Robustness of decoherence free subspaces for quantum computation. The second part of the day will start by covering several advanced topics in aqc, including a sketch of the proof of the equivalence between aqc and the circuit model, rigorous formulations of the adiabatic theorem, the geometry of aqc, and a timeoptimized brachistochrone approach to aqc. Therefore, different from the traditional dfss, the ancillary systems are not necessary in inducing holonomy, which saves qubits used in the holonomic quantum. A fourdimensional dfs is constituted to protect quantum information when the full symmetry of interaction between system and environment is broken in a specific way, and entangling twoqubit logic gates and noncommuting singlequbit gates are implemented in such.
Quantum computation in the decoherencefree subspaces with. Theory of decoherencefree faulttolerant universal quantum. Quantum computing in decoherencefree subspaces with. It is shown that these subspaces are stable to perturbations and moreover, that universal quantum computation is possible within them. Robustness of decoherencefree subspaces for quantum computation. Scalable quantum computation in decoherencefree subspaces. This detailed but accessible text describes the concepts, formalism, interpretation, and experimental observation of decoherence and explains how decoherence is responsible for the emergence, from the realm of quantum mechanics, of the. We show how to realize, by means of nonabelian quantum holonomies, a set of universal quantum gates acting on decoherence free subspaces and subsystems. Holonomic quantum computation in decoherencefree subspaces. Decoherence, control, and symmetry in quantum computers by dave morris bacon. Daniel lidars group decoherencefree subspaces and subsystems. The ultimate introduction, textbook, and reference on decoherence and the quantumtoclassical transition.
Download decoherence and the foundations of quantum mechanics book pdf free download link or read online here in pdf. Geometric quantum computation in decoherencefree subspaces is of great practical importance because it can protect quantum information from both control errors and collective dephasing. We show how to realize nonadiabatic holonomic quantum computation in timedependent decoherence free subspaces tdfss. Decoherence offers a theoretical framework in which the measurement problem can be swept under the carpet pushed into a system larger than that which we can observe. We present a scheme to implement quantum computation in decoherencefree subspaces dfss with four atoms in a singlemode cavity. Df subspaces are thus ideal for quantum memory applications. Decoherence remains the most important obstacle to. The role of decoherence was recognized by a wide spectrum of practicing. Decoherence, the measurement problem, and interpretations.
For universal quantum computation, a controlled twoqubit gate is required. The partial swap operator that can be realized using the exchange interaction is used as the underlying resource for defining models of quantum computation, quantum communication, quantum memory and decoherence free subspaces. In our scheme, the holonomy is not generated by computational bases in dfss but timedependent bases of tdfss. We demonstrate how to realize the scheme via decoherencefree subspaces. Read online decoherence and the foundations of quantum mechanics book pdf free download link book now. Scalable faulttolerant quantum computation in decoherencefree subspaces zhengwei zhou,1 bo yu,1 xingxiang zhou,2 marc j.
Feldman,2 and guangcan guo1 1key laboratory of quantum information, university of science and technology of china. Magnetic resonance realization of decoherencefree quantum computation. We propose a decoherence free subspaces dfs scheme to realize scalable quantum computation with trapped ions. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system. Magnetic resonance realization of decoherence free quantum computation. W e discuss the implementation of this sc h eme in the context of. Thus, to perform robust quantum computation in df subspaces, they must be supplemented with.
When the systembath interaction has certain symmetry, a promising scheme based on the decoherencefree subspaces dfs was developed. Universal quantum computation in waveguide qed using decoherence free subspaces view the table of contents for this issue, or go to the journal homepage for more home search collections journals about contact us my iopscience. A decoherence free subspace dfs is a subspace of a quantum systems hilbert space that is invariant to nonunitary dynamics. Universal quantum computation in waveguide qed using decoherence free subspaces. Quantum computation is discussed as a prime victim to decoherence. The interaction of quantum emitters with onedimensional photonlike. The spindependent coulomb interaction is exploited, and the universal set of. In this paper, i propose new models of quantum information processing using the exchange interaction in physical systems. In this manner w e bring together the quantum co h erence stabilizatio n virtues of decoherence free subspaces and the faulttolerance of. Download decoherence and the transition from quantum to classical. Decoherence has been a principal impediment in quantum information processing applications. A fourdimensional dfs is constituted to protect quantum information when the full symmetry of interaction between system and environment is broken in a specific way, and entangling twoqubit logic gates and noncommuting singlequbit gates are.
Universal quantum computation in decoherencefree subspaces. Aug 15, 2006 quantum computation is discussed as a prime victim to decoherence. Indeed, i am surprised and gratified by how much the field has evolved over the last decade. Decoherence and the quantumtoclassical transition the. Quantum information processing using the exchange interaction. Expedited holonomic quantum computation via net zeroenergy. Browse the amazon editors picks for the best books of 2019, featuring our favorite.
Pdf decoherence free subspaces for quantum computation. A generic condition is presented for errorless quantum computation. A quantum trajectory description of decoherence, a b decoherencefree subspaces for quantum computation from arxiv dan stahlke. Whaley2 1department of physics, the university of california, berkeley, california 94720. Decoherence and the transition from quantum to classicalrevisited. Well then switch gears and provide an introduction to decoherencefree subspaces, noiseless. Decoherence free subspaces for quantum computation. In this case, the minimal system to encode the operation is the n 4 atom case, where two decoherence free logical qubits can be obtained. Conditions for the existence of decoherencefree subspaces hamiltonian formulation. A decoherencefree subspace dfs is a subspace of a quantum systems hilbert space that is. Buy decoherence and the quantumtoclassical transition.
We propose a decoherencefree subspaces dfs scheme to realize scalable quantum computation with trapped ions. Nov 16, 2000 universal quantum computation with the exchange interaction. Simply put, they require that the coherence of states be preserved and that decoherence is managed, in order to actually perform quantum computation. Holonomic quantum computation by time dependent decoherence. Universal quantum computation in waveguide qed using. In this way we unify quantum robustness merits of this faulttolerant control scheme, the conventional hqc and decoherence free subspace, and propose an expedited holonomic quantum computation protocol.
The interaction of quantum emitters with onedimensional photonlike reservoirs induces strong and longrange dissipative couplings that give rise to the emergence of the socalled decoherence free subspaces dfss which are decoupled from dissipation. Expedited holonomic quantum computation via net zero. A scheme is proposed to implement distributed quantum computation in decoherence free subspaces dfss via adiabatic passage. Geometric quantum computation in decoherence free subspaces is of great practical importance because it can protect quantum information from both control errors and collective dephasing. We give a full characterisation of decoherence free subspaces of a given quantum markov semigroup with generator in a generalised lindbald form which is valid also for infinitedimensional systems. Nov 16, 2000 various physical implementations of quantum computers are being investigated, although the requirements1 that must be met to make such devices a reality in the laboratory at present involve. Decoherencefree subspace is a special set of quantum states which is insensitive to some particular noise.
Theory of decoherencefree universal fault tolerant quantum computation, phys. Alternatively stated, they are a small section of the system hilbert space where the system is decoupled from the environment and thus its evolution is completely unitary. Feldman,2 and guangcan guo1 1key laboratory of quantum information, university of science and technology of china, hefei 230026, peoples republic of china 2superconducting digital electronics laboratory, electrical and computer engineering department. Decoherencefree subspaces and subsystems springerlink. Distributed quantum computing in decoherencefree subspace. Decoherencefree subspaces for quantum computation decoherence and the transition from quantum to classical. The generalization from subspaces to subsystems formed a foundation for combining most known decoherence prevention and nulling strategies. If what you really want to know is how a decoherence free subspace might work, i can give an example as an answer. Part of the lecture notes in physics book series lnp, volume 622. The areas include quantum data compression, accessible information, entanglement concentration, limits to quantum computation due to decoherence, quantum errorcorrection, and the first experimental implementations of quantum information protocols. Free subspaces, noiseless subsystems, and dynamical. Free decoherencefree subspaces and subsystems, phys. Quantum computing in decoherencefree subspaces with superconducting charge qubits.
Thus, techniques such as decoherencefree subspaces dfss. Pdf decoherencefree subspaces for open quantum random. Decoherence in quantum computers is formulated within the semigroup approach. For quantum computation, however, the stability result does not extend beyond.
We show how to realize, by means of nonabelian quantum holonomies, a set of universal quantum gates acting on decoherencefree subspaces and subsystems. Quantum decoherence is the loss of quantum coherence. We demonstrate how to realize the scheme via decoherence free subspaces. Decoherence represents a challenge for the practical realization of quantum computers, since such machines are expected to rely heavily on the undisturbed evolution of quantum coherences. Decoherencefree subspaces decoherencefree subspaces and subsystems,springer lecture notes in physics 622 2003, by d. Relevance of decoherence to various interpretations of qm is discussed. Robustness of decoherencefree subspaces for quantum computation d. This is possible using a concatenation of df and qecc codes, as was shown in ref. Implications of decoherence for interpretations of quantum mechanics and for the. Scalable faulttolerant quantum computation in decoherence free subspaces zhengwei zhou,1 bo yu,1 xingxiang zhou,2 marc j. Read open access proceedings from science conferences worldwide books. Various physical implementations of quantum computers are being investigated, although the requirements1 that must be met to make such devices a reality in the laboratory at present involve. Well then switch gears and provide an introduction to decoherence free subspaces, noiseless.
In order to build the controlledz gate, we use one of the auxiliary states. Since quantum computers cannot be isolated from their environment i. Our results, extending those available in the literature concerning finitedimensional systems, are illustrated by some examples. It is shown that these subspaces are stable to perturbations and, moreover, that universal quantum computation is possible within them. A decoherencefree subspace dfs is a subspace of a quantum systems hilbert space that is invariant to nonunitary dynamics. Conditions for the existence of decoherence free subspaces hamiltonian formulation. Decoherence and the transition from quantum to classical. Jan 17, 2017 we show how to realize nonadiabatic holonomic quantum computation in timedependent decoherence free subspaces tdfss. Nov 12, 20 we present a scheme to implement quantum computation in decoherence free subspaces dfss with four atoms in a singlemode cavity.
Chuang i l and whaley k b 1998 decoherencefree subspaces for quantum computation phys. Whaley2 1department of physics, the university of california, berkeley, california 94720 2department of chemistry, the university of california, berkeley, california 94720 received 10 february 1999. Correlations and measurements a convenient starting point for the discussion of the measurement problem and, more generally, of the emergence of classical behavior from quantum dynamics is the analysis. Decoherence free subspace is a special set of quantum states which is insensitive to some particular noise. Decoherence has been hailed as the solution to longstanding foundational problems dating back to.
Consider an ndimensional quantum system s coupled to a bath b and described by the combined systembath hamiltonian as. In this way we unify quantum robustness merits of this faulttolerant control scheme, the conventional hqc and decoherencefree subspace, and propose an expedited holonomic quantum computation protocol. A comparison of decoherencefree subsystemsubspace for. Decoherencefree subspaces in quantum key distribution. As a simple example, suppose we have two localized spins12 particles, which are subject to some random static magnetic field for simplicity along the zaxis. Decoherence free subspaces for quantum computation d. The logical singlequbit is encoded in two atoms trapped in a singlemode cavity and the cavities are connected by an optical fiber. Over the course of the past decade, decoherence has become a ubiquitous scienti. Robustness of decoherencefree subspaces for quantum. Introduction to topological quantum computation by jiannis k. In this case, the minimal system to encode the operation is the n 4 atom case, where two decoherencefree logical qubits can be obtained. All books are in clear copy here, and all files are secure so dont worry about it. Universal quantum computation on decoherencefree subspaces and subsystems dfss is examined with particular emphasis on using only physically relevant.
A scheme is proposed to implement distributed quantum computation in decoherencefree subspaces dfss via adiabatic passage. In quantum computing, decoherenceinduced deviations from the desired computational trajectory at the singlequbit level will quickly accumulate if left uncorrected. Robustness of decoherence free subspaces for quantum computation d. Here, we propose a feasible scheme without these two problems. Universal quantum computation with the exchange interaction.
Decoherence free subspaces of a quantum markov semigroup. The partial swap operator that can be realized using the exchange interaction is used as the underlying resource for defining models of quantum computation, quantum communication, quantum memory and decoherencefree subspaces. Pdf holonomic quantum computation in decoherencefree subspaces. We study the performance of the 3quhit decoherence free subsystem and the 4quhitdecoherence free subspace in the presence of partially correlated noise. Adiabatic quantum computation, decoherencefree subspaces. Read online decoherence and the transition from quantum to classical. Theory of decoherencefree universal faulttolerant quantum computation, phys. Scalable faulttolerant quantum computation in decoherence. Universal quantum computation on decoherence free subspaces and subsystems dfss is examined with particular emphasis on using only physically relevant. The interaction of quantum emitters with onedimensional photon like. However, previous proposed schemes have either states leakage or fourbody interactions problems. Whaley 1department of chemistry, the university of california, berkeley, california 94720 2ibm almaden research center, san jose, california 94120 received 27 april 1998decoherence in quantum computers is formulated. Pdf we study decoherencefree subspaces in a type of quantum markov. Decoherence, control, and symmetry in quantum computers by dave morris bacon double b.
Whaleya a department of chemistry, the university of california, berkeley, ca 94720 b ibm almaden research center, san jose, ca 94120 decoherence in quantum computers is formulated within the semigroup approach. We study the performance of the 3quhit decoherencefree subsystem and the 4quhitdecoherencefree subspace in the presence of partially correlated noise. Nov 10, 2014 we give a full characterisation of decoherence free subspaces of a given quantum markov semigroup with generator in a generalised lindbald form which is valid also for infinitedimensional systems. The ultimate introduction, textbook, and reference on decoherence and the quantum toclassical transition. Decoherence, the measurement problem, and interpretations of. Decoherence, control, and symmetry in quantum computers. Decoherence and the foundations of quantum mechanics pdf.