Similarly, an arbitrary quantum operation can be implemented via introducing an ancilla and performing a suitable unitary evolution.

Similarly to a classical bit where the state of a transistor in a processor, the magnetization of a surface in a hard disk and the presence of current in a cable can all be used to represent bits in the same computer, an eventual quantum computer is likely to use various combinations of qubits in its design.

Similarly, Paul Dirac, one of the founders of quantum mechanics, began his academic career as an electrical engineer before proceeding to mathematics and later theoretical physics.

Similarly, in the de Broglie – Bohm theory, there are anomalous initial conditions which would produce measurement statistics in violation of the Born rule ( i. e., in conflict with the predictions of standard quantum theory ).

Similarly, a quantum particle moving in a potential can be described by a superposition of paths, each with a phase: the thermal variations in the shape across the collection have turned into quantum uncertainty in the path of the quantum particle.

Similarly, quantum fluctuations of the order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero-temperature ( an important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantitity and does not have any quantum fluctuations ).

Similarly, the quantum group U < sub > q </ sub >( G ) can be regarded as an algebra over the field Q ( q ), the field of all rational functions of an indeterminate q over Q ( see below in the section on quantum groups at q

A highest weight module is a module generated by a weight vector v, subject to for all weights μ, and for all i. Similarly, a quantum group can have a lowest weight representation and lowest weight module, i. e. a module generated by a weight vector v, subject to for all weights λ, and for all i.

Similarly, a quantum algorithm is a step-by-step procedure, where each of the steps can be performed on a quantum computer.

Similarly, let A be an observable of a quantum mechanical system.

Similarly, a periodic structure of alternating thin films of different materials may collectively form a so-called superlattice which exploits the phenomenon of quantum confinement by restricting electronic phenomena to two-dimensions.

Similarly, the argument for BPP almost goes through for BQP, but we have to additionally show that quantum queries can be performed in coherent superposition.

Similarly, quantum measurement tomography works to find out what measurement is being performed.

Similarly experience itself can be conventionalized so that people react to certain preconceived clues for behavior without awareness of the vitality of their experiential field.

Similarly, the intensity of electromagnetic forces depends upon the strength ( electric charge ) of the electromagnetic field.

Similarly, the acceleration field is given by

Similarly, the Catholic Institute for International Relations ( CIIR, now known as " Progressio "), a human rights organization which identifies itself with liberation theology, had summarized Contra operating procedures in their 1987 human rights report: " The record of the contras in the field, as opposed to their official professions of democratic faith, is one of consistent and bloody abuse of human rights, of murder, torture, mutilation, rape, arson, destruction and kidnapping.

Similarly, if only the magnetic field () is non-zero and is constant in time, the field is said to be a magnetostatic field.

Similarly, the multiplicative group of the field is a cyclic group.

Similarly, the set of all solutions to Einstein's field equations is simpler than a specific solution.

Despite the nomenclature, the " field " under study is the gravitational potential, φ, rather than the gravitational field, g. Similarly, when classical field theory is used to study electromagnetism, the " field " of interest is the electromagnetic four-potential ( V / c, A ), rather than the electric and magnetic fields E and B.

Similarly, at a fixed temperature below the critical temperature, superconducting materials cease to superconduct when an external magnetic field is applied which is greater than the critical magnetic field.

Similarly, if the length scales are much longer than the wave ’ s wavelength, as is often the case for light in the field of optics, one can treat the waves as light rays which correspond locally to plane waves.

Similarly, the manual for the ORCA / M assembler refers to a field indicating the order of the bytes in a number field as, and the Mac OS X operating system refers to " byte sex " in its compiler tools .</ ref > The usual contrast is whether the most significant or least significant byte is ordered first — i. e., at the lowest byte address — within the larger data item.

Similarly, the manual for the ORCA / M assembler refers to a field indicating the order of the bytes in a number field as, and the Mac OS X operating system refers to " byte sex " in its compiler tools .</ ref > x86 computers do not have the same " byte sex ", as HC11 computers, for example.

Similarly, Barnum Brown claimed to have seen over 500 skulls in the field.

Similarly, autonomy has been and probably will continue to be considered an extension of the controls field.

Similarly, biproducts exist in the category of vector spaces over a field.

Similarly, the completeness property cannot be expected to carry over, because the reals are the unique complete ordered field up to isomorphism.

Similarly, Robert Nozick argues for a theory that is mostly consequentialist, but incorporates inviolable " side-constraints " which restrict the sort of actions agents are permitted to do.

Similarly, a consequentialist theory may aim at the maximization of a particular virtue or set of virtues.

Similarly, Herman's theory of doublespeak having an inherent nature to be manipulative and Chomsky's theory of ' dichotomization ' relates directly to the practice of doublespeak and how doublespeak is deliberately deceptive in nature.

Similarly, demand-and-supply theory predicts a new price-quantity combination from a shift in demand ( as to the figure ), or in supply.

Similarly, a mathematician does not restrict his study of numbers to the integers ; rather he considers more abstract structures such as rings, and in particular number rings in the context of algebraic number theory.

Similarly, Belgium took no direct influence from the Statute or English copyright theory, but Joris Deene of the University of Ghent identifies an indirect influence " at two levels "; the criteria for what constitutes copyrightable material, which comes from the work of English theorists such as Locke and Edward Young, and the underlying justification of copyright law.

Similarly, deep structure was devised largely for technical reasons relating to early semantic theory.

Similarly, an experiment that provides a counterexample can disprove a theory or hypothesis.

Similarly, liberalism draws upon the work of Kant and Rousseau, with the work of the former often being cited as the first elaboration of democratic peace theory.

Similarly, probability theory states that the probability of an event can be described by a combination of the probabilities of certain specific other events ( see Mathematical treatment ).

4 ) Similarly, the Moore – Smith theory of convergence via nets, as supplemented by Kelley's notion of a universal net, leads to the criterion that a space is compact if and only if each universal net on the space converges.

Similarly, in social theory, a single direct action producing a social change is a first-order control system.

Similarly, many who avail themselves of magic do so without feeling the need to understand a causal theory behind it.

His need to provide a liberal justification for criminal law practice thus lead him to moral philosophy, and to the development of an original " consensual " theory of punishment which combined the merits of the retributive and utilitarian ( see deterrence ) varieties while avoiding their respective difficulties Similarly, the problems presented by the characterization of criminal conduct stimulated his work in the field of philosophy of action.

Similarly, object relations theory would point to the way ' in perversion there is the refusal, the terror of strangeness '; to the way ' the " pervert "... attacks imaginative elaboration through compulsive action with an accomplice ; and this is done to mask psychic pain '.

Similarly, Fermat's last theorem is stated in term of elementary arithmetic, which is a part of commutative algebra, but its proof involves deep results of both algebraic number theory and algebraic geometry.

Similarly, a theory consists of some indeterminate conjunction of hypotheses,

Similarly, in graph theory, this is sometimes referred to as " almost surely ".

" Similarly, Maria Todorova notes that, although it minimized the Ottoman contribution and displayed " emotional or evaluative overtones ", such a perspective ran against the divisive interpretations of the Balkans, offering a working paradigm for a global history of the region: " Although Iorga's theory may be today 2009 no more than an exotic episode in the development of Balkan historiography, his formulation Byzance après Byzance is alive not only because it was a fortunate phrase but because it reflects more than its creator would intimate.

Similarly, every cobordism theory has an extraordinary cohomology theory, with homology (" bordism ") groups and cohomology (" cobordism ") groups for any space.