![]() For this to happen, the performance of quantum computing hardware needs to improve and software needs to seamlessly integrate quantum and classical processors together to form a new architecture that we are calling quantum-centric supercomputing. Meanwhile, achieving a computational advantage in the near term may be possible by combining multiple QPUs through circuit knitting techniques, improving the quality of solutions through error suppression and mitigation, and focusing on heuristic versions of quantum algorithms with asymptotic speedups. Extracting the full potential of computation and realizing quantum algorithms with a super-polynomial speedup will most likely require major advances in quantum error correction technology. The essential idea is to design stabilizer codes in layers, with $N_1$ inner qubits and $N_2$ outer qubits, and to assemble a universal set of fault tolerant gates on the inner qubits.įor the first time in history, we are seeing a branching point in computing paradigms with the emergence of quantum processing units (QPUs). Finally, we develop an approach to circumventing the Eastin-Knill Theorem which states that no QECC can implement a universal set of logical gates through transversal gates alone. We provide a simple alternative to the standard method of deriving the coset weight distributions (based on Dickson normal form) that may be of independent interest. ![]() We construct new families of CSS codes using cosets of the first order Reed Muller code defined by quadratic forms. These constraints are a perfect fit to divisible codes, and represent an opportunity to take advantage of the extensive literature on classical codes with two or three weights. They are used to design signals for communications and sensing, and this paper explores how they can be used to protect quantum information as it is transformed by logical gates. Divisible codes are defined by the property that codeword weights share a common divisor greater than one. ![]()
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