{"id":164459,"date":"2018-11-06T17:22:28","date_gmt":"2018-11-07T01:22:28","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/efficient-decomposition-of-single-qubit-gates-into-v-basis-circuits\/"},"modified":"2018-11-06T17:22:28","modified_gmt":"2018-11-07T01:22:28","slug":"217-efficient-decomposition-of-single-qubit-gates-into-v-basis-circuits","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/217-efficient-decomposition-of-single-qubit-gates-into-v-basis-circuits\/","title":{"rendered":"Efficient Decomposition of Single-Qubit Gates into V Basis Circuits"},"content":{"rendered":"
\n

We develop efficient algorithms for compiling single-qubit unitary gates into circuits over the universal V<\/span><\/span><\/span><\/span><\/span> basis<\/i>. The V<\/span><\/span><\/span><\/span><\/span> basis<\/i> is an alternative universal basis to the more commonly studied basis consisting of Hadamard and \u03c0<\/span>\/<\/span>8<\/span><\/span><\/span><\/span><\/span><\/span> gates. We propose two classical algorithms for quantum circuit compilation: the first algorithm has expected polynomial time [in precision log<\/span>(<\/span>1<\/span>\/<\/span>\u03b5<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span>] and produces an \u03b5<\/span><\/span><\/span><\/span><\/span> approximation to a single-qubit unitary with a circuit depth \u2264<\/span>12<\/span><\/span>log<\/span>5<\/span><\/span>(<\/span>2<\/span>\/<\/span>\u03b5<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>. The second algorithm performs optimized direct search and yields circuits a factor of 3 to 4 times shorter than our first algorithm, but requires time exponential in log<\/span>(<\/span>1<\/span>\/<\/span>\u03b5<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span>; however, we show that in practice the runtime is reasonable for an important range of target precisions. Decomposing into the V<\/span><\/span><\/span><\/span><\/span> basis may offer advantages when considering the fault-tolerant implementation of quantum circuits.<\/p>\n<\/div>\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

We develop efficient algorithms for compiling single-qubit unitary gates into circuits over the universal V basis. The V basis is an alternative universal basis to the more commonly studied basis consisting of Hadamard and \u03c0\/8 gates. We propose two classical algorithms for quantum circuit compilation: the first algorithm has expected polynomial time [in precision log(1\/\u03b5)] 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