This work gives a simplified proof of this fact based on the estimation of exponential sums that extremal sets containing d+1 mutually unbiased bases are known to exist.Expand

It is demonstrated that maximal sets of MUBs come with a rich combinatorial structure by showing that they actually are the same objects as the complex projective 2-designs with angle set {0, 1/d}.Expand

This paper derives asymmetric codes using a combination of Bose–Chaudhuri–Hocquenghem (BCH) and finite geometry low-density parity-check (LDPC) codes and shows that the asymmetric quantum codes offer two advantages, namely to allow a higher rate without sacrificing performance when compared with symmetric codes and vice versa to allowed a higher performance whenCompared with symmetrical codes of comparable rates.Expand

It is established that for all three variants of AES key size 128, 192, and 256i¾źbit that are standardized in FIPS-PUB 197, there are precise bounds for the number of qubits and thenumber of elementary logical quantum gates that are needed to implement Grover's quantum algorithm to extract the key from a small number of AES plaintext-ciphertext pairs.Expand

An implementation of Shor's quantum algorithm to factor n-bit integers using only 2n+2 qubits using a purely Toffoli based modular multiplication circuit that evades most of the cost overheads originating from rotation synthesis and enables testing and localization of some faults in both, the logical level circuit and an actual quantum hardware implementation.Expand

The results indicate that, for current parameters at comparable classical security levels, the number of qubits required to tackle elliptic curves is less than for attacking RSA, suggesting that indeed ECC is an easier target than RSA.Expand

It is shown that any quantum convolutional code contains a subcode of finite index which has a non-catastrophic encoding circuit and the encodes and their inverse constructed by the method naturally can be applied online, i.e., qubits can be sent and received with constant delay.Expand

A reversible circuit compiler called ReVerC is presented, which has been formally verified in F* and compiles circuits that operate correctly with respect to the input program and provably cleans temporary values.Expand

Q# is presented, a quantum-focused domain-specific language explicitly designed to correctly, clearly and completely express quantum algorithms that provides a type system; a tightly constrained environment to safely interleave classical and quantum computations; specialized syntax; symbolic code manipulation to automatically generate correct transformations of quantum operations.Expand

The construction is based on an algebraic method which allows to construct classical convolutional codes from block codes, in particular BCH codes, which have the property that they contain their Euclidean and Hermitian dual codes.Expand