Note on Needle in a Haystack

Introduced below is a quantum database method, not only for retrieval but also for creation. It uses a particular structure of true’s and false’s in a state vector of n qubits, permitting up to 2**2**n words, vastly more than for classical bits. Several copies are produced so that later they can be destructively observed and a word determined with high probability. Grover’s algorithm is proposed below to read out, nondestructively the unknown contents of a given stored state vector using only one state vector. Data Storage in a State Vector of Qubits Holding data in a quantum system is clearly problematic, since such systems quickly become incoherent, although systems of the future might be designed to be more stable. This paper assumes a quantum system with m identical sets of n qubits, where each set is assumed to form a state vector. Then each state vector is loaded with 1’s and 0’s with an appropriate normalization factor. For n qubits a state vector has dimension 2 which theoretically holds n 2 2 binary codes. An interesting and practical subset of a general state vector is to initialize qubits to combinations of H |0> = (1 1)’/√2, |1> = (0 1)’, and |0> = (1 0)’. Each state vector will then have a particular structure termed here the H10 structure: For 2 entries, either the pattern repeats in the other half (2) entries, or one of the halves is filled with 0s. For example, one may have 0011, 0000/√2 for n = 3, this being |0> |1> H |0>. Note that anything similar to 0111, 0000 is impossible under H10 symmetry, since this rule also applies to each quarter (block of 2) and so on down to blocks of 2 states. If any one state is true and all others false, the result is just a binary count of n items, a given combination of n computational basis qubits. Readout is probabilistic. For example, if copies of 0011, 0000 are read a few times, there is a very good chance that entries |0>, |1>, |0> and |1), |1>, |1> will result, permitting reconstruction of the stored word 0011, 0000. (Simply note that the entries corresponding to combinations of computational basis qubits count up in binary from the left). The H10 structure has the advantage that it can be produced without complex quantum gates. It should be mentioned that the number of codes using H10 symmetry is far more than 2 but still far less than the n 2 2 available by arbitrarily placing true’s