We use this implementation to establish a new example of quantum advantage by Clifford circuits over CNOT gate circuits and find optimal Clifford 2-designs for up to 4 qubits. We demonstrate how to extract arbitrary optimal 6-qubit Clifford circuit in 0.0009358 and 0.0006274 s using consumer- and enterprise-grade computers (hardware) respectively, while relying on this database. it’s not possible to produce any arbitrary unitary just using a combination of Clifford operators, as. In this paper, we report a set of algorithms, along with their C++ implementation, that implicitly synthesize optimal circuits for all 6-qubit Clifford group elements by storing a subset of the latter in a database of size 2.1TB (1kB = 1024B). A Quantum Circuit that only contains Clifford gates can be efficiently simulated on a classical computer 1, and because the Clifford Group doesn’t include the T gate or Toffoli (CCX) they cannot by themselves achieve universality (i.e. We will say that a n-qubit state is a Clifford. For n = 6, the number of Clifford group elements is about 2.1 × 1023. The Clifford group is the set of gates generated by controlled-Z gates, the phase gate and the Hadamard gate. Finding short circuits is a hard problem despite Clifford group being finite, its size grows quickly with the number of qubits n, limiting known optimal implementations to n = 4 qubits. The ability to utilize Clifford group elements in practice relies heavily on the efficiency of their circuit-level implementation. Clifford group lies at the core of quantum computation-it underlies quantum error correction, its elements can be used to perform magic state distillation and they form randomized benchmarking protocols, Clifford group is used to study quantum entanglement, and more.
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