They are the building blocks of quantum circuits, like classical logic gates are for conventional digital circuits. In the holonomic approach to quantum computation information is encoded in a degenerate eigenspace of a parametric family of hamiltonians and manipulated by the associated holonomic gates. Implementing a one qubit holonomic quantum gate in. Holonomic quantum computation in subsystems request pdf. Holonomic quantum computation hqc based on the adiabatic geometric phase was then proposed for faulttolerant quantum gates by zanardi and rasetti in 19995, and. Quantum gates modern computers are built using logic gates. Our implementation of the allgeometric quantum computation is based on laser manipulation of a set of trapped ions. Oct 30, 2017 holonomic quantum computation is a quantum computation strategy that promises some builtin noiseresilience features. Non abelian geometric phases are attracting increasing interest because of possible experimental application in quantum computation. The solution is analytically and numerically investigated and the behavior of the fidelity.
A quantum network is a device consisting of quantum logic gates whose computational steps are synchronised in time. Holonomic quantum computing operates quantum systems using berrys phase, or more generally, aharanovanandan phase. The nonadiabatic holonomic quantum computation with the advantages of fast and robustness attracts widespread attention in recent. We introduce a generalized method of holonomic quantum computation hqc based on encoding in subsystems. In a similar way quantum computation also uses logic gates. Quantum holonomies for quantum computing international. Circuitbased quantum computation relies on the ability to perform a universal set of quantum gate operations on a set of quantum mechanical bits qubits. We study the effects of the environment modeled as an ensemble of harmonic oscillators on a holonomic transformation and write the corresponding. Although holonomic quantum gates are robust against some errors, being. Holonomic gates for quantum computation are commonly considered to be robust against certain kinds of parametric noise, the very motivation of this robustness. These criteria pose a dilemma in that the qubit must be. Holonomic quantum computation request pdf researchgate. We demonstrate by means of this expression the cancellation of the small squeezing control.
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. This is very different from the more conventional kind of quantum computing where qubits in a register of some kind are acted upon by various logic operations to dynamically evolve the system in time toward a result. Erik sjoqvist 1,2, d m tong 3, l mauritz andersson 4, bjorn hessmo 1, markus johansson 1,2 and kuldip singh 1. 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.
Pdf holonomic quantum computation via adiabatic shortcut. Experimental realization of universal geometric quantum. Geometric manipulation of trapped ions for quantum computation. It is proved that quantum gates implemented by using these geometric phases are more robust against certain errors. Universal holonomic quantum gates over geometric spin qubits. Here, the first scheme to realize theoretically universal single. Universal nonadiabatic holonomic quantum computation in decoherencefree subspaces with quantum dots inside a cavity jun liu et al 2017 laser physics letters 14 055202. Expedited holonomic quantum computation via net zero.
Accordingly, the methods of faulttolerant holonomic computation 26, 27 can be applied. While enormous theoretical strategies for conventional quantum gate implementation have been proposed, there is a revived interest in using geometric phases to perform circuitbased quantum computation, termed as holonomic quantum computation hqc 4, which is enabled by the adiabatic quantum theorem. Here we discuss the issue of robustness of holonomic quantum gates under. Fast holonomic quantum computation based on solidstate spins. Here, we propose a scheme for nonadiabatic holonomic quantum computation with nitrogenvacancy center electron spins, which are characterized by fast quantum gates and long qubit coherence times. It has been known for a long time that the twobit gates, and and or, and the onebit gate not, are universal for classical computation, in the sense that they are sufficient to simulate any function of the form illustrated in diagram 1. We theoretically propose a feasible scheme to realize holonomic quantum computation with chargephase qubits placed in a microwave cavity. It has received increasing attention for its intrinsic robustness against errors accrued as the quantum system evolves.
By appropriately adjusting the controllable parameters, each chargephase qubit is set as an effective fourlevel subsystem, based on which a universal set of holonomic quantum gates can be realized. Quantum computation is founded on quantum mechanical principles, and is performed by unitary quantum gates. A possible approach towards robust quantum computation is to implement quantum gates by means of different types of geometric phases 1,2,3,4. On the robustness of holonomic quantum computation fedoa. Robust hadamard gate for optical and ion trap holonomic quantum computers article in physics letters a 34156. The expression for its fidelity determining the gate stability with respect to the errors in the singlemode squeezing parameter control is analytically derived. This method, termed holonomic quantum computation eliminates or avoids the lowcon. Aps aps march meeting 2020 event implementing robust. Now, a fast scheme for holonomic quantum computation on superconducting ci. Such geometric gates depend solely on the path of a system evolution, rather than its dynamical details.
This creates its superiorities that are not available for classical computation. Experimental realization of nonadiabatic shortcut to non. Nov 17, 2008 researchers have tried to avoid this problem by using geometric phase shifts in the design of quantum gates to perform information processing. This indicated that quantum computation could have significant. A universal gate set may consist of a quantum phase gate s gate, a hadamard gate h gate, a. Osa universal holonomic single quantum gates over a. Robust hyperparallel photonic quantum entangling gate with. Researchers have tried to avoid this problem by using geometric phase shifts in the design of quantum gates to perform information processing. These effects lead to a refining of the optimal strategy to achieve a robust computation. Scalable nonadiabatic holonomic quantum computation on a. However, all these schemes rely on a universal set of holonomic quantum gates based on adiabatic evolution. By varying the detuning, amplitudes, and phase difference of lasers applied to a.
Building a quantum computer is a daunting challenge since it requires good control but also. We propose an experimentally feasible scheme to achieve quantum computation based solely on geometric manipulations of a quantum system. In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate or simply quantum gate is a basic quantum circuit operating on a small number of qubits. 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. Sep 12, 2019 geometric phase is an indispensable element for achieving robust and highfidelity quantum gates due to its builtin noiseresilience feature. In particular, nonadiabatic holonomic quantum computation, which involves nonabelian. A quantum algorithm consists of the given computation ut that acts on the quantum state.
We study the effects of the environment modelled as an ensemble of harmonic oscillators on a holonomic transformation and write the corresponding master equation. Realization of efficient quantum gates with a superconducting qubit. Holonomic quantum gates represent a promising route to noisetolerant quantum operations. Nonadiabatic holonomic quantum computation provides the means to perform fast and robust quantum gates by utilizing the resilience of nonabelian geometric phases to fluctuations of the path in state space. Under the balance condition of the diamond nitrogen vacancy center embedded in an optical cavity as a result of cavity quantum electrodynamics, we present a robust hyperparallel photonic controlledphaseflip gate for a twophoton system in both the polarization and spatialmode degrees of freedom dofs, in which the noise caused by the inequality of two reflection. Geometric phase is an indispensable element for achieving robust and high fidelity quantum gates due to its builtin noiseresilience feature. In the past few years, several schemes of holonomic quantum computation in decoherence free subspaces have been proposed. Quantum states moving through a geometry pick up a phase called a geometric phase gp, or holonomy. Experimental realization of a universal set of quantum logic gates is the central requirement for the implementation of a quantum computer. Holonomic quantum computation hqc 1 is a general procedure for building universal sets of robust gates using nonabelian geometric. Robust hadamard gate for optical and ion trap holonomic quantum computers. Learning robust pulses for generating universal quantum gates. Nov 25, 2016 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. Nonadiabatic holonomic quantum computation in decoherence.
Our implementation of the allgeometric quantum computation is based on laser manipulation. A gentle introduction eleanor rieffel and wolfgang polak. Geometric phase is an indispensable element for achieving robust and highfidelity quantum gates due to its builtin noiseresilience feature. Request pdf on researchgate holonomic quantum computation. Expedited holonomic quantum computation via net zeroenergycost control in decoherencefree subspace. The holonomic approach can be viewed as the application of nonabelian geometric phasesto quantum information processing, it is believed to be faulttolerantwith respect of certain kind of parametric noise. We consider one possible implementation of hadamard gate for optical and ion trap holonomic quantum computers. We study the effects of the environment modelled as an ensemble of harmonic oscillators on a holonomic transformation and write the corresponding master. Holonomic quantum computation hqc, first proposed by zanardi and rasetti 1, is a general procedure for implementing quantum gates using nonabelian geometric phases. Published 23 october 2012 iop publishing and deutsche physikalische gesellschaft new journal of physics, volume 14, october 2012. It is well known that a suitable set of singlequbit and twoqubit quantum gates can accomplish universal quantum computation. Fast and robust quantum gates are the cornerstones of faulttolerance quantum computation.
Universal holonomic quantum gates over geometric spin qubits with. Here we analyze the realization of various quantum gates by. 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. Hqc is conventionally based on adiabatic evolution. For the holonomic quantum computation proposed recently 47, the computational space c is always an eigenspace. The nonadiabatic holonomic quantum computation has attracted much attention in recent years because of its fastness and robustness.
Such gates require long runtime, which may further aggravate original problems of fault tolerance and decoherence. Robust pulses for high fidelity nonadiabatic geometric. 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 difficult. Expedited holonomic quantum computation via net zeroenergy. Besides the common merits of nonadiabatic holonomic quantum computation such as the robustness and the. Implementing universal nonadiabatic holonomic quantum gates with. Experiments and simulations have shown that these gates may be tolerant to certain types of faults, and may therefore be useful for robust quantum computation. While holonomic gates have been realized in many systems, extra degrees of freedom are usually required. In hqc, states undergo adiabatic closedloopparallel transport in parameter space, acquiring berry phases or matrices also called nonabelian holonomiesor wilsonloops 8 thatcanbecombinedtoachieve universal computation. Exact analysis of gate noise effects on nonadiabatic transformations of spinorbit qubits lara ulcakar and anton ramsak 2017 new journal of physics 19 093015. Fast quantum gates based on geometric phases provide a platform for performing robust quantum computation. Robustness against parametric noise of non ideal holonomic gates. Geometric quantum computation in this form is often referred as holonomic quantum computation hqc.
Holonomic quantum computation hqc 1 is a general procedure for. Holonomic quantum computing in symmetryprotected ground. Realization ofarbitrarygates in holonomic quantum computation. Holonomic quantum gates provide us with a robust way towards universal quantum computation, as these quantum gates are actually induced. Nonadiabatic holonomic quantum computation in linear. Nonadiabatic holonomic quantum computation in decoherencefree subspaces protects quantum information from control imprecisions and decoherence. Holonomic quantum computing is one of the approaches for constructing robust and fast quantum gate operations based on geometric phases. Classical and quantum logic gates university of rochester. This allows purely geometric rotation around an arbitrary axis by any angle defined by light polarization and phase using a degenerate threelevel. The blue orange quantum circuits indicate the operation. Read robust hadamard gate for optical and ion trap holonomic quantum computers, physics letters a on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.
Abelian geometric phases is proposed, using resonant interaction. Optical holonomic single quantum gates with a geometric. They are the building blocks of quantum circuits, like classical logic gates are for conventional digital circuits unlike many classical logic gates, quantum logic gates are. Nonadiabatic holonomic quantum computation in linear system. Nonadiabatic holonomic quantum computation with rydberg. A universal quantum computer is defined by the statespace h. We demonstrate universal nonadiabatic nonabelian holonomic single quantum gates over a geometric electron spin with phasemodulated polarized light and 93% average fidelity. Gps have proven to be useful in quantum information, and more particularly, when building robust quantum gates for quantum information processing. As an application, we propose a scheme for applying holonomic gates to unencoded qubits by. Fast nonabelian geometric gates via transitionless quantum. Holonomic quantum computation is a quantum computation strategy that promises some builtin noiseresilience features. This fact along with the adiabatic fashion in which gates are performed makes in principle hqc an appealing way towards universal faulttolerant qc. Robust hadamard gate for optical and ion trap holonomic. Robust gates for holonomic quantum computation core.
Cn for data encoding and by a universal set of quantum gates. Under the balance condition of the diamond nitrogen vacancy center embedded in an optical cavity as a result of cavity quantum electrodynamics, we present a robust hyperparallel photonic controlledphaseflip gate for a twophoton system in both the polarization and spatialmode degrees of freedom dofs, in which the noise caused by the inequality of two reflection coefficients can be. A gentle introduction eleanor rieffel and wolfgang polak the mit press cambridge, massachusetts london, england. Fast holonomic quantum computation based on solidstate. 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. The solution is analytically and numerically investigated and. Holonomic quantum computation hqc is a general procedure for building universal sets of robust gates using nonabelian geometric phases. Universal singlequbit nonadiabatic holonomic quantum gates in.
Meanwhile, their application to faulttolerant holonomic quantum computing was proposed, and the geometric phase gate or holonomic. In this chapter we will look at the types of logic gates used within circuits and how the notions of logic gates need to be modi. In particular, the noncommutativity nature of nonabelian geometric phases 2,5 makes it suitable for implementing quantum gates. Fast holonomic quantum computation on superconducting.
Here, a feasible and fast scheme for universal quantum computation on superconducting circuits with nonadiabatic non. Now, imperfect control of the hamiltonian during gate operations may become. We develop a nonadiabatic generalization of holonomic quantum computation in which highspeed universal quantum gates can be realized using nonabelian geometric phases. Nonadiabatic holonomic quantum computation iopscience. Realization of arbitrary gates in holonomic quantum. We show how a set of nonadiabatic holonomic one and twoqubit gates can be implemented by utilizing optical transitions in a generic threelevel 3con. In this chapter we will discuss how the notions of logic gates need to be modified in the quantum context and how they are used in the solution of the problems. Fast holonomic quantum computation on superconducting circuits with optimal control. Osa robust hyperparallel photonic quantum entangling gate. The geometric nature of the holonomic gate provides robustness, but the first proposals.
In view of their geometrical nature the holonomic gates are robust against several kind of perturbations and imperfections. However, such superiorities rely on the ability to perform high. New geometric effects that describe the behavior of noisy holonomic gates are presented. In hqc, unitary operations can be implemented by varying the system hamiltonian with degenerate energy levels to make the system evolve along a closed path in the parameter space. Experimental state control by fast nonabelian holonomic. Holonomic quantum control with continuous variable systems. The third gate is an effective controlledphase gate on coherent states of two different oscillators. The desired geometric operations are obtained by driving the quantum system to undergo appropriate adiabatic cyclic evolutions. Some schemes of adiabatic holonomic quantum computation in decoherencefree subspaces have been proposed in the past few years.
A key challenge in achieving this goal is to find implementations of gates that are resilient to certain kinds of errors. Nonabelian geometric phases are attracting increasing interest because of possible experimental application in quantum computation. Introduction the creation of robust and fast quantum gates is one of the. Holonomic quantum computation with superconducting charge. 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. Universal holonomic quantum gates over geometric spin. Singleloop multiplepulse nonadiabatic holonomic quantum. These gates would be done in sequence, creating a composite function that represents f on all of its n inputs. Furthermore, the system realizes a conditional geometric gate which may be used for holonomic non adiabatic quantum computing. Nonadiabatic holonomic quantum computation has received increasing attention due.
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