Robustness of decoherence free subspaces for quantum computation d. 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. Decoherence, the measurement problem, and interpretations. Theory of initializationfree decoherencefree subspaces and. 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 dfs. Demonstration of universal quantum computation on decoherencefreesubspaces with ions in thermal motion l. Decoherence, control, and symmetry in quantum computers.
Therefore, different from the traditional dfss, the ancillary systems are not necessary in inducing holonomy, which saves qubits used in the holonomic quantum. 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. To implement a onequbit quantum gate in dfs, we consider a four physical qubit system with the hamiltonian. Nov 16, 2000 these codes are referred to both as decoherence free subspaces and their generalization, the decoherence free subsystems 8,10,14, and also as noiseless subspaces and subsystems 9,15,16. Quantum computation in the decoherencefree subspaces with.
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. Pdf holonomic quantum computation in decoherencefree subspaces. However, previous proposed schemes have either states leakage or fourbody interactions problems. A scheme is proposed to implement distributed quantum computation in decoherence free subspaces dfss via adiabatic passage. Theory of decoherencefree universal faulttolerant quantum computation, phys. He is the director and cofounder of the usc center for quantum information. A decoherence free subspace dfs is a subspace of a quantum systems hilbert space that is invariant to nonunitary dynamics. Demonstration of universal quantum computation on decoherence free subspaces with ions in thermal motion l.
We discuss the implementation of this scheme in the context of quantum information processing using trapped ions and quantum dots. It is shown that these subspaces are stable to perturbations and, moreover, that universal quantum computation is possible within them. 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. These all follow a unitary quantum evolution, apart from the final measurement. A quantum computer is used to perform such computation, which can be implemented theoretically or physically there are two main approaches to physically implementing a quantum computer currently, analog and digital. Decoherence free subspaces of a quantum markov semigroup. He wrote some of the founding papers on decoherencefree subspaces, most. Suppressing decoherence of quantum algorithms by jump codes.
We show how to realize, by means of nonabelian quantum holonomies, a set of universal quantum gates acting on decoherencefree subspaces and subsystems. Box 5046, 2600 ga delft, the netherlands and kavli institute of nanoscience delft, delft university of. Browse other questions tagged quantummechanics quantum. Here we briefly recall the method to realize a universal set of quantum gates acting on the dfs as firstly proposed in ref. Scalable quantum computing in decoherencefree subspaces with. Robust quantumnetwork memory using decoherenceprotected. Expedited holonomic quantum computation via net zeroenergy. Birgitta whaley, chair computers built on the physical principles of quantum theory o er the possibility of tremendous computational advantages over conventional computers. If what you really want to know is how a decoherence free subspace might work, i can give an example as an answer.
Quantum decoherence is the loss of quantum coherence. In quantum computation, quantum coherence must be maintained during the quantum gate operation. A comparison of decoherencefree subsystemsubspace for. Decoherence free subspace is based on the symmetry structure of the systemenvironment interaction 21,22,23,24,25. In addition, depending on the geometric size of the onedimensional resonator and the wavelength of cavity field, the number of scalable qubits is generally limited. Maximilian schlosshauer is an internationally recognized researcher in the foundations of quantum mechanics in general and in quantum decoherence in particular.
You last book is quantum computation and quantum information, which you already referred to. Quantum computing is the use of quantum mechanical phenomena such as superposition and entanglement to perform computation. Protecting the dynamics of coupled quantum systems from decoherence by the environment is a key challenge for solidstate quantum information processing 1,2. We present a scheme to implement quantum computation in decoherencefree subspaces dfss with four atoms in a singlemode cavity. As long as there exists a definite phase relation between different states, the system is said to be. Our results, extending those available in the literature concerning finitedimensional systems, are illustrated by some examples. Geometric quantum computation in decoherencefree subspaces is of great practical importance because it can protect quantum information from both control errors and collective dephasing. What especially differentiates a quantum system from a classical system is the concept of a superposition of states. These codes are referred to both as decoherencefree subspaces and their generalization, the decoherencefree subsystems 8,10,14, and also as noiseless subspaces and subsystems 9,15,16. A scheme is proposed to implement distributed quantum computation in decoherencefree subspaces dfss via adiabatic passage. W e discuss the implementation of this sc h eme in the context of. We show how to realize, by means of nonabelian quantum holonomies, a set of universal quantum gates acting on decoherence free subspaces and subsystems. Demonstration of universal quantum computation on decoherence.
Therefore, different from the traditional dfss, the ancillary systems are not necessary in inducing holonomy, which saves qubits used in the holonomic. Robustness of decoherencefree subspaces for quantum computation d. Molmer lundbeck foundation theoretical center for quantum system research department of physics and astronomy, university of aarhus, ny munkegade, bld. Decoherence and its implications in quantum computing and. Quantum computation, communication, decoherence and all that lecture notes in physics 587 on free shipping on qualified orders. Decoherence free subspaces dfss shield quantum information from errors induced by the interaction with an uncontrollable environment. Control of qubits encoded in decoherencefree subspaces. The intent of this book is to make quantum computing accessible to a wide audience.
There are many possible materials for lasers crystals, organic dye molecules, semiconductors, free electrons and likewise there are many. Universal quantum computation with the exchange interaction. A decoherencefree subspace dfs is a subspace of a quantum systems hilbert space that is invariant to nonunitary dynamics. In this manner we bring together the quantum coherence stabilization virtues of decoherencefree subspaces and the faulttolerance of allgeometric holonomic control. Decoherencefree subspace is based on the symmetry structure of the systemenvironment interaction 21,22,23,24,25. Well then switch gears and provide an introduction to decoherence free subspaces, noiseless. Universal quantum computation in a neutralatomdecoherence free subspace e. In the quantum realm, the formalism allows us to state that a particle is in a superposition of positions say, and. If the noise acts along the zdirec quantum information and quantum computation control of qubits encoded in decoherence free subspaces p. Mykonos, greece, gonis, antonios, turchi, patrice e. 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. Chuang 2000, quantum computation and quantum information,cambridge university press. Is it possible to use this effect to create decoherence free subspaces that would be useful in transmitting information within the polarization state of single photons.
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. Osa experimental demonstration of decoherence suppression. In this manner we bring together the quantum coherence stabilization virtues of decoherence free subspaces and the faulttolerance of allgeometric holonomic control. These subspaces prevent destructive environmental interactions by isolating quantum information. The best quantum computing books five books expert. Quantum computing software is discussed elsewhere, such as in ref. Adiabatic quantum computation, decoherencefree subspaces.
Anyone who is seriously getting into quantum computation uses it. This book came out in 2000, so almost 20 years ago now. Taminiau, and ronald hanson qutech, delft university of technology, p. Lidar2 1physics department, and center for quantum information and quantum control, university of toronto, 60 st. Decoherence, control, and symmetry in quantum computers by dave morris bacon doctor of philosophy in physics university of california at berkeley professor k. Here we experimentally demonstrate that decoherence due to amplitude damping can be suppressed by exploiting quantum measurement reversal in which a weak measurement and the reversing measurement are introduced before and after the decoherence channel, respectively. Physics stack exchange is a question and answer site for active researchers, academics and students of physics. Buy principles of quantum computation and information. Quantum computing ppt quantum computing quantum mechanics. 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. Experimental demonstration of decoherence suppression via. Universal quantum computation in decoherencefree subspaces. Universal faulttolerant quantum computation in the presence of spontaneous emission and collective dephasing, phys. Theory of initialization free decoherence free subspaces and subsystems alireza shabani1 and daniel a.
This is a free digital textbook that will teach you the concepts of quantum computing while you learn to use the qiskit sdk. Robust quantumnetwork memory using decoherenceprotected subspaces of nuclear spins andreas reiserer, norbert kalb, machiel s. Universal quantum computation on decoherencefree subspaces and subsystems dfss is examined with particular emphasis on using only physically relevant interactions. Nov 12, 20 we present a scheme to implement quantum computation in decoherence free subspaces dfss with four atoms in a singlemode cavity.
In our scheme, the holonomy is not generated by computational bases in dfss but timedependent bases of tdfss. Distributed quantum computing in decoherencefree subspace. Decoherence free subspaces for quantum computation d. Shor 1995 scheme for reducing decoherence in quantum computer memory, phys. If the noise acts along the zdirecquantum information and quantum computation control of qubits encoded in decoherencefree subspaces p. Decoherence in quantum computers is formulated within the semigroup approach. However, it is a more general phenomenon, that can be readily understood in terms of the dynamical time evolution of quantum systems. Thus, techniques such as decoherence free subspaces dfss. Quantum computing ppt free download as powerpoint presentation. Theory of decoherencefree faulttolerant universal quantum.
Expedited holonomic quantum computation via net zero. However, nonadiabatic holonomic quantum computation in decoherencefree subspaces, which avoids long runtime requirement but with all the robust advantages, remains an open problem. Robustness of decoherencefree subspaces for quantum. Distributed quantum computing in decoherencefree subspace via adiabatic passage.
Decoherence, the measurement problem, and interpretations of. Universal quantum computation in a neutralatomdecoherence. Nonadiabatic holonomic quantum computation in decoherence. Decoherencefree subspaces dfss shield quantum information from errors induced by the interaction with an uncontrollable environment. Jan 17, 2017 we show how to realize nonadiabatic holonomic quantum computation in timedependent decoherence free subspaces tdfss. As early as 1959 the american physicist and nobel laureate richard feynman noted that, as electronic components begin to reach microscopic scales, effects predicted by quantum mechanics. Holonomic quantum computation in decoherencefree subspaces. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system. 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. Suppressing decoherence of quantum algorithms by jump codes o. On the other hand, one should expand quantum gate operations with high fidelities to multiqubit system, aimed at obtaining the scalable faulttolerant quantum computing. In quantum computing, decoherenceinduced deviations from the desired computational trajectory at the singlequbit level will quickly accumulate if left uncorrected.
Taming decoherence is essential in realizing quantum computation and quantum communication. Quantum computer, device that employs properties described by quantum mechanics to enhance computations. Holonomic quantum computation by time dependent decoherence. The development of quantum walks in the context of quantum computation, as generalisations of random walk techniques, has led rapidly to several new quantum algorithms. Thanks for contributing an answer to physics stack exchange. However in physical implementations, various couplings with the environment are unavoidable, and lead to a dephasing of a quantum bit qubit. Decoherence free subspaces in large quantum spin systems. It is the bible and its an enormous book, some 700 pages long. However, nonadiabatic holonomic quantum computation in decoherence free subspaces, which avoids long runtime requirement but with all the robust advantages, remains an open problem. Robust quantum network memory using decoherenceprotected subspaces of nuclear spins andreas reiserer, norbert kalb, machiel s. The distance between the line connected with circuits and the center line is d, and l r denotes the geometric length of the onedimensional transmission line resonator along the x direction.
In the classical realm of physics, we would say that a particle is at a position x,y,z. Quantum computing is the use of quantummechanical phenomena such as superposition and entanglement to perform computation. The logical singlequbit is encoded in two atoms trapped in a singlemode cavity and the cavities are connected by an optical fiber. Universal quantum computation in waveguide qed using. After completing his undergraduate education at freiburg university, germany, he graduated from lund university, sweden, with a master of science degree in 2001. Decoherencefree subspaces in quantum key distribution. Decoherence free subspaces in large quantum spin systems currently active.
Theory of initializationfree decoherencefree subspaces. Tell a friend about us, add a link to this page, or visit the webmasters page for free fun content. Introduction if quantum entanglement 1 is to be regarded as a physical resource 2, then it seems sensible to consider the en. Computers that perform quantum computations are known as quantum computers i5 quantum computers are believed to be able to solve certain computational problems, such as integer factorization which underlies rsa encryption, substantially faster than. Decoherencefree subspaces in large quantum spin systems currently active. 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. We show how to realize nonadiabatic holonomic quantum computation in timedependent decoherence free subspaces tdfss. 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. Robustness of decoherencefree subspaces for quantum computation. The primary source is the interaction of a system with its environment. A closed, isolated quantum system evolves under the schrodinger equation and its state at an earlier time is always related to its state at a later time via a unitary transformation a transformation that. The logical singlequbit is encoded in two atoms trapped in a singlemode cavity and the cavities are connected by an.
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