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تسجيل مستخدم جديدNear-linear constructions of exact unitary 2-designs
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A unitary 2-design can be viewed as a quantum analogue of a 2-universal hash function: it is indistinguishable from a truly random unitary by any procedure that queries it twice. We show that exact unitary 2-designs on n qubits can be implemented by quantum circuits consisting of ~O(n) elementary gates in logarithmic depth. This is essentially a quadratic improvement in size (and in width times depth) over all previous implementations that are exact or approximate (for sufficiently strong approximations).
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Unitary $t$-designs are `good finite subsets of the unitary group $U(d)$ that approximate the whole unitary group $U(d)$ well. Unitary $t$-designs have been applied in randomized benchmarking, tomography, quantum cryptography and many other areas of
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