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Physical Review Letters

Experimental Realization of Decoherence-Free Subspace in Neutron Interferometry

Dmitry A. Pushin, M. G. Huber, M. Arif, David G. Cory

Published Oct 6, 2011• 41 citations
Publisher

Abstract

A decoherence-free subspace (DFS) is an important class of quantum-error-correcting (QEC) codes that have been proposed for fault-tolerant quantum computation. The applications of QEC techniques, however, are not limited to quantum-information processing (QIP). Here we demonstrate how QEC codes may be used to improve experimental designs of quantum devices to achieve noise suppression. In particular, neutron interferometry is used as a test bed to show the potential for adding quantum error correction to quantum measurements. We built a five-blade neutron interferometer that incorporates both a standard Mach-Zender configuration and a configuration based on a DFS. Experiments verify that the DFS interferometer is protected against low-frequency mechanical vibrations. We anticipate these improvements will increase the range of applications for matter-wave interferometry.

DOI
10.1103/physrevlett.107.150401

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A decoherence-free subspace (DFS) is an important class of quantum-error-correcting (QEC) codes that have been proposed for fault-tolerant quantum computation. The applications of QEC techniques, however, are not limited to quantum-information processing (QIP). Here we demonstrate how QEC codes may be used to improve experimental designs of quantum devices to achieve noise suppression. In particular, neutron interferometry is used as a test bed to show the potential for adding quantum error correction to quantum measurements. We built a five-blade neutron interferometer that incorporates both a standard Mach-Zender configuration and a configuration based on a DFS. Experiments verify that the DFS interferometer is protected against low-frequency mechanical vibrations. We anticipate these improvements will increase the range of applications for matter-wave interferometry.
Perfect single-crystal neutron interferometers are adversely sensitive to environmental disturbances, particularly mechanical vibrations. The sensitivity to vibrations results from the slow velocity of thermal neutrons and the long measurement time that are encountered in a typical experiment. Consequently, to achieve a good interference solutions for reducing vibration other than those normally used in optical experiments must be explored. Here we introduce a geometry for a neutron interferometer that is less sensitive to low-frequency vibrations. This design may be compared with both dynamical decoupling methods and decoherence-free subspaces that are described in quantum information processing. By removing the need for bulky vibration isolation setups, this design will make it easier to adopt neutron interferometry to a wide range of applications and increase its sensitivity.
Quantum error correction (QEC) faces a significant challenge in realistic noisy intermediate-scale quantum (NISQ) devices: correlated decoherence. Building upon the foundational QEC-C protocol, we introduce QEC-C II, a scalable framework that delivers robust fault tolerance against spatially and temporally correlated noise. By integrating decoherence-free subspace (DFS) principles and correlation-aware adaptive feedback, QEC-C II achieves exponential error suppression in simulation under correlated noise models, with fewer physical qubits than typical topological baselines for the same target error in our benchmarks. The protocol leverages an enhanced scaling law, β(n) = 0.788 e 0.360n , and efficiently suppresses noise with minimal computational overhead. We validate QEC-C II on 28-qubit GHZ states, extend it to 56-qubit subspaces, and conduct 84-qubit stress-test simulations under correlated noise models. The results demonstrate sustained fidelities exceeding 99.99 % in simulations under realistic dephasing, amplitude-damping, burst-error, and correlated decoherence scenarios, with rapid convergence (typically ≤ 2 iterations in our simulations). QEC-C II significantly reduces both resource and control complexity, simplifying hardware integration and improving performance with increasing system size. This work provides a practical pathway toward resource-efficient fault tolerance in quantum processors operating in real-world correlated environments.
Quantum error-correcting codes (QECCs) and decoherence-free subspace (DFS) codes provide active and passive means, respectively, to address certain types of errors that arise during quantum computation. The latter technique is suitable to correct correlated errors with certain symmetries and the former to correct independent errors. The concatenation of a QECC and a DFS code results in a degenerate code that splits into actively and passively correcting parts, with the degeneracy impacting either part, leading to degenerate errors as well as degenerate stabilizer operators. The concatenation of the two types of code can aid universal fault-tolerant quantum computation when a mix of correlated and independent errors is encountered. In particular, we show that for sufficiently strongly correlated errors, the concatenation with the DFS as the inner code provides better entanglement fidelity, whereas for sufficiently independent errors, the concatenation with the QECC as the inner code is preferable. As illustrative examples, we examine in detail the concatenation of a two-qubit DFS code and a three-qubit repetition code or five-qubit Knill-Laflamme code, under independent and correlated errors.
Decoherence-free subspaces (DFSs) shield quantum information from errors induced by the interaction with an uncontrollable environment. Here we study a model of correlated errors forming an Abelian subgroup (stabilizer) of the Pauli group (the group of tensor products of Pauli matrices). Unlike previous studies of DFSs, this type of error does not involve any spatial symmetry assumptions on the system-environment interaction. We solve the problem of universal, fault-tolerant quantum computation on the associated class of DFSs. We do so by introducing a hybrid DFS quantum error-correcting-code approach, where errors that arise due to departure of the codewords from the DFS are corrected actively.
Decoherence-free subspaces (DFSs) are constructed without the assumption of spatially symmetric system-bath coupling. Instead the underlying assumption is that subgroups of the full Pauli group of errors are responsible for the decoherence. The corresponding decoherence-free states can protect quantum information in the presence of multiple-qubit errors, and are stabilizer codes. It is shown how to perform universal fault tolerant quantum computation on this class of DFSs. This is the first demonstration that it is possible to use only one- and two-body quantum gates to perform full-blown quantum computation on a class of DFSs, with a finite number of measurements.
Decoherence-free subspace (DFS) provides a crucial mechanism for passive error mitigation in quantum computation by encoding information within symmetry-protected subspaces of the Hilbert space, which are immune from collective decoherence. Constructing a complete set of orthogonal basis states for the DFS is essential to realize fault-tolerant quantum computation by using the DFS codes. However, existing methods for preparing these basis states are often non-scalable, platform-specific, or yield mixed states. Here, we propose a deterministic approach to prepare pure, orthogonal and complete DFS basis states for systems of arbitrary size composed of qubits. Our method employs projective measurements and quantum circuits with single-qubit, two-qubit and Toffoli gates. We provide a rigorous resource cost analysis both mathematically and numerically. Meanwhile, we demonstrate the realizability of our method on NISQ devices by discussing how to implement our method on a superconducting chip. The proposed method offers a universal solution for preparing the DFS basis states across diverse quantum computing platforms and system sizes, which is realizable in the NISQ era.