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Optimal Error Correcting Code For Ternary Quantum Systems
TL;DR: It is proved that 5 qutrits are necessary to correct a single error, which makes the proposed 6-qutrit quantum error correcting code near-optimal in the number of qUTrits.
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Abstract: Multi-valued quantum systems can store more information than binary ones for a given number of quantum states. For reliable operation of multi-valued quantum systems, error correction is mandated. In this paper, we propose a 5-qutrit quantum error-correcting code and provide its stabilizer formulation. Since 5 qutrits are necessary to correct a single error, our proposed code is optimal in the number of qutrits. We prove that the error model considered in this paper spans the entire $(3 \times 3)$ operator space. Therefore, our proposed code can correct any single error on the codeword. This code outperforms the previous 9-qutrit code in (i) the number of qutrits required for encoding, (ii) our code can correct any arbitrary $(3 \times 3)$ error, (ii) our code can readily correct bit errors in a single step as opposed to the two-step correction used previously, and (iii) phase error correction does not require correcting individual subspaces.
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Asymptotically improved circuit for a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi></mml:math> -ary Grover's algorithm with advanced decomposition of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math> -qudit Toffoli gate
28 Jun 2022
TL;DR: In this paper , a generalized Toffoli gate is realized using higher-dimensional qudits to attain a logarithmic depth decomposition without ancilla qudit, and the circuit for Grover's algorithm has then been designed for any $d$-ary quantum system, where $d\ensuremath{\ge}2
Primitive quantum gates for an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> discrete subgroup: Binary tetrahedral
TL;DR: In this article , a primitive gate set for the digital quantum simulation of the binary tetrahedral group on two quantum architectures was constructed, which serves as a crude approximation to lattice gauge theory while requiring five qubits or one quicosotetrit per gauge link.
Approximate Ternary Quantum Error Correcting Code with Low Circuit Cost
Ritajit Majumdar,Susmita Sur-Kolay +1 more
- 01 Nov 2020
TL;DR: In this article, the authors proposed a 6-qutrit approximate QECC (AQECC) of CSS structure which can simultaneously correct phase errors in upto six qutrits, and one bit error in only four of the six qubits, without sharing prior entanglement.
6
Primitive Quantum Gates for an SU(2) Discrete Subgroup: BT
Erik Gustafson,Henry Lamm,Felicity Lovelace,Damian Musk +3 more
- 25 Aug 2022
TL;DR: A primitive gate set for the digital quantum simulation of the binary tetrahedral group on two quantum architectures serves as a crude approximation to SU (2) lattice gauge theory while requiring two qubits or one quicosotetrit per gauge link.
3
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Exploiting degeneracy to construct good ternary quantum error correcting code.
TL;DR: This proposed 7-qutrit error-correcting code for the ternary quantum system is proposed and shows that it is possible to design better codes explicitly for ternARY quantum systems instead of simply carrying over codes from binary quantum systems.
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