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unstructured database Grover s algorithm is probabilistic, as are most quantum algorithms and provides an answer with high probability The probability of correctness can be increased by repeating the algorithm Suppose that we have an unstructured sea of data in which is hidden some information we want There are keywords x based on n qubits such that 0 r x r2n 1 The number of keywords in the database is N = 2n We include an additional qubit to tag a keyword of interest Overall there are at least n + 1 qubits in this keyword system, not counting those needed for scratchpad calculations A quantum Boolean function f (x) is now constructed that will tag the keyword of interest no matter where it is located in a sea of data.

If you need anytime, anywhere access to your GTD system, try Vitalist (www.vitalist. com). This Web site offers free and paid accounts and is set up to manage all your

Cloud Application (eg SaaS)

Every new Catalyst project contains a single state which by default is named Page1. Projects can, however, contain as many states as are needed. States are managed in the Pages/States panel at the top of the screen (see Figure 10.1). You can create new states either from scratch or as a duplicate of an existing state. Most often, states contain assets and components from other existing states; therefore, you generally create them as duplicates of other states.

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The function is de ned on integers x so that f (x) = 0 for all x except x = x0 A state vector is prepared for n + 1 qubits (associated with 2n integers y and a tag qubit) as in boxes 1 and 2 in Figure 10-1 This places the n qubits into a standard superposition In box 3 we apply a unitary transform Uf corresponding to f (x) Box 3 in this application has been termed an oracle because it tags the desired keyword with a negative sign where the function is true This can be interpreted as tagging x0 with a negative sign corresponding to the location x0 of the hidden keyword We do not know the value of x0, but once tagged, the oracle knows where it is Finding it has been compared to nding a needle in a haystack.

If you have more than one linear equation, you can group each of them into a single matrix. For example, consider the following three linear equations:

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For this text field, there s no need to specify any validation beyond it being a required field. 3. From the Preview states list, choose Required. Change the error message from A value is required to Required. The background color applied to the form field is part of the style for this form field state; you ll learn how to modify it later in this chapter. Now, you can apply the same basic steps to the second text field. 4. Hover your mouse over the companyTxt form field and click the Spry tab when it appears. In the Property inspector, choose Validate on: Blur and make sure the Required option is selected. From the Preview states list, choose Required. Change the error message to Required (Figure 10-22).

By default, the Tool Presets palette, which includes the pop-up version, shows all the tool presets. This can make it difficult to quickly select, say, a preset Rectangular Marquee tool from the crowd. Fear not! At the bottom of the palettes is an option to show presets for only the currently selected tool (Figure 3-40). Appropriately enough, it s called Current Tool Only. If you have an aversion to pressing buttons, you can choose Show Current Tool Presets from the palette menu.

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The following algorithm ignores any symmetry or special properties resulting from an application of Uf In special cases, there might be a shortcut to identifying x0, which is still a topic of ongoing research The algorithm for the general case is outlined as follows: Step 1 The qubits are prepared as in boxes 1 and 2 in Figure 10-1 This is assumed equivalent to Hadamard transform on p rst n qubits and the initializing the last qubit to the quantity (|0i |1i)= 2 Step 2 Repeat steps (a) and (b) below a number of times equal to m (de ned below) (a) Apply Uf (b) Apply to the n qubits the unitary operator D = I + 2J/N, where J is the all-1 s matrix Step 3 Observe (destructively) the qubits and observe a keyword x Step 4 Evaluate f (x).