Flux-controlled quantum computation with Majorana fermions

Abstract

Majorana fermions hold promise for quantum computation, because their non-Abelian braiding statistics allows for topologically protected operations on quantum information. Topological qubits can be constructed from pairs of well-separated Majoranas in networks of nanowires. The coupling to a superconducting charge qubit in a transmission line resonator (transmon) permits braiding of Majoranas by external variation of magnetic fluxes. We show that readout operations can also be fully flux-controlled, without requiring microscopic control over tunnel couplings. We identify the minimal circuit that can perform the initialization-braiding-measurement steps required to demonstrate non-Abelian statistics. We introduce the Random Access Majorana Memory, a scalable circuit that can perform a joint parity measurement on Majoranas belonging to a selection of topological qubits. Such multi-qubit measurements allow for the efficient creation of highly entangled states and simplify quantum error correction protocols by avoiding the need for ancilla qubits.After the first signatures were reported [1][2][3][4] of Majorana bound states in superconducting nanowires [5][6][7], the quest for non-Abelian braiding statistics [8][9][10][11] has intensified. Much interest towards Majorana fermions arises from their technological potential in fault-tolerant quantum computation [12][13][14][15][16]. Their non-Abelian exchange statistics would allow to perform quantum gates belonging to the Clifford group with extremely good accuracy. Moreover, topological qubits encoded non-locally in well-separated Majorana bound states would be resilient against many sources of decoherence. Even without the applications in quantum information processing, observing a new type of quantum statistics would be a milestone in the history of physics.The two central issues for the application of Majorana fermions are (i) how to unambiguously demonstrate their non-Abelian exchange statistics and (ii) how to exploit their full potential for quantum information processing. The first issue requires an elementary circuit that can perform three tasks: initialization of a qubit, braiding (exchange) of two Majoranas, and finally measurement (readout) of the qubit. In view of the second issue, this circuit should be scalable and serve as a first step towards universal fault-tolerant quantum computation.Here we present such a circuit, using a superconducting charge qubit in a transmission line resonator (transmon [17][18][19][20]) to initialize, control, and measure the topological qubit. In such a hybrid system, named top-transmon [21], the long-range Coulomb couplings of Majorana fermions can be used to braid them and to read out their fermion parity [21,22]. While there exist several proposals to control or measure Majorana fermions in nanowires [11,[21][22][23][24][25][26][27][28][29][30][31][32], combining braiding and measurement without local adjustment of microscopic parameters remains a challenge. We show that full macroscopic control is possible if during the...

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