 Award ID(s):
 1917383
 NSFPAR ID:
 10189442
 Date Published:
 Journal Name:
 nternational Conference on Reversible Computation (RC), Springer LNCS
 Volume:
 11497
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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A basic question in the theory of faulttolerant quantum computation is to understand the fundamental resource costs for performing a universal logical set of gates on encoded qubits to arbitrary accuracy. Here we consider qubits encoded with constant space overhead (i.e. finite encoding rate) in the limit of arbitrarily large code distance d through the use of topological codes associated to triangulations of hyperbolic surfaces. We introduce explicit protocols to demonstrate how Dehn twists of the hyperbolic surface can be implemented on the code through constant depth unitary circuits, without increasing the space overhead. The circuit for a given Dehn twist consists of a permutation of physical qubits, followed by a constant depth local unitary circuit, where locality here is defined with respect to a hyperbolic metric that defines the code. Applying our results to the hyperbolic Fibonacci TuraevViro code implies the possibility of applying universal logical gate sets on encoded qubits through constant depth unitary circuits and with constant space overhead. Our circuits are inherently protected from errors as they map local operators to local operators while changing the size of their support by at most a constant factor; in the presence of noisy syndrome measurements, our results suggest the possibility of universal fault tolerant quantum computation with constant space overhead and time overhead of O ( d / log d ) . For quantum circuits that allow parallel gate operations, this yields the optimal scaling of spacetime overhead known to date.more » « less

Abstract Suppressing errors is the central challenge for useful quantum computing^{1}, requiring quantum error correction (QEC)^{2–6}for largescale processing. However, the overhead in the realization of errorcorrected ‘logical’ qubits, in which information is encoded across many physical qubits for redundancy^{2–4}, poses substantial challenges to largescale logical quantum computing. Here we report the realization of a programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits. Using logicallevel control and a zoned architecture in reconfigurable neutralatom arrays^{7}, our system combines high twoqubit gate fidelities^{8}, arbitrary connectivity^{7,9}, as well as fully programmable singlequbit rotations and midcircuit readout^{10–15}. Operating this logical processor with various types of encoding, we demonstrate improvement of a twoqubit logic gate by scaling surfacecode^{6}distance from
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Quantum computing is an emerging technology that has the potential to achieve exponential speedups over their classical counterparts. To achieve quantum advantage, quantum principles are being applied to fields such as communications, information processing, and artificial intelligence. However, quantum computers face a fundamental issue since quantum bits are extremely noisy and prone to decoherence. Keeping qubits error free is one of the most important steps towards reliable quantum computing. Different stabilizer codes for quantum error correction have been proposed in past decades and several methods have been proposed to import classical error correcting codes to the quantum domain. Design of encoding and decoding circuits for the stabilizer codes have also been proposed. Optimization of these circuits in terms of the number of gates is critical for reliability of these circuits. In this paper, we propose a procedure for optimization of encoder circuits for stabilizer codes. Using the proposed method, we optimize the encoder circuit in terms of the number of 2qubit gates used. The proposed optimized eightqubit encoder uses 18 CNOT gates and 4 Hadamard gates, as compared to 14 single qubit gates, 33 2qubit gates, and 6 CCNOT gates in a prior work. The encoder and decoder circuits are verified using IBM Qiskit. We also present encoder circuits for the Steane code and a 13qubit code, that are optimized with respect to the number of gates used, leading to a reduction in number of CNOT gates by 1 and 8, respectively.more » « less

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