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We present an algorithm for computing depth-optimal decompositions of logical operations, leveraging a meet-in-the-middle technique to provide a significant speed-up over simple brute force algorithms. As an illustration of our method we implemented this algorithm and found factorizations of the commonly used quantum logical operations into elementary gates(More)
Two orthonormal bases B and B ′ of a d-dimensional complex inner-product space are called mutually unbiased if and only if |b|b ′ | 2 = 1/d holds for all b ∈ B and b ′ ∈ B ′. The size of any set containing pairwise mutually unbiased bases of C d cannot exceed d + 1. If d is a power of a prime, then extremal sets containing d + 1 mutually unbiased bases are(More)
— We present an algorithm to construct quantum circuits for encoding and inverse encoding of quantum convo-lutional codes. We show that any quantum convolutional code contains a subcode of finite index which has a non-catastrophic encoding circuit. Our work generalizes the conditions for non-catastrophic encoders derived in a paper by Ollivier and Tillich(More)
— Unitary error bases generalize the Pauli matrices to higher dimensional systems. Two basic constructions of unitary error bases are known: An algebraic construction by Knill, which yields nice error bases, and a combinato-rial construction by Werner, which yields shift-and-multiply bases. An open problem posed by Schlingemann and Werner relates these two(More)
Recently, it was shown that Repeat-Until-Success (RUS) circuits can achieve a 2.5 times reduction in expected depth over ancilla-free techniques for single-qubit unitary decomposition. However, the previously best-known algorithm to synthesize RUS circuits requires exponential classical runtime. In this work we present an algorithm to synthesize an RUS(More)
It has been known for some time that graph isomorphism reduces to the hidden subgroup problem (HSP). What is more, most exponential speedups in quantum computation are obtained by solving instances of the HSP. A common feature of the resulting algorithms is the use of quantum coset states, which encode the hidden subgroup. An open question has been how hard(More)
— Quantum convolutional codes can be used to protect a sequence of qubits of arbitrary length against decoherence. We introduce two new families of quantum convolutional codes. Our construction is based on an algebraic method which allows to construct classical convolutional codes from block codes, in particular BCH codes. These codes have the property that(More)