The philosophical foundation of **quantum** mechanics is based on the duality concept of complementary notions indicated by Dutta [11], particles and waves, discrete and continuous, localized and non-localized characteristics of **quantum** behaviour expressed through the equations for energy and momentum as E = h υ and p = h λ − 1 , respectively. These equations fundamentally signify the qualitative aspect of **quantum** mechanics, because the quantitative aspect, involving the **quantum** **measurement** **problem**, is governed by the uncertainty relations that restrict the simultaneous accurate determination of position and momentum, energy and time etc. The uncertainty or imprecision in the measured values is an inherent feature of the subatomic world. In our view, this subatomic world is controlled by the **quantum** mechanical activities of these TCP and TRP with which any matter as well as any mind is constituted. And the functional state of mind is consciousness which, in turn, plays the most prominent role in the **quantum** **measurement**. Thus the **quantum** **measurement** involving the role of consciousness is governed by these TCP, TRP, T F (micro), T F (macro), and

Show more
This theorem raises the question as to whether the generalisation of the unitary evolu tions to non-unitary evolutions should be understood in the context of larger systems whose evolutions are unitary; in other words, we might ask whether the apparent non- unitary evolutions are a result of % becoming entangled with ' HQ' H, where H Q ' H models an environment, or whether the interaction is ju st irreducibly non-unitary. Sim ilar questions can be asked about POV-measures. The present chapter, however, is not concerned with whether the physics of **measurement** interactions is best described by unitary operators or by other operators. Assuming that interactions are described by unitary operators, given a specific **quantum** **measurement** I show th a t there are many unitary operators satisfying the standard conditions for an interaction operator for such **measurement**: they are the ones that share the common mathematical “core” W , a partial isometric contraction which I will shortly define. I also show th at, in some more general circumstances, no such unitary operators can be defined. I do not discuss here whether this implies th at it is appropriate to abandon the idea of unitary evolu tion. The physical arguments on this are unclear (for more on this in the context of **quantum** mechanics see, for instance, Davies [25]; for a discussion of this in the context of the **quantum** **measurement** **problem**, see for example Cartwright [18, Essay 9]); on the other hand the question is surely underdetermined: there are many more options than just rejecting unitarity.

Show more
190 Read more

The **quantum** **measurement** **problem** has been there for almost a century. [1] In the Orthodox Copenhagen interpretation, wave function collapses during a **measurement**, which is a process that cannot be described by Schrodinger’s equation. This obviously causes problems for the **quantum** theory. Another **problem** is the “Schrodinger’s cat”: according to **quantum** mechanics, the cat is in a “**quantum**” superposition state of being dead and alive, while to human observers the cat is always either alive or dead, i.e. being “classical”. The “classical” picture of the world, which is based on humans’ experience, is completely different from the “**quantum**” picture described by **quantum** mechanics. “Why does the world appear classical to us, in spite of its supposed underlying **quantum** nature, which would, in principle, allow for arbitrary superpositions?” [2] These problems are together referred as the **measurement** **problem**. [3-5]

Show more
In [6] the authors have extended the formulation of the **quantum** brachistochrone **problem** by allowing that the time-evolution operator may be associated to non- Hermitian Hamiltonians which are PT -symmetric, that is those with real eigenvalues. Here we did not insist on the PT -symmetry of the Hamiltonian, but allowed this symmetry to be completely broken. In order to take the most extreme case, we did not just spontaneously break the PT -symmetry for the wavefunction, which would re- sult in complex conjugate pairs for the energy eigenfunc- tion, but we allowed in addition that the PT -symmetry is also broken for the Hamiltonian. Thus we have consid- ered an effective Hamiltonian whose energy eigenvalues have a negative imaginary part, such that it is associated to dissipative systems. We found the same intriguing fea- ture as observed in [6] for the **quantum** brachistochrone **problem** for PT -symmetric non-Hermitian Hamiltonians, namely that the passage time can be made arbitrarily small also for non-Hermitian Hamiltonians associated to these type of systems. Our observations suggest that this type of phenomenon may occur when one projects between orthonormal states, which are not eigenstates of the non-Hermitian Hamiltonian associated to the time- evolution operator, irrespective of whether this Hamilto- nian is PT -symmetric or not.

Show more
7 what he means by this distinction. A factual attribute of a result seems fairly clear it is a matter of whether the result occurs or not. What is a methodological attribute? It seems to be a matter of whether the result is expected to happen. But if so, we just have the **problem** re-phrased in new terminology. And anyway, it seems to be the wrong kind of distinction to solve the **problem**. I could imagine this distinction solving the **problem** if methodological attributes and factual attributes were probabilistically independent. Then a result being guaranteed to happen (factual) would have no relevance to whether it was expected to happen (methodological). But s

Show more
11 Read more

Our next consideration regards the set of all possible values of the initial state vector y for a given **measurement** sequence. In the applications of QT in physics, this set is assumed to cover the entire Hilbert space in which they are defined. We are not justified to adopt this assumption in psychology, it would be too strong: one could argue that the initial states in a given experiment may be forbidden to attain values within certain areas of the Hilbert space. At the same time, it seems even less reasonable to allow for the possibility that the initial state for a given **measurement** sequence is always fixed at one particular value. The initial state vectors, as follows from both the QT principles and common sense, should depend on the system’s history prior to the given experiment, and this should create some variability from one replication of this experiment to another. This is important, because, given a set of observables, specially chosen initial state vectors may exhibit ‘‘atypical’’ behaviors, those that would disappear if the state vector were modified even slightly. It is known [7] that in physical systems very close states may have very different physical properties. We need therefore to confine our analysis to properties that, while they may not hold for the entire Hilbert space, are stable with respect to very small changes in the initial states for which they hold. This leads us to adopting the following

Show more
Recent advances in the theory of **quantum** gravity show that the Ricci flow serves as the time evolution operator for the vacuum energy density and that in the presence of baryonic matter, the Ricci flow is analogous to the heat equation in the presence of a heat sink. Here we show using the equations of **quantum** gravity, that **quantum** information can be modelled as a thermal fluid consisting of a superposition of weakly excited eigenstates of a **quantum** field and that each eigenstate vector has an associated eigenstate potential well. The depth of the potential well depends on the amplitude of the eigenstate vector. **Measurement** is then considered as a selection by tuning process which only allows an eigenstate resonating with the detector to be detected. During the detection process, the resonating eigenstate vector increases in amplitude, deepening its potential well such that the other weakly excited states rapidly drain their small excitation energies into it via the principle of minimum action. This draining process is the act of collapsing the wave function to a specific state. Also, the presence of the eigenstate potential wells is what cancels out the infinities from high energy interactions.

Show more
14 Read more

As Lombardi and Dieks observe in [15]: “In modal interpretations the event space on which the (preferred) prob- ability measure is defined is a space of possible events, among which only one becomes actual. The fact that the actual event is not singled out by these interpretations is what makes them fundamentally probabilistic. This aspect distinguishes modal interpretations from many-worlds interpretations, where the “probability measure” is defined on a space of events that are all actual. Nevertheless, this does not mean that all modal interpretations agree about the interpretation of probability.” We share the MHI point of view that adopt a possibilist conception, according to which possible events possibilia constitute a basic ontological category (see Menzel [16]). The probability measure is in this case seen as a representation of an ontological propensity of a possible **quantum** event to become actual [17]. The Modal Interpretation does not assume that the state changes after a property instantiates and it assumes that the evolution is always unitary. Nevertheless it is assumed implicitly that after the observation of a property the disposition of the system in its subsequent evolution is the same as the one the system would have had if the state had collapsed. Therefore, the ontology of states and events appear to be well suited to this interpretation. However, here the relevant kind of events corresponds to instantiations of properties both of macroscopic and microscopic systems and therefore they do not necessarily correspond to phenomena.

Show more
10 Read more

20 Read more

Continuing our journey up the software stack, we now move onto client code, which is entirely written in Python. To specify the waveforms to send to the sequencer, we use objects internally called Gates. A Gate object contains the machinery to generate waveforms for the channels of a qubit given a few input parameters. A Gate object often corresponds to a **quantum** gate. For example, a Pi gate corresponds to either an X or Y gate depending on what phase the user specifies. We construct the Pi gate with a reference to a specific qubit, and at runtime, the gate object looks up the qubit specific π pulse parameters in the registry and constructs a waveform. Multiple gates acting on any number of qubits are then combined into a gate sequence, which can also contain gate-like objects which correspond to FPGA jump table commands, such as looping over a set of gates a number of times.

Show more
242 Read more

In 1935 Einstein, Podolsky and Rosen [127] proved the incompatibility among three hy- potheses: 1) **quantum** mechanics is correct; 2) **quantum** mechanics is complete; 3) the following criterion of local reality holds: “If, without in any way disturbing a system, we can predict with certainty [...] the value of a physical quantity, then there exists an ele- ment of physical reality corresponding to this quantity.” The paper opened a long and as yet unsettled debate about which one of the three hypotheses should be discarded. While Einstein suggested to abandon the completeness of **quantum** mechanics, Bohr [128] refused the criterion of reality. The most important step forward in this debate was Bell’s theorem of 1965 [129], which proved that there is an intrinsic incompatibility between the assumptions 1) and 3), namely the correctness of **quantum** mechanics and Einstein’s “criterion of reality”. In Bell’s approach, a source produces a pair of corre- lated particles, which travel along opposite directions and impinge into two detectors. The two detectors measure two dichotomic observables A(α) and B(β) respectively, α and β denoting experimental parameters which can be varied over different trials, typically the polarization/spin angle of detection at each apparatus. Assuming that each **measurement** outcome is determined by the experimental parameters α and β and by an “element of reality” or “hidden variable” λ, Bell proved an inequality which holds for any theory that satisfies Einstein’s “criterion of reality”, while it is violated by **quantum** mechanics. Such a fundamental inequality, which allows an experimen- tal discrimination between local hidden–variable theories and **quantum** mechanics, has been the focus of interest in a number of experimental works [130].

Show more
163 Read more

How does the situation changes from the perspective of alternatives to the standard formalism, like objective collapse models (e.g., GRW or CSL) or de Broglie-Bohm mechanics? In the first case, given that the spontaneous collapses occur into highly localized states, and that the efficiency of the collapse process increases rapidly with the number of elementary constituents of the system, the theory straightforwardly predicts that the macroscopic apparatus will necessarily end-up in a state with well-defined pointer position (i.e., one of the terms in the first basis and not the second); and that is enough to determine, given the **quantum** description, what it is that the apparatus actually measures. Regarding Bohmian mechanics, a similar thing happens but for a different reason. In such case the apparatus also ends-up in a state with well-defined pointer position, but this time because the fundamental Bohmian description contains, beside the **quantum** state, the Bohmian particles, which always posses well-defined positions. As a result, the theory also unambiguously dictates that the first basis is the appropriate one to describe the system of our example.

Show more
15 Read more

• Looks like an expensive task by testing all possible paths.. • Euler: Desired path exits only if the coordination of each edge is even![r]

22 Read more

A comparison of the MacAndrew alcoholism scale and the Michigan Alcoholism Screening Test in a sample of problem drinkers.. Identifying alcohol problems among elderly hospital patients.[r]

335 Read more

The main **quantum** ingredient that we employ is a primitive called **quantum** lightning, formally introduced by Zhandry [Zha19] and inspired by Lutomirski et al.’s notion of collision resistant **quantum** money [LAF + 09]. In a public-key **quantum** money scheme, a bank is entrusted with generating **quantum** states (we refer to these as **quantum** banknotes) with an associated serial number, and a public verification procedure allows anyone in possession of the banknote to check its validity. Importantly, trust is placed in the fact that the central bank will not create multiple **quantum** banknotes with the same serial number. A **quantum** lightning scheme has the additional feature that no generation procedure, not even the honest one (and hence not even a bank!), can produce two valid money states with the same serial number, except with negligible probability. This opens to the possibility of having a completely decentralized **quantum** money scheme. However, if the system ought to be trust-less, some issues need to be addressed: most importantly, who is allowed to mint money? Who decides which serial numbers are valid? Our solution leverages a (classical) blockchain to address these questions.

Show more
44 Read more

The main contribution of this work is a genetic algorithm that leverages a specific chromosome encoding where each gene controls the iterative selection of a **quantum** gate to be inserted in the solution, over a lexicographic double-key **quantum** gate ranking returned by a heuristic function re- cently published in the literature. We have performed an ex- perimental campaign, testing our algorithm against a Quan- tum Circuit Compilation **Problem** benchmark known in the literature, proving that the proposed algorithm exhibits very convicing performance compared with recently published results against the same benchmark. To make the compar- ison more interesting, we have also proposed a complete re- implemenation of our Greedy Randomized Search originally presented in (Oddi and Rasconi 2018), demonstrating im- proved performance w.r.t. the previous version, despite such results remain inferior compared to the ones obtained with the genetic algorithm proposed in this work.

Show more
An early Response to Intervention (RTI) Model. In 1977, Deno and Mirkin (1977) presented a **problem**-solving assessment model entitled “Data-based Program Modification. (DBPM)” The basic premise of that model was that modifications in student programs could be tested by collecting progress monitoring data reflecting student growth in relation to changes implemented to increase student academic and social development. The model was created as a tool for educators to evaluate the success of their interventions and to determine the level of special education service required to solve the problems precipitating referral and initial assessment. The DBPM model was complete in that it included specification of the observational data to be used for evaluating **problem**-solving efforts. At the same time, the technical adequacy of the assessment procedures had not been empirically investigated, nor had the potential effectiveness of using those procedures to improve programs been tested.

Show more
46 Read more

The vector function x is obtained using the ex- perimental data (vibrations of supports) where the noise is present. Therefore it is convenient to think that each component of vector function x and function u belongs to L 2 [0, T]. Under this conditions the **problem** of

PI1ASE SPACE FOP BULATION OF TIE QUANTUM HANY BODY PROBLEM Thesis by Paul Hersh Levine In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy Ca lifornia Institute of Techno[.]

231 Read more

Reference frame is one of the most fundamental notions in physics. When a **measurement** in physics is performed or described, a reference frame has always been explicitly or implicitly used. As ordinarily formulated, reference frame idealizationally uses the rulers and clocks to label the spacetime for simplicity, which have well-defined values of coordinates and are considered most perfect, absolute, classical, and external. This fundamentally classical notion of reference frame has been using in almost all area of physics including today’s textbook **quantum** physics, although **quantum** mechanics has been discovered for a century. The **quantum** mechanics tells us that all measuring devices are subject to some level of **quantum** fluctuations, certainly applying to the rulers and clocks, namely the spacetime. Such idealizational treatment works well in **quantum** mechanics and **quantum** field theory when the equations of them cast in terms of the variables that are really measured by physical rulers and clocks in ordinary laboratory. This is, to a large extent, due to the fact that gravitational effects are not seriously taken into account in most laboratory experiments. Since according to the standard theory of gravity, the general relativity, the spacetime is dynamical and relational. It is as expected, when the **quantum** mechanics is applied to the cosmology which is gravity dominated, severe difficulty arises: the cosmological constant **problem**, see for instance [1–3] and references therein.

Show more
15 Read more