On Fault Tolerance of Circuits with Intermediate Qutrit-assisted Gate
Decomposition
- URL: http://arxiv.org/abs/2212.07866v2
- Date: Tue, 12 Sep 2023 11:40:31 GMT
- Title: On Fault Tolerance of Circuits with Intermediate Qutrit-assisted Gate
Decomposition
- Authors: Ritajit Majumdar, Amit Saha, Amlan Chakrabarti, Susmita Sur-Kolay
- Abstract summary: An intermediate qutrit implies that a qubit is operated as a qutrit in a particular execution cycle.
We study the challenges of including fault-tolerance in such a decomposition.
- Score: 3.452050192629253
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The use of a few intermediate qutrits for efficient decomposition of 3-qubit
unitary gates has been proposed, to obtain an exponential reduction in the
depth of the decomposed circuit. An intermediate qutrit implies that a qubit is
operated as a qutrit in a particular execution cycle. This method, primarily
for the NISQ era, treats a qubit as a qutrit only for the duration when it
requires access to the state $\ket{2}$ during the computation. In this article,
we study the challenges of including fault-tolerance in such a decomposition.
We first show that any qubit that requires access to the state $\ket{2}$ at any
point in the circuit, must be encoded using a qutrit quantum error correcting
code (QECC), thus resulting in a circuit with both qubits and qutrits at the
outset. Since qutrits are noisier than qubits, the former is expected to
require higher levels of concatenation to achieve a particular accuracy than
that for qubit-only decomposition. Next, we derive analytically (i) the number
of levels of concatenation required for qubit-qutrit and qubit-only
decompositions as a function of the probability of error, and (ii) the
criterion for which qubit-qutrit decomposition leads to a lower gate count than
qubit-only decomposition. We present numerical results for these two types of
decomposition and obtain the situation where qubit-qutrit decomposition excels
for the example circuit of the quantum adder by considering different values
for quantum hardware-noise and non-transversal implementation of the
2-controlled ternary CNOT gate.
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