Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1708.00468 · Quantum Information Processing

Implementing a noise protected logical qubit in methyl groups via microwave irradiation

Razieh Annabestani, David G. Cory

Published Dec 16, 2017• 0 citations
arXivHTMLPDF

Abstract

We propose a proof-of-principle experiment to encode one logical qubit in noise protected subspace of three identical spins in a methyl group. The symmetry analysis of the wavefunction shows that this fermionic system exhibits a symmetry correlation between the spatial degree of freedom and the spin degree of freedom. We show that one can use this correlation to populate the noiseless subsystem by relying on the interaction between the electric dipole moment of the methyl group with a circularly polarized microwave field. Logical gates are implemented by controlling both the intensity and phase of the applied field.

DOI
10.1007/s11128-017-1792-7

Related papers

Collective Dynamics in NMR and Quantum Noise

Razieh Annabestani

We introduced an open quantum system model to describe the statistical fluctuations of a spin ensemble in NMR. The model considers an ensemble measurement where the detection coil does not distinguish spins, and accounts for the state update rule. The analysis brings clarity and accuracy in describing the notion of spin noise and derives a correct statistical distribution and correlation function for the spin noise signal. \n \nWe propose a proof-of-principle experiment to encode one logical qubit in the noise protected subspace of three identical spins in a methyl group. We use a symmetry analysis to derive the dipole moment allowed transitions, which enable us to access the noiseless subsystem. We fur- ther analyze the symmetry of the hetronuclear dipolar relaxation, which is one of the responsible mechanisms for observing a noise protected state. Our analytical calculations predict features of of the NMR peaks that are in agreement with the experimental observations. \n \nWe propose a quantum key distribution protocol that simplifies the task of classical data processing in a trusted relay network. A new announcement strategy is proposed which leads to reassigning the task of error correction and privacy amplification from the intermediate user to the end-node users. We examine the security of the proposed protocol analytically, derive the key rate for two well-known examples of BB84 and 6-state protocols numerically, and consider a few imperfections arising in practical QKD.

•Oct 17, 2016•0 citations

Exploring noiseless subsystems via nuclear magnetic resonance

Evan M. Fortunato, Lorenza Viola, Marco A. Pravia +4 more

Noiseless subsystems offer a general and efficient method for protecting quantum information in the presence of noise that has symmetry properties. A paradigmatic class of error models displaying nontrivial symmetries emerges under collective noise behavior, which implies a permutationally invariant interaction between the system and the environment. We expand our previous investigation of the noiseless subsystem idea [L. Viola et al., Science 293, 2059 (2001)] by reporting and analyzing NMR experiments that demonstrate the preservation of a qubit encoded in a three-qubit noiseless subsystem for general collective noise. A complete set of input states is used to determine the superoperator for the implemented one-qubit process and to confirm that the fidelity of entanglement is improved for a large, noncommutative set of engineered errors. To date, this is the largest set of error operators that has been successfully corrected for by any quantum code.

arXiv:quant-ph/0210057•Physical Review A•Jun 19, 2003•39 citations

Experimental Realization of Noiseless Subsystems for Quantum Information Processing

Lorenza Viola, Evan M. Fortunato, Marco A. Pravia +3 more

We demonstrate the protection of one bit of quantum information against all collective noise in three nuclear spins. Because no subspace of states offers this protection, the quantum bit was encoded in a proper noiseless subsystem. We therefore realize a general and efficient method for protecting quantum information. Robustness was verified for a full set of noise operators that do not distinguish the spins. Verification relied on the most complete exploration of engineered decoherence to date. The achieved fidelities show improved information storage for a large, noncommutative set of errors.

Science•Sep 14, 2001•235 citations

Implementing one-photon three-qubit quantum gates using spatial light modulators

Ayman F. Abouraddy, Giovanni Di Giuseppe, Timothy M. Yarnall +2 more

Increasing the information-carrying capacity of a single photon may be achieved by utilizing multiple degrees of freedom. We describe here an approach that utilizes two degrees of freedom to encode three qubits per photon: one in polarization and two in the spatial-parity symmetry of the transverse field. In this conception, a polarization-sensitive spatial light modulator corresponds to a three-qubit controlled-unitary gate with one control qubit (polarization) and two target (spatial-parity-symmetry) qubits. We describe the construction of controlled-not (cnot), $\sqrt[n]{cnot}$, controlled-phase, and Fredkin gates, and the preparation of one-photon, three-qubit Greenberger-Horne-Zeilinger (GHZ) and $W$ states. This approach enables simple optical implementations of few-qubit tasks in quantum information processing.

Physical Review A•Nov 8, 2012•31 citations

Control of qubits encoded in decoherence-free subspaces

Paola Cappellaro, J. S. Hodges, Timothy F. Havel +1 more

Decoherence-free subspaces protect quantum information from the effects of noise that is correlated across the physical qubits used to implement them. Given the ability to impose suitable Hamiltonians upon such a multi-qubit system, one can also implement a set of logical gates which enables universal computation on this information without compromising this protection. Real physical systems, however, seldom come with the correct Hamiltonians built-in, let alone the ability to turn them off and on at will. In the course of our development of quantum information processing devices based on liquid-state NMR, we have found the task of operating on quantum information encoded in decoherence-free subspaces rather more challenging than is commonly assumed. This contribution presents an overview of these challenges and the methods we have developed for overcoming them in practice. These methods promise to be broadly applicable to many of the physical systems proposed for the implementation of quantum information processing devices.

Laser Physics•Apr 1, 2007•5 citations

Recursive encoding and decoding of the noiseless subsystem and decoherence-free subspace

Chi-Kwong Li, Mikio Nakahara, Yiu‐Tung Poon +2 more

When an environmental disturbance to a quantum system has a wavelength much larger than the system size, all qubits in the system are under the action of the same error operator. The noiseless subsystem and decoherence-free subspace are immune to such collective noise. We construct simple quantum circuits that implement these error-avoiding codes for a small number $n$ of physical qubits. A single logical qubit is encoded with $n=3$ and 4, while two and three logical qubits are encoded with $n=5$ and 7, respectively. Recursive relations among subspaces employed in these codes play essential roles in our implementation.

arXiv:1106.5210•Physical Review A•Oct 5, 2011•13 citations
We propose a proof-of-principle experiment to encode one logical qubit in noise protected subspace of three identical spins in a methyl group. The symmetry analysis of the wavefunction shows that this fermionic system exhibits a symmetry correlation between the spatial degree of freedom and the spin degree of freedom. We show that one can use this correlation to populate the noiseless subsystem by relying on the interaction between the electric dipole moment of the methyl group with a circularly polarized microwave field. Logical gates are implemented by controlling both the intensity and phase of the applied field.
We introduced an open quantum system model to describe the statistical fluctuations of a spin ensemble in NMR. The model considers an ensemble measurement where the detection coil does not distinguish spins, and accounts for the state update rule. The analysis brings clarity and accuracy in describing the notion of spin noise and derives a correct statistical distribution and correlation function for the spin noise signal. \n \nWe propose a proof-of-principle experiment to encode one logical qubit in the noise protected subspace of three identical spins in a methyl group. We use a symmetry analysis to derive the dipole moment allowed transitions, which enable us to access the noiseless subsystem. We fur- ther analyze the symmetry of the hetronuclear dipolar relaxation, which is one of the responsible mechanisms for observing a noise protected state. Our analytical calculations predict features of of the NMR peaks that are in agreement with the experimental observations. \n \nWe propose a quantum key distribution protocol that simplifies the task of classical data processing in a trusted relay network. A new announcement strategy is proposed which leads to reassigning the task of error correction and privacy amplification from the intermediate user to the end-node users. We examine the security of the proposed protocol analytically, derive the key rate for two well-known examples of BB84 and 6-state protocols numerically, and consider a few imperfections arising in practical QKD.
Noiseless subsystems offer a general and efficient method for protecting quantum information in the presence of noise that has symmetry properties. A paradigmatic class of error models displaying nontrivial symmetries emerges under collective noise behavior, which implies a permutationally invariant interaction between the system and the environment. We expand our previous investigation of the noiseless subsystem idea [L. Viola et al., Science 293, 2059 (2001)] by reporting and analyzing NMR experiments that demonstrate the preservation of a qubit encoded in a three-qubit noiseless subsystem for general collective noise. A complete set of input states is used to determine the superoperator for the implemented one-qubit process and to confirm that the fidelity of entanglement is improved for a large, noncommutative set of engineered errors. To date, this is the largest set of error operators that has been successfully corrected for by any quantum code.
We demonstrate the protection of one bit of quantum information against all collective noise in three nuclear spins. Because no subspace of states offers this protection, the quantum bit was encoded in a proper noiseless subsystem. We therefore realize a general and efficient method for protecting quantum information. Robustness was verified for a full set of noise operators that do not distinguish the spins. Verification relied on the most complete exploration of engineered decoherence to date. The achieved fidelities show improved information storage for a large, noncommutative set of errors.
Increasing the information-carrying capacity of a single photon may be achieved by utilizing multiple degrees of freedom. We describe here an approach that utilizes two degrees of freedom to encode three qubits per photon: one in polarization and two in the spatial-parity symmetry of the transverse field. In this conception, a polarization-sensitive spatial light modulator corresponds to a three-qubit controlled-unitary gate with one control qubit (polarization) and two target (spatial-parity-symmetry) qubits. We describe the construction of controlled-not (cnot), cnotn\sqrt[n]{cnot}ncnot​, controlled-phase, and Fredkin gates, and the preparation of one-photon, three-qubit Greenberger-Horne-Zeilinger (GHZ) and WWW states. This approach enables simple optical implementations of few-qubit tasks in quantum information processing.
Decoherence-free subspaces protect quantum information from the effects of noise that is correlated across the physical qubits used to implement them. Given the ability to impose suitable Hamiltonians upon such a multi-qubit system, one can also implement a set of logical gates which enables universal computation on this information without compromising this protection. Real physical systems, however, seldom come with the correct Hamiltonians built-in, let alone the ability to turn them off and on at will. In the course of our development of quantum information processing devices based on liquid-state NMR, we have found the task of operating on quantum information encoded in decoherence-free subspaces rather more challenging than is commonly assumed. This contribution presents an overview of these challenges and the methods we have developed for overcoming them in practice. These methods promise to be broadly applicable to many of the physical systems proposed for the implementation of quantum information processing devices.
When an environmental disturbance to a quantum system has a wavelength much larger than the system size, all qubits in the system are under the action of the same error operator. The noiseless subsystem and decoherence-free subspace are immune to such collective noise. We construct simple quantum circuits that implement these error-avoiding codes for a small number nnn of physical qubits. A single logical qubit is encoded with n=3n=3n=3 and 4, while two and three logical qubits are encoded with n=5n=5n=5 and 7, respectively. Recursive relations among subspaces employed in these codes play essential roles in our implementation.