Geometric manipulation of trapped ions for quantum. Nonadiabatic holonomic quantum computing has received great attention due to its advantages of avoiding longterm evolution of the system and maintaining the robustness of holonomic gates to control errors. Nonadiabatic holonomic quantum computation nhqc has been developed to shorten the construction times of geometric quantum gates. Jun 27, 2005 holonomic quantum computation exploiting nonabelian geometrical phases holonomies was primarily proposed in ref. Pdf robust and fast holonomic quantum gates with encoding. Holonomic quantum computation was a general procedure for building universal sets of robust gates using nonabelian geometric phases. In hqc, states undergo adiabatic closedloopparallel transport in parameter space, acquiring berry phases or matrices also called nonabelian holonomiesor wilsonloops 8 thatcanbecombinedtoachieve universal computation. However, previous nhqc gates require the driving hamiltonian to satisfy a set of rather restrictive conditions, reducing the robustness of the resulting geometric gates against control errors. Robust gates for holonomic quantum computation core. Abelian geometric phases is proposed, using resonant. Request pdf scalable nonadiabatic holonomic quantum computation on a superconducting qubit lattice geometric phase is an indispensable element for achieving robust and highfidelity quantum. Recently, an extensible holonomic quantum computation hqc was proposed and demonstrated in a recent superconducting experiment yan et al. However, the adiabatic condition requires that the process be very slow and thus limits its application in quantum computation, where quantum gates are preferred to be fast due to the limited. We study the effects of the environment modeled as an ensemble of harmonic oscillators on a holonomic transformation and write.
Experimental realization of robust geometric quantum gates. Universal holonomic quantum gates over geometric spin. Universal holonomic quantum gates over geometric spin qubits. Therefore, due to its intrinsic operational robustness, quantum manipulation induced by geometric phases is one of the promising strategies. Geometric manipulation of trapped ions for quantum computation. However, because of the parametric restriction of previous schemes, the main robust advantage of holonomic quantum gates is smeared. The desired geometric operations are obtained by driving the quantum system to undergo appropriate adiabatic cyclic evolutions. However, nonadiabatic holonomic quantum computation in decoherencefree subspaces, which avoids a long runtime requirement but with all the robust advantages, remains an open problem. C n for data encoding and by a universal set of quantum gates. However, this kind of robust feature is challenged since the usual way of realizing nonadiabatic holonomic gates introduces. Aug, 2018 meanwhile, their application to faulttolerant holonomic quantum computing 5,6,7,9,10 was proposed, and the geometric phase gate or holonomic quantum gate has been experimentally demonstrated in a. However, due to the complexity of manipulation and the intrinsic leakage of the encoded quantum information to a nonlogicalqubit basis, the experimental realization of universal nonadiabatic holonomic quantum computation is very difficult. However, the longer gate time for geometric operations and more physical difficulties with regard to implementation hinder its practical and wide application.
Sorry, we are unable to provide the full text but you may find it at the following locations. G florio, p facchi, r fazio, v giovannetti, s pascazio. Dynamicaldecouplingprotected nonadiabatic holonomic. However, because of the parametric restrictions in previous schemes, the main robust advantage of holonomic quantum gates is reduced. Digital quantum simulation of nonadiabatic geometric gates via. The solution is analytically and numerically investigated and the behavior of the fidelity analyzed. A gentle introduction eleanor rieffel and wolfgang polak. Nonadiabatic holonomic quantum computation in decoherence. New geometric effects that describe the behavior of noisy holonomic gates are presented. Here, a feasible and fast scheme for universal quantum computation on superconducting circuits with nonadiabatic non. Implementing universal nonadiabatic holonomic quantum gates with. Holonomic quantum gates provide us with a robust way towards universal quantum computation, as these quantum gates are actually induced by nonabelian geometric phases. Errortolerant multiqubit holonomic entangling gates. It then discusses the implementation of holonomic quantum computation, and summarizes the potential advantages of using geometrical evolution to implement quantum gates.
Nonadiabatic geometric quantum computation with optimal control. Dynamically corrected nonadiabatic holonomic quantum gates. The geometric phase has been experimentally demonstrated in. On the robustness of holonomic quantum computation. Implementing a one qubit holonomic quantum gate in. Jun 05, 2017 adiabatic quantum control is a powerful tool for quantum engineering and a key component in some quantum computation models, where accurate control over the timing of the involved pulses is not needed. For instance, the local random errors along the evolution path caused by some unwanted interaction would have very small influence on the global property. Dec 10, 2019 geometric phase is an indispensable element for achieving robust and highfidelity quantum gates due to its builtin noiseresilience feature. Such a subspace, denoted by \cal c, will represent our quantum code, whose elements will be the quantum information encoding codewords. Our scheme, which is based on laser manipulation of a set of trapped ions, fulfills all the requirements for holonomic quantum computation and fits well the status of current technology. Nonadiabatic universal holonomic quantum gates based on abelian holonomies utkan gungordu et al 2014 journal of the physical society of japan 83 034001.
Xia, nonadiabatic holonomic quantum computation using. Therefore, due to its intrinsic operational robustness, quantum manipulation induced by geometric phases. Plugandplay approach to nonadiabatic geometric quantum. Oct 01, 2014 in an allgeometric approach to quantum computation 1,2, the quantum gates are implemented using berry phases 3 and their nonabelian extensions, holonomies 4, from geometric transformation. Nonadiabatic noncyclic geometric quantum computation in. Nonadiabatic holonomic quantum computation, focusing mainly on implementing universal single and twoqubit gates, commonly suffers gate fidelity losses inevitably due to the presence of systematic errors. Holonomic quantum computation hqc may not show its full potential in quantum speedup due to the prerequisite of a long coherent runtime imposed by the adiabatic condition. Expedited holonomic quantum computation via net zeroenergy. Namely, it was suggested to realize the hqc within quantum optics optical hqc. A quantum algorithm consists of the given computation ut that acts on the quantum state in encoding initial data, its realization as a network of basic gates, along with a measurement prescription for.
Nonadiabatic geometric quantum computation ngqc and nonadiabatic holonomic quantum computation nhqc have been proposed to reduce the run time of geometric quantum gates. Robust gates for holonomic quantum computation nasaads. For the holonomic quantum computation proposed recently 47, the computational space c is always an eigenspace. Geometric quantum logic gates 22,23 based on adiabatic or nonadiabatic geometric phase 2427, which depends only on the global properties of the evolution paths, provides us the possibility for robust quantum computation 2834. Sep 14, 2020 highfidelity and robust quantum manipulation is the key for scalable quantum computation. The idea is to encode a set of qubits in a set of degenerate eigenstates of a parameterdependent hamiltonian and to adiabatically transport these states. Furthermore, the system realizes a conditional geometric gate which may be used for holonomic non adiabatic quantum computing. Experimental realization of universal geometric quantum gates. Expedited holonomic quantum computation via net zero. Universal, highfidelity quantum gates based on superadiabatic. Experimental realization of nonadiabatic holonomic single. Robust gates for holonomic quantum computation giuseppe florio,1,2 paolo facchi,3,2 rosario fazio,4,5 vittorio giovannetti,4 and saverio pascazio1,2 1dipartimento di fisica, universita di bari, i70126 bari, italy.
Oct 23, 2012 quantum computation in noiseless subsystems with fast nonabelian holonomies j. A 73, 022327 2006 robust gates for holonomic quantum computation. However, the longer gate time for geometric operations and more physicalimplementation difficulties hinder its practical and wide applications. Optical holonomic single quantum gates with a geometric spin. Pdf on the robustness of holonomic quantum computation. Non abelian geometric phases are attracting increasing interest because of possible experimental application in quantum computation. Fast holonomic quantum computation on superconducting. Berryphasebased quantum gates assisted by transitionless. Quantum computation is essentially the implementation of a universal set of quantum gate operations on a set of qubits, which is reliable in the presence of noise. Nonadiabatic holonomic quantum computation iopscience. Our implementation of the allgeometric quantum computation is based on laser manipulation of a set of trapped ions.
Nonadiabatic holonomic quantum computation has robust feature in suppressing control errors because of its holonomic feature. However, due to the complexity of manipulation and the intrinsic leakage of the encoded quantum information to nonlogicalqubit basis, the experimental realization of universal nonadiabatic holonomic quantum computation is very. Apr 23, 2020 highfidelity and robust quantum manipulation is the key for scalable quantum computation. Nonadiabatic holonomic quantum gates in an atomic system. Nonadiabatic holonomic quantum computation allows for highspeed implementation of wholegeometric quantum gates, making quantum computation robust. Holonomic quantum computation hqc based on the adiabatic geometric phase was then proposed for faulttolerant quantum gates by zanardi and rasetti in 19995, and generalized to nonadiabatic hqc by wang and matsumoto in 20016,7 and zhu and wang in 20028.
Robust quantum computing is one central issue in building a quantum computer. Nonadiabatic holonomic quantum computation in linear. Ret rw u t, 0, 1 n where w is the target unitary operator 18, and the unitary evolution operator. Nonabelian geometric phases are attracting increasing interest because of possible experimental application in quantum computation. The unitary holonomies \refhol are the main ingredient of our approach to qc. Jan 08, 2021 the main obstacles to the realization of highfidelity quantum gates are the control errors arising from inaccurate manipulation of a quantum system and the decoherence caused by the interaction between the quantum system and its environment. Quantum gates based on the geometrical phase 3 are robust against. We study the effects of the environment modeled as an ensemble of harmonic oscillators on a holonomic transformation and write the corresponding master equation.
Zanghi, robustness of nonabelian holonomic quantum gates against parametric noise, phys. Dec 20, 1999 a universal quantum computer is defined by the statespace h. Holonomic quantum computation quantum information wiley. Robust hadamard gate for optical and ion trap holonomic. Jan 23, 2020 geometric phases induced in quantum evolutions have built. The key for realizing faulttolerant quantum computation lies in maintaining the coherence of all the qubits so that highfidelity and robust qubit. These effects lead to a refining of the optimal strategy to achieve a robust computation. Superadiabatic holonomic quantum computation in cavity qed. Abelian generalization of the geometric phase, or holonomy. Robust and fast holonomic quantum gates with encoding on.
Geometric phase is an indispensable element for achieving robust and highfidelity quantum gates due to its builtin noiseresilience feature. Quantum holonomies for quantum computing international. Quantum computation with quantum gates induced by geometric phases is regarded as a promising strategy in fault tolerant quantum. Oct 24, 2012 some schemes of adiabatic holonomic quantum computation in decoherencefree subspaces have been proposed in the past few years.
Various implementations of holonomic quantum computer hqc have been proposed recently. In this paper, we study a scheme for implementing nonadiabatic holonomic computation using two blockaded rydberg atoms. Here we propose and elaborate how to efficiently implement universal nonadiabatic holonomic quantum gates on simpler superconducting circuits, with a single transmon serving as. The gates are realized by applying sequences of short laser pulses that drive.
Scalable nonadiabatic holonomic quantum computation on a. Jun 08, 2020 quantum computation with quantum gates induced by geometric phases is regarded as a promising strategy in fault tolerant quantum computation, due to its robustness against operational noises. Fast holonomic quantum computation based on solidstate. We study the effects of the environment modelled as an ensemble of harmonic oscillators on a holonomic transformation and write the corresponding master equation. However, this kind of robust feature is challenged since the usual way of realizing nonadiabatic holonomic gates introduces errors due to systematic errors in the control parameters. Room temperature highfidelity nonadiabatic holonomic quantum. Holonomic quantum control with continuous variable systems. Highfidelity and robust quantum manipulation is the key for scalable quantum computation.
Recently,geometricormore generally holonomic quantum computation 12 has attracted a lot of attention due to the robustness of geometric quantum gates against certain types of noise 5, 18. Adiabatic holonomic quantum gates for a single qubit. Therefore, due to the intrinsic operational robustness, quantum manipulation induced by geometric phases is one of the promising candidates. With the presence of the rydberg blockade effect, we realized. Some schemes of adiabatic holonomic quantum computation in decoherencefree subspaces have been proposed in the past few years. Hqc 1 is a general procedure for building universal sets of robust gates. This indicated that quantum computation could have significant. Holonomic quantum computation with superconducting charge. Composite nonadiabatic holonomic quantum computation core. Hqc is conventionally based on adiabatic evolution. Jul 26, 2011 in holonomic quantum computation, singlequbit gates are performed using driving protocols that trace out closed loops on the bloch sphere, making them robust to certain pulse errors. Geometric phases induced in quantum evolutions have built. This is an advantage of holonomic quantum computation, which makes it robust against certain types of errors. On the robustness of holonomic quantum computation fedoa.
Sep 01, 2020 nonabelian geometric phases acquired in cyclic quantum evolution can be utilized as natural resources for constructing robust holonomic gates for quantum information processing. A quantum computer based on a quantum gate and quantum circuits is. Although holonomic quantum gates are robust against some errors, being. We propose an experimentally feasible scheme to achieve quantum computation based solely on geometric manipulations of a quantum system. Here, we experimentally demonstrate a solution scheme, demonstrating. Implementation of nonadiabatic holonomic quantum computation. Here, we experimentally demonstrate a solution scheme, obtaining.
Oct 23, 2012 holonomic quantum computation hqc is a general procedure for building universal sets of robust gates using nonabelian geometric phases. Dynamicaldecouplingprotected nonadiabatic holonomic quantum. Composite nonadiabatic holonomic quantum computation. Holonomic quantum gates provide us with a robust way towards universal quantum computation, as these quantum gates are actually induced by nonabelian. Mar 08, 2017 nonadiabatic holonomic quantum computation has a robust feature in suppressing control errors because of its holonomic feature. Fast holonomic quantum computation on superconducting circuits. Nov 24, 2020 quantum computation with quantum gates induced by geometric phases is regarded as a promising strategy in faulttolerant quantum computation, owing to its robustness against operational noise. Implementing universal nonadiabatic holonomic quantum. In holonomic quantum computation, singlequbit gates are performed using driving protocols that trace out closed loops on the bloch sphere, making them robust to certain pulse errors. We propose a scheme to perform robust gates in an atomic fourlevel system using the idea of nonadiabatic holonomic quantum computation proposed in 1. Implementing universal nonadiabatic holonomic quantum gates. In contrast to the earlier adiabaticprocessbased geomet.
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