![]() ![]() Our main technique is the use of a Pauli basis decomposition, which we believe should lead to further progress in deriving such bounds. These bounds on p are notably better than previous bounds, yet are incomparable because of the somewhat different circuit model that we are using. Moreover, if the only allowed gate on more than one qubit is the two-qubit CNOT gate, then our bound becomes 29.3%. For the important special case of k=2, our bound is p>35.7%. For any non-unitary qubit channel $\mathcal), the output of any such circuit of large enough depth is essentially independent of its input, thereby making the circuit useless. ![]() In this work, using a minimal model for quantum fault tolerance, we establish a general lower bound on the space overhead required to achieve fault tolerance. A recent work by Fawzi, Grospellier and Leverrier (FOCS 2018) building on a result by Gottesman (QIC 2013) has shown that the space overhead can be asymptotically reduced to a constant independent of the circuit provided we only consider circuits with a length bounded by a polynomial in the width. The threshold theorem is a fundamental result in the theory of fault-tolerant quantum computation stating that arbitrarily long quantum computations can be performed with a polylogarithmic overhead provided the noise level is below a constant level. So, how can we correct quantum errors Encoding and decoding The idea of quantum error correction is to encode your state on a larger system, using redundant qubits. ![]()
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