantum disjunctions. While the quantum logic program is not as popular as it once was, a crucial question remains unsettled: what is the relationship between the logical structures of classical and quantum mechanics? In this essay we answer this question by showing that the original arguments promoting quantum logic contain serious flaws, and that quantum theory does satisfy the classical distributivity law once the full meaning of quantum propositions is properly taken into account. Moreover, we show that quantum mechanics can generate a distributive lattice of propositions, which, unlike the one of quantum logic, includes statements about expectation values which are of undoubtable physical interest. Lastly, we show that the lattice of statistical propositions in classical mechanics follows the same structure, yielding an analogue non-commutative sublattice of classical propositions. This fact entails that the purported difference between classical and quantum logic stems from a misconstructed parallel between the two theories.

Dionysius' teaching on divine names is considered from its formal logical side.

Second, we give a proposal for reliable implementation of quantum logic gates and long decoherence times in a quantum dots system based on nuclear magnetic resonance (NMR), where the nuclear resonance is controlled by the ground state... more

Second, we give a proposal for reliable implementation of quantum logic gates and long decoherence times in a quantum dots system based on nuclear magnetic resonance (NMR), where the nuclear resonance is controlled by the ground state transitions of few-electron QDs in an external magnetic field. The dynamical evolution of these systems in the presence of environmentally-induced decoherence effects is also discussed.

Het belangrijkste onderwerp van dit boek is een puur wiskundig model van de fysieke werkelijkheid. Het boek fungeert als een overzicht van het Hilbert Book Model project. Het project betreft een goed gefundeerd, puur wiskundig model van... more

Het belangrijkste onderwerp van dit boek is een puur wiskundig model van de fysieke werkelijkheid. Het boek fungeert als een overzicht van het Hilbert Book Model project. Het project betreft een goed gefundeerd, puur wiskundig model van fysische realiteit. Het project berust op de overtuiging dat de fysieke werkelijkheid zijn eigen soort van wiskunde bezit en dat deze wiskunde de uitbreiding van het fundament tot meer gecompliceerde niveaus van de structuur en het gedrag van de fysieke werkelijkheid begeleid en inperkt. Dit resulteert in een model dat meer en meer lijkt op de fysieke werkelijkheid die mensen kunnen observeren. Het boek behandelt verschillende onderwerpen die rechtstreeks verband houden met het hoofdonderwerp. Het boek introduceert nieuwe fysica en nieuwe wiskunde.

This thesis is an attempt to give a concise presentation of the syntax, semantics and proof theory of the language LQP, introduced by Baltag and Smets in [2], as well as to apply it in an "Entanglement Specificational setting" to some... more

This thesis is an attempt to give a concise presentation of the syntax, semantics and proof theory of the language LQP, introduced by Baltag and Smets in [2], as well as to apply it in an "Entanglement Specificational setting" to some results mostly taken from [4].

Excitonic and spin excitations of single semiconductor quantum dots currently attract attention as possible candidates for solid state based implementations of quantum logic devices. Due to their rather short decoherence times in the... more

Excitonic and spin excitations of single semiconductor quantum dots currently attract attention as possible candidates for solid state based implementations of quantum logic devices. Due to their rather short decoherence times in the picosecond to nanosecond range, such implementations rely on using ultrafast optical pulses to probe and control coherent polarizations. In this article, we review our recent work on

In this paper we introduced a new variant of quantum dynamic logic, and we proved its decidability, by showing that it is translatable into the first-order logic of complex numbers (whose decidability follows from a classical result by... more

In this paper we introduced a new variant of quantum dynamic logic, and we proved its decidability, by showing that it is translatable into the first-order logic of complex numbers (whose decidability follows from a classical result by Tarski [12]).

This is the Spanish translation of Haack's first book, DEVIANT LOGIC, here in full text. It covers many issues raised by non-standard (and specifically deviant) logics, and studies of many different many-valued, intuitionist, free, etc.... more

This is the Spanish translation of Haack's first book, DEVIANT LOGIC, here in full text. It covers many issues raised by non-standard (and specifically deviant) logics, and studies of many different many-valued, intuitionist, free, etc. logical systems.

An exploration of the relational ontology of space, time and light.

The goal of this paper is to summarise the first steps in developing a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum... more

The goal of this paper is to summarise the first steps in developing a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. In doing so we provide a new answer to Heidegger's timeless question ``What is a thing?''.
Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics uses the topos of sets. Other theories involve a different topos. For the types of theory discussed in this paper, a key goal is to represent any physical quantity AAA with an arrow breveAphi:SiphimapRphi\breve{A}_\phi:\Si_\phi\map\R_\phibreveAphi:SiphimapRphi where Siphi\Si_\phiSiphi and Rphi\R_\phiRphi are two special objects (the `state-object' and `quantity-value object') in the appropriate topos, tauphi\tau_\phitauphi. We discuss two different types of language that can be attached to a system,$S$. The first, PLS\PL{S}PLS, is a propositional language; the second, LS\L{S}LS, is a higher-order, typed language. Both languages provide deductive systems with an intuitionistic logic. With the aid of PLS\PL{S}PLS we expand and develop some of the earlier work (By CJI and collaborators.) on topos theory and quantum physics. A key step is a process we term `daseinisation' by which a projection operator is mapped to a sub-object of the spectral presheaf Sig\SigSig--the topos quantum analogue of a classical state space. The topos concerned is SetH\SetH{}SetH: the category of contravariant set-valued functors on the category (partially ordered set) V\V{}V of commutative sub-algebras of the algebra of bounded operators on the quantum Hilbert space Hi\HiHi.

This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged dynamics of stochastic systems. To... more

This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged dynamics of stochastic systems. To illustrate the technique we give examples involving Raman processes, Bloch-Siegert shifts and Quantum Logic Gates.

If we go through a list of some of the main problematiques 1 that are defining the new Century, such as water, forced migrations, poverty, environmental crises, violence, terrorism, neo-imperialism, destruction of social fabric, we must... more

If we go through a list of some of the main problematiques 1 that are defining the new Century, such as water, forced migrations, poverty, environmental crises, violence, terrorism, neo-imperialism, destruction of social fabric, we must conclude that none of them can be ...

We present a method to enact a deterministic, measurement-free, optically generated controlled-phase gate on two qubits defined by single electrons trapped in large-area quantum dots in a planar microcavity. This method is robust to... more

We present a method to enact a deterministic, measurement-free, optically generated controlled-phase gate on two qubits defined by single electrons trapped in large-area quantum dots in a planar microcavity. This method is robust to optical quantum dot inhomogeneity, requires only a modest-$Q$ planar cavity, employs only a single laser pulse, and allows the integration of many entangled qubits on one semiconductor chip. We present the gate in the contexts of both adiabatic evolution and geometric phases, and calculate the degradation of performance in the presence of both spontaneous emission and cavity loss.

A concise overview of quantum logic written in Croatian language.

Kratki prikaz razvoja kvantne logike.

It is generally accepted that quantum mechanics entails a revision of the classical propositional calculus as a consequence of its physical content. However, the universal claim according to which a new quantum logic is indispensable in... more

It is generally accepted that quantum mechanics entails a revision of the classical propositional calculus as a consequence of its physical content. However, the universal claim according to which a new quantum logic is indispensable in order to model the propositions of every quantum theory is challenged. In the present essay we critically discuss this claim by showing that classical logic can be rehabilitated in a quantum context by taking into account Bohmian mechanics. It will be argued, indeed, that such a theoretical framework provides the necessary conceptual tools to reintroduce a classical logic of experimental propositions in virtue of its clear metaphysical picture and its theory of measurement. More precisely, it will be showed that the rehabilitation of a classical propositional calculus is a consequence of the primitive ontology of the theory, a fact which is not yet sufficiently recognized in the literature concerning Bohmian mechanics. This work aims to fill this gap.

The debate between Bergson and Einstein regarding the nature of time presents an opportunity to investigate the Logic of Three as the underlying logic that relates quantum mechanics to relativity theory. The Logic of Three is the... more

The debate between Bergson and Einstein regarding the nature of time presents an opportunity to investigate the Logic of Three as the underlying logic that relates quantum mechanics to relativity theory. The Logic of Three is the formative principle of " relational objects " or images.