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arXiv:2307.14103 · Physical review. B./Physical review. B

Error channels in quantum nondemolition measurements on spin systems

Benjamin Joecker, Holly G. Stemp, Irene Fernández de Fuentes, Mark A. I. Johnson, Andrea Morello

Published Feb 7, 2024• 10 citations
arXivHTMLPDF

Abstract

Quantum nondemolition measurements (QNDMs) are a precious resource for quantum computing. They are an integral part of the surface code, the holy grail of quantum error correction, and can boost initialization and readout fidelities through repeated measurements. In spin systems, scalable QNDMS are achievable by coupling to ancillary spins read via charge reservoirs. Here, the authors develop a model to quantify how small deviations from true QNDMs in real spin system can introduce bit-flip errors and analyze how they can be minimized.

DOI
10.1103/physrevb.109.085302

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Quantum nondemolition measurements (QNDMs) are a precious resource for quantum computing. They are an integral part of the surface code, the holy grail of quantum error correction, and can boost initialization and readout fidelities through repeated measurements. In spin systems, scalable QNDMS are achievable by coupling to ancillary spins read via charge reservoirs. Here, the authors develop a model to quantify how small deviations from true QNDMs in real spin system can introduce bit-flip errors and analyze how they can be minimized.
Quantum error correction is of crucial importance for fault-tolerant quantum computers.As an essential step toward the implementation of quantum error-correcting codes, quantum nondemolition measurements are needed to efficiently detect the state of a logical qubit without destroying it.Here we implement quantum nondemolition measurements in a Si/SiGe two-qubit system, with one qubit serving as the logical qubit and the other serving as the ancilla.Making use of a two-qubit controlled-rotation gate, the state of the logical qubit is mapped onto the ancilla, followed by a destructive readout of the ancilla.Repeating this procedure enhances the logical readout fidelity from 75.5 Æ 0.3% to 94.5 Æ 0.2% after 15 ancilla readouts.In addition, we compare the conventional thresholding method with an improved signal processing method called soft decoding that makes use of analog information in the readout signal to better estimate the state of the logical qubit.We demonstrate that soft decoding leads to a significant reduction in the required number of repetitions when the readout errors become limited by Gaussian noise, for instance, in the case of readouts with a low signal-to-noise ratio.These results pave the way for the implementation of quantum error correction with spin qubits in silicon.
The performance of quantum-error-correction schemes depends sensitively on the physical realizations of the qubits and the implementations of various operations. For example, in quantum-dot spin qubits, readout is typically much slower than gate operations, and conventional surface-code implementations that rely heavily on syndrome measurements could therefore be challenging. However, fast and accurate reset of quantum-dot qubits, without readout, can be achieved via tunneling to a reservoir. Here we propose small-scale surface-code implementations for which syndrome measurements are replaced by a combination of Toffoli gates and qubit reset. For quantum-dot qubits, this enables much faster error correction than measurement-based schemes, but requires additional ancilla qubits and non-nearest-neighbor interactions. We have performed numerical simulations of two different coding schemes, obtaining error thresholds on the orders of ${10}^{\ensuremath{-}2}$ for a one-dimensional architecture that only corrects bit-flip errors and ${10}^{\ensuremath{-}4}$ for a two-dimensional architecture that corrects bit- and phase-flip errors.
Quantum systems operate using quantum bits (qubits), which are highly sensitive to external noises and disturbances and they are easily prone to errors. In the Noisy Intermediate-Scale Quantum (NISQ) era, these errors make difficult to build reliable, fault tolerant quantum circuits for real world deployment. This work provides an overview of need for Quantum Error Correction (QEC) in NISQ devices, as qubits commonly get affected by bit-flip, phase-flip, and combined errors that degrades system performance and examines Quantum Error Correction Code (QECC) techniques usage in communication, computation, and quantum multimedia applications such as image and video transmission. In addition, a simple three-qubit repetition circuit is introduced to demonstrate an error-mitigation approach. These findings, also show how QEC improves fidelity, reduces logical errors, and improves noise tolerance. The analysis also identifies challenges and outlines the future research direction aimed at achieving efficient and scalable fault tolerant quantum circuits.
Quantum error correction (QEC) requires non-invasive measurements for fault tolerant quantum computing. Deviations from ideal quantum non-demolition (QND) measurements can disturb the encoded information. To address this challenge, we develop a readout protocol for a D−D-D−dimensional system that, after a single positive outcome, switches to probing only the D−1D{-}1D−1 remaining subspace. This adaptive switching strategy minimizes measurement-induced errors by relying on negative-result measurement results that do not perturb the Hamiltonian. We apply the protocol on an 8-dimensional 123Sb^{123}{\rm Sb}123Sb nuclear qudit in silicon, and achieve an increase in the readout fidelity from (98.93±0.07)%(98.93\pm0.07)\%(98.93±0.07)% to (99.61±0.04)%(99.61\pm0.04)\%(99.61±0.04)%, while reducing threefold the overall readout time. To highlight the broader relevance of measurement-induced errors, we study a 10-dimensional 73Ge^{73}{\rm Ge}73Ge nuclear spin read out through Pauli spin blockade, revealing nuclear spin flips arising from hyperfine and quadrupole interactions. These results unveil the effect of non-ideal QND readout across diverse platforms, and introduce an efficient readout protocol that can be implemented with minimal FPGA logic on existing hardware.
Quantum systems operate using quantum bits (qubits), which are highly sensitive to external noises and disturbances and they are easily prone to errors. In the Noisy Intermediate-Scale Quantum (NISQ) era, these errors make difficult to build reliable, fault tolerant quantum circuits for real world deployment. This work provides an overview of need for Quantum Error Correction (QEC) in NISQ devices, as qubits commonly get affected by bit-flip, phase-flip, and combined errors that degrades system performance and examines Quantum Error Correction Code (QECC) techniques usage in communication, computation, and quantum multimedia applications such as image and video transmission. In addition, a simple three-qubit repetition circuit is introduced to demonstrate an error-mitigation approach. These findings, also show how QEC improves fidelity, reduces logical errors, and improves noise tolerance. The analysis also identifies challenges and outlines the future research direction aimed at achieving efficient and scalable fault tolerant quantum circuits.