Quantum computingwith atomic qubits and ...

1 [quant-ph] 24 Jul 2016 Quantum computing with atomic qubits andRydberg interactions: Progress and challengesM. SaffmanDepartment of Physics, University of Wisconsin-Madison, 1150 UniversityAvenue, Madison, Wisconsin, 53706, present a review of Quantum computation with neutral atomqubits. After an overview of architectural options and approaches to preparinglarge qubit arrays we examine Rydberg mediated gate protocols and fidelity fortwo- and multi-qubit interactions. Quantum simulation andRydberg dressingare alternatives to circuit based Quantum computing for exploring many bodyquantum dynamics. We review the properties of the dressing interaction andprovide a quantitative figure of merit for the complexity of the coherent dynamicsthat can be accessed with dressing. We conclude with a summary of the currentstatus and an outlook for future to:J. Phys. BQuantum computing with atomic qubits and Rydberg interactions: Progress and challenges21. IntroductionQuantum computing is attracting great interest dueto its potential for solving classically intractable prob-lems.

2 Several physical platforms are under develop-ment and have been demonstrated at small scale in-cluding superconductors, semiconductors, atoms, andphotons[1]. Experiments with trapped ions[2, 3, 4]and superconducting qubits [5, 6] have achieved highfidelity Quantum logic operations that are close to, andin some cases exceed, known thresholds for error cor-recting Quantum codes[7, 8]. In addition to the need forhigh fidelity logic gates there are several other require-ments for translating demonstrations of Quantum bitsand Quantum logic operations into a useful quantumcomputing device. These were enumerated by DiVin-cenzo some years ago[9] and still serve as a useful checklist when considering physical approaches to this review we take a critical look at theprospects for developing scalable Quantum computa-tion based on neutral atom qubits with Rydberg statemediated entanglement. Although there has been sig-nificant progress in the last year[10, 11], a high fidelitytwo-qubit entangling gate remains to be demonstratedwith neutral atoms.

3 It is therefore tempting to focuson gate fidelity as the most important challenge facingneutral atom Quantum computation. Nevertheless wewill argue that gate fidelity is but one of several chal-lenges, most of which have received much less attentionthan logic gate review will be divided into sections corre-sponding to the DiVincenzo criteria as follows. In we briefly recall the main elements of a neutral atomquantum computing architecture. Approaches to large,scalable qubit arrays are presented in Sec. The im-portant issue of trap lifetime is discussed in Sec. Sec. 3 we review what has been achieved for neutralatom coherence times. In Sec. 4 we present approachesto qubit initialization and measurement with a focus onimplementing these operations with low crosstalk in amulti-qubit 5 presents the current state of the art forneutral atom logic gates. The discussion is divided intoconsideration of one-qubit operations in Sec. andtwo-qubit operations in Sec. The fundamentallimits to gate fidelity are examined in Sec.

4 Aparticular feature of Rydberg mediated gates is thepotential for multi-atom gate operations that are moreFigure for a neutral atom Quantum inset shows a fluorescence image of a 49 site qubit array[13].efficient than a decomposition into universal one- andtwo-qubit gates. Section presents the protocolsthat have been proposed for multi-qubit challenges for high fidelity gates areexplored in Sec. We conclude with a review ofalternative approaches including Quantum simulation,Rydberg dressing, and hybrid interactions in Sec. 6followed an outlook for the future in Sec. 7. Primaryattention is paid to developments in the last five detailed presentation of the basic ideas and earlierresults on the use of Rydberg atoms for quantuminformation can be found in [12].2. Neutral atom architectureNeutral atoms are being intensively developed forstudies of Quantum simulation[14, 15, 16] andcomputation[17]. Aspects of Quantum computationwith trapped neutral atoms have been reviewed in[18, 19, 12, 20, 21, 22, 23, 24, 25, 26, 27].

5 One vi-sion for a neutral atom Quantum computer as depictedin Fig. 1 is based on an array of single atom qubits inoptical or magnetic traps. The array is loaded from areservoir of laser cooled atoms at K temperature anda fiducial logical state encoded in hyperfine-Zeemanground substates is prepared with optical gates are performed with some combination ofoptical and microwave fields and the results are mea-sured with resonance fluorescence. In this way all ofthe DiVincenzo criteria for computation can in prin-ciple be fulfilled and experiments over the last decadehave demonstrated all of the required capabilities, al-beit not in a single platform, and not yet with sufficientfidelity for error correction and computing with atomic qubits and Rydberg interactions: Progress and challenges3 Figure aKqubit Quantum register with neutralatoms. a) Standard method with one two-level atom per ) ensemble encoding withNtwo-level atoms per qubit. c)Collective encoding withKqubits in one ensemble using atomswithK+ 1 internal experimental work to date on neutral atomquantum logic has used the heavy alkalis Rb andCs which are readily laser cooled and optically ormagnetically trapped.

6 qubits can be encoded inZeeman or hyperfine ground states which afford longcoherence times and GHz scale qubit frequencies in thecase of hyperfine qubits . The heavy alkalis also havewell resolved excited state hyperfine splittings which isimportant for state initialization by optical pumpingand qubit measurements by resonance gates are usefully divided into one- andtwo-qubit operations. One-qubit gates on hyperfinequbits can be performed with microwaves, two-frequency stimulated optical Raman transitions, or acombination of Stark shifting light and defer a discussion of the current state of theart of one-qubit gate operations to Sec. Two-qubit entangling gates are possible based on severaldifferent approaches. The first demonstration ofentanglement of a pair of neutral atoms used atom-photon-atom coupling between long lived circularRydberg states[28]. This was followed by latticeexperiments that created entanglement between manypairs of trapped atoms using collisional interactions[29,30].

7 A recent experiment demonstrated collisionalentanglement of a single pair of atoms trapped inmovable optical tweezers[31]. In this review we willconcentrate on Rydberg mediated gates[32] which havebeen demonstrated in several experiments[33, 34, 35,10, 11]. The physics of the Rydberg interactionbetween individual atoms has been treated in detailelsewhere[36, 37, 38, 39, 40, 41], including a review inthis special issue[27]. Here we focus on the applicationof Rydberg interactions to Quantum computationincluding a detailed discussion of the status andprospects for high fidelity Rydberg gates in Sec. different approaches to qubit encoding arepossible. Figure 2a) shows the standard approach ofencoding aKqubit register in an array ofKidenticaltwo-level atoms, each encoding one qubit. TheRydberg blockade interaction can be used to restricta multi-particle ensemble to a two-dimensional logicalsubspace[42]. This ensemble encoding is shown in ) and requiresKensembles, each containingNtwo-level atoms to encode the array.

8 The qubit basis statesin the ensemble encoding are themselves multi-particleentangled states in the physical basis. Preparation andverification of entanglement in ensemble qubits usingRydberg blockade was demonstrated recently[43, 44].The ensemble approach can be further extended to oneNatom ensemble collectively encodingKqubits if eachatom has at leastK+1 internal levels andN K[45].Collective encoding has not yet been demonstratedexperimentally but could in principle form the basisof a 1000 qubit scale experiment by coupling multiplecollective ensembles[46].There are several intrinsic features of neutralatoms that make them well suited for multi-qubitexperiments. As with trapped ion qubits , neutralatoms are all identical so that the qubit frequency qis the same for each and every qubit. Althoughthe situation is more complicated when the qubitsare trapped with electromagnetic fields, to first orderthe qubits are all identical. This is an importantfeature of natural, as opposed to synthetic qubits ,which greatly reduces the control system complexitythat is otherwise needed to address heterogeneousqubits.

9 Not surprisingly there is also a flip sideto this argument in that the identical character ofatomic qubits renders them susceptible to unwantedcrosstalk during preparation, logic, and measurementoperations. Furthermore, in some engineered systemssuch as superconducting qubits , the availability ofdifferent qubit frequencies is an important feature forexercising control with low cross talk[47].It remains a matter for debate as to whetheridentical or heterogeneous qubits are better suited forengineering large scale systems. It has been arguedrecently in the context of trapped ion architectures,that identical qubits present an advantage due tothe simplified control requirements as well as betterpossibilities for dynamically reconfigurable qubitinterconnections[48]. Much the same arguments applyto neutral atom architectures, and in this section,as well as Sec. 4, we highlight opportunities andchallenges that exist in a neutral atom architecturebased on identical Qubit arraysNeutral atom qubit arrays may be based on trappingin optical[49, 50] or magnetic[51, 52, 53, 54] lattices,examples of which are shown in Fig.

10 3. Due to the veryQuantum computing with atomic qubits and Rydberg interactions: Progress and challenges4 Figure images of atoms in a 100 site 2D opticaltrap array (left from [64]) and a 2D magnetic trap array (rightfrom [54]).weak magnetic dipole and van der Waals interactionsof ground state atoms arrays with lattice constantsof a few m are suitable for long coherence timequbit memory while allowing site specific control withfocused optical beams[55], or with a gradient magneticfield[56]. In the last few years several experiments havedemonstrated the ability to coherently control singleatoms in 2D[57, 58, 59, 10] and 3D[60, 61] arrays ofoptical number of qubits that can be implemented ina 2D or 3D array is limited by several factors. Foroptical traps large arrays require more laser power needed per trap site depends on the desiredtrap depth and the detuning from the nearest opticaltransitions. Small detuning gives deeper traps, witha depth scaling as 1/ , where is the detuningfrom the nearest strong electronic transition.