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:1511.06592 · Physical Review A

Quantum memories with zero-energy Majorana modes and experimental constraints

Matteo Ippoliti, Matteo Rizzi, Vittorio Giovannetti, Leonardo Mazza

Published Jun 20, 2016• 15 citations
arXivHTMLPDF

Abstract

In this work we address the problem of realizing a reliable quantum memory based on zero-energy Majorana modes in the presence of experimental constraints on the operations aimed at recovering the information. In particular, we characterize the best recovery operation acting only on the zero-energy Majorana modes and the memory fidelity that can be therewith achieved. In order to understand the effect of such restriction, we discuss two examples of noise models acting on the topological system and compare the amount of information that can be recovered by accessing either the whole system, or the zero modes only, with particular attention to the scaling with the size of the system and the energy gap. We explicitly discuss the case of a thermal bosonic environment inducing a parity-preserving Markovian dynamics in which the memory fidelity achievable via a read-out of the zero modes decays exponentially in time, independent from system size. We argue, however, that even in the presence of said experimental limitations, the Hamiltonian gap is still beneficial to the storage of information.

DOI
10.1103/physreva.93.062325

Related papers

Robustness of quantum memories based on Majorana zero modes

Leonardo Mazza, Matteo Rizzi, Mikhail D. Lukin +1 more

We analyze the rate at which quantum information encoded in zero-energy Majorana modes is lost in the presence of perturbations. We show that information can survive for times that scale exponentially with the size of the chain both in the presence of quenching and time-dependent quadratic dephasing perturbations, even when the latter have spectral components above the system's energy gap. The origin of the robust storage, namely the fact that a sudden quench affects in the same way both parity sectors of the original spectrum, is discussed, together with the memory performance at finite temperatures and in the presence of particle exchange with a bath.

arXiv:1212.4778•Physical Review B•Nov 26, 2013•52 citations

Decay rates for topological memories encoded with Majorana fermions

Garry Goldstein, Claudio Chamon

Recently there have been numerous proposals to create Majorana zero modes in solid state heterojunctions, superconducting wires, and optical lattices. Putatively the information stored in qubits constructed from these modes is protected from various forms of decoherence. Here we present a generic method to study the effect of external perturbations on these modes. We focus on the case where there are no interactions between different Majorana modes either directly or through intermediary fermions. To quantify the rate of loss of the information stored in the Majorana modes we study the two-time correlators for qubits built from them. We analyze a generic gapped fermionic environment (bath) interacting via tunneling with different components of the qubit (different Majorana modes). We present examples with both static and dynamic perturbations (noise), and using our formalism derive a rate of information loss, for Majorana memories, that depends on the spectral density of both the noise and the fermionic bath.

arXiv:1107.0288•Physical Review B•Nov 10, 2011•116 citations

Effects of nonequilibrium noise on a quantum memory encoded in Majorana zero modes

François Konschelle, Fabian Hassler

In order to increase the coherence time of topological quantum memories in systems with Majorana zero modes, it has recently been proposed to encode the logical qubit states in nonlocal Majorana operators which are immune to localized excitations involving the unpaired Majorana modes. In this encoding, a logical error only happens when the quasiparticles, subsequent to their excitation, travel a distance of the order of the spacing between the Majorana modes. Here, we study the decay time of a quantum memory encoded in a clean topological nanowire interacting with an environment with a particular emphasis on the propagation of the quasiparticles above the gap. We show that the nonlocal encoding does not provide a significantly longer coherence time than the local encoding. In particular, the characteristic speed of propagation is of the order of the Fermi velocity of the nanowire and not given by the much slower group velocity of quasiparticles which are excited just above the gap.

arXiv:1306.2519•Physical Review B•Aug 22, 2013•20 citations

Quantum Memory Architectures based on Topological Quantum States

Jincheng Zhang

The development of practical quantum computers hinges critically on the ability to reliably store and retrieve quantum information – a challenge known as quantum memory. Current quantum computing approaches face significant decoherence issues, limiting the duration and fidelity of quantum computations. This work investigates the potential of utilizing topological quantum states, specifically Majorana fermions, as a foundation for robust quantum memory architectures. We explore theoretical designs leveraging the unique topological protection inherent in these states, aiming to mitigate decoherence and enable long-term quantum storage. This research presents a novel approach to quantum memory that directly addresses the fundamental limitations of conventional qubit technologies. The core concept revolves around encoding quantum information within the non-local properties of Majorana fermions, offering a pathway towards fault-tolerant quantum storage. The presented architectures focus on creating and manipulating these states to perform quantum memory operations, and the underlying mathematical framework is detailed throughout this document. The investigation considers various approaches to controlling and reading out the state of Majorana fermions, and outlines the key challenges and potential solutions for realizing such a system.

•Aug 28, 2026•0 citations

Disorder-assisted error correction in Majorana chains

Sergey B. Bravyi

It was recently realized that quenched disorder may enhance the reliability of topological qubits by reducing the mobility of anyons at zero temperature. Here we compute storage times with and without disorder for quantum chains with unpaired Majorana fermions - the simplest toy model of a quantum memory. Disorder takes the form of a random site-dependent chemical potential. The corresponding one-particle problem is a one-dimensional Anderson model with disorder in the hopping amplitudes. We focus on the zero-temperature storage of a qubit encoded in the ground state of the Majorana chain. Storage and retrieval are modeled by a unitary evolution under the memory Hamiltonian with an unknown weak perturbation followed by an error-correction step. Assuming dynamical localization of the one-particle problem, we show that the storage time grows exponentially with the system size. We give supporting evidence for the required localization property by estimating Lyapunov exponents of the one-particle eigenfunctions. We also simulate the storage process for chains with a few hundred sites. Our numerical results indicate that in the absence of disorder, the storage time grows only as a logarithm of the system size. We provide numerical evidence for the beneficial effect of disorder on storage times and show that suitably chosen pseudorandom potentials can outperform random ones.

•Aug 16, 2016•47 citations

Enhanced thermal stability of the toric code through coupling to a bosonic bath

Fabio L. Pedrocchi, Adrian Hutter, James R. Wootton +1 more

We propose and study a model of a quantum memory that features self-correcting properties and a lifetime growing arbitrarily with system size at nonzero temperature. This is achieved by locally coupling a two-dimensional $L\ifmmode\times\else\texttimes\fi{}L$ toric code to a three-dimensional (3D) bath of bosons hopping on a cubic lattice. When the stabilizer operators of the toric code are coupled to the displacement operator of the bosons, we solve the model exactly via a polaron transformation and show that the energy penalty to create anyons grows linearly with $L$. When the stabilizer operators of the toric code are coupled to the bosonic density operator, we use perturbation theory to show that the energy penalty for anyons scales with $\mathrm{ln}(L)$. For a given error model, these energy penalties lead to a lifetime of the stored quantum information growing, respectively, exponentially and polynomially with $L$. Furthermore, we show how to choose an appropriate coupling scheme in order to hinder the hopping of anyons (and not only their creation) with energy barriers that are of the same order as the anyon creation gaps. We argue that a toric code coupled to a 3D Heisenberg ferromagnet realizes our model in its low-energy sector. Finally, we discuss the delicate issue of the stability of topological order in the presence of perturbations. While we do not derive a rigorous proof of topological order, we present heuristic arguments suggesting that topological order remains intact when perturbative operators acting on the toric code spins are coupled to the bosonic environment.

arXiv:1309.0621•Physical Review A•Dec 10, 2013•39 citations
In this work we address the problem of realizing a reliable quantum memory based on zero-energy Majorana modes in the presence of experimental constraints on the operations aimed at recovering the information. In particular, we characterize the best recovery operation acting only on the zero-energy Majorana modes and the memory fidelity that can be therewith achieved. In order to understand the effect of such restriction, we discuss two examples of noise models acting on the topological system and compare the amount of information that can be recovered by accessing either the whole system, or the zero modes only, with particular attention to the scaling with the size of the system and the energy gap. We explicitly discuss the case of a thermal bosonic environment inducing a parity-preserving Markovian dynamics in which the memory fidelity achievable via a read-out of the zero modes decays exponentially in time, independent from system size. We argue, however, that even in the presence of said experimental limitations, the Hamiltonian gap is still beneficial to the storage of information.
We analyze the rate at which quantum information encoded in zero-energy Majorana modes is lost in the presence of perturbations. We show that information can survive for times that scale exponentially with the size of the chain both in the presence of quenching and time-dependent quadratic dephasing perturbations, even when the latter have spectral components above the system's energy gap. The origin of the robust storage, namely the fact that a sudden quench affects in the same way both parity sectors of the original spectrum, is discussed, together with the memory performance at finite temperatures and in the presence of particle exchange with a bath.
Recently there have been numerous proposals to create Majorana zero modes in solid state heterojunctions, superconducting wires, and optical lattices. Putatively the information stored in qubits constructed from these modes is protected from various forms of decoherence. Here we present a generic method to study the effect of external perturbations on these modes. We focus on the case where there are no interactions between different Majorana modes either directly or through intermediary fermions. To quantify the rate of loss of the information stored in the Majorana modes we study the two-time correlators for qubits built from them. We analyze a generic gapped fermionic environment (bath) interacting via tunneling with different components of the qubit (different Majorana modes). We present examples with both static and dynamic perturbations (noise), and using our formalism derive a rate of information loss, for Majorana memories, that depends on the spectral density of both the noise and the fermionic bath.
In order to increase the coherence time of topological quantum memories in systems with Majorana zero modes, it has recently been proposed to encode the logical qubit states in nonlocal Majorana operators which are immune to localized excitations involving the unpaired Majorana modes. In this encoding, a logical error only happens when the quasiparticles, subsequent to their excitation, travel a distance of the order of the spacing between the Majorana modes. Here, we study the decay time of a quantum memory encoded in a clean topological nanowire interacting with an environment with a particular emphasis on the propagation of the quasiparticles above the gap. We show that the nonlocal encoding does not provide a significantly longer coherence time than the local encoding. In particular, the characteristic speed of propagation is of the order of the Fermi velocity of the nanowire and not given by the much slower group velocity of quasiparticles which are excited just above the gap.
The development of practical quantum computers hinges critically on the ability to reliably store and retrieve quantum information – a challenge known as quantum memory. Current quantum computing approaches face significant decoherence issues, limiting the duration and fidelity of quantum computations. This work investigates the potential of utilizing topological quantum states, specifically Majorana fermions, as a foundation for robust quantum memory architectures. We explore theoretical designs leveraging the unique topological protection inherent in these states, aiming to mitigate decoherence and enable long-term quantum storage. This research presents a novel approach to quantum memory that directly addresses the fundamental limitations of conventional qubit technologies. The core concept revolves around encoding quantum information within the non-local properties of Majorana fermions, offering a pathway towards fault-tolerant quantum storage. The presented architectures focus on creating and manipulating these states to perform quantum memory operations, and the underlying mathematical framework is detailed throughout this document. The investigation considers various approaches to controlling and reading out the state of Majorana fermions, and outlines the key challenges and potential solutions for realizing such a system.
It was recently realized that quenched disorder may enhance the reliability of topological qubits by reducing the mobility of anyons at zero temperature. Here we compute storage times with and without disorder for quantum chains with unpaired Majorana fermions - the simplest toy model of a quantum memory. Disorder takes the form of a random site-dependent chemical potential. The corresponding one-particle problem is a one-dimensional Anderson model with disorder in the hopping amplitudes. We focus on the zero-temperature storage of a qubit encoded in the ground state of the Majorana chain. Storage and retrieval are modeled by a unitary evolution under the memory Hamiltonian with an unknown weak perturbation followed by an error-correction step. Assuming dynamical localization of the one-particle problem, we show that the storage time grows exponentially with the system size. We give supporting evidence for the required localization property by estimating Lyapunov exponents of the one-particle eigenfunctions. We also simulate the storage process for chains with a few hundred sites. Our numerical results indicate that in the absence of disorder, the storage time grows only as a logarithm of the system size. We provide numerical evidence for the beneficial effect of disorder on storage times and show that suitably chosen pseudorandom potentials can outperform random ones.
We propose and study a model of a quantum memory that features self-correcting properties and a lifetime growing arbitrarily with system size at nonzero temperature. This is achieved by locally coupling a two-dimensional $L\ifmmode\times\else\texttimes\fi{}L$ toric code to a three-dimensional (3D) bath of bosons hopping on a cubic lattice. When the stabilizer operators of the toric code are coupled to the displacement operator of the bosons, we solve the model exactly via a polaron transformation and show that the energy penalty to create anyons grows linearly with LLL. When the stabilizer operators of the toric code are coupled to the bosonic density operator, we use perturbation theory to show that the energy penalty for anyons scales with ln(L)\mathrm{ln}(L)ln(L). For a given error model, these energy penalties lead to a lifetime of the stored quantum information growing, respectively, exponentially and polynomially with LLL. Furthermore, we show how to choose an appropriate coupling scheme in order to hinder the hopping of anyons (and not only their creation) with energy barriers that are of the same order as the anyon creation gaps. We argue that a toric code coupled to a 3D Heisenberg ferromagnet realizes our model in its low-energy sector. Finally, we discuss the delicate issue of the stability of topological order in the presence of perturbations. While we do not derive a rigorous proof of topological order, we present heuristic arguments suggesting that topological order remains intact when perturbative operators acting on the toric code spins are coupled to the bosonic environment.