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arXiv:cond-mat/0606587 · Physical Review B

Full control of qubit rotations in a voltage-biased superconducting flux qubit

Luca Chirolli, Guido Burkard

Published Nov 15, 2006• 20 citations
arXivHTMLPDF

Abstract

We study a voltage-controlled version of the superconducting flux qubit [Chiorescu et al., Science 299, 1869 (2003)] and show that full control of qubit rotations on the entire Bloch sphere can be achieved. Circuit graph theory is used to study a setup where voltage sources are attached to the two superconducting islands formed between the three Josephson junctions in the flux qubit. Applying a voltage allows qubit rotations about the $y$ axis, in addition to pure $x$ and $z$ rotations obtained in the absence of applied voltages. The orientation and magnitude of the rotation axis on the Bloch sphere can be tuned by the gate voltages, the external magnetic flux, and the ratio $\ensuremath{\alpha}$ between the Josephson energies of the junctions via a flux-tunable junction. We compare the single-qubit control in the known regime $\ensuremath{\alpha}<1$ with the unexplored range $\ensuremath{\alpha}>1$ and estimate the decoherence due to voltage fluctuations.

DOI
10.1103/physrevb.74.174510

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We study a voltage-controlled version of the superconducting flux qubit [Chiorescu et al., Science 299, 1869 (2003)] and show that full control of qubit rotations on the entire Bloch sphere can be achieved. Circuit graph theory is used to study a setup where voltage sources are attached to the two superconducting islands formed between the three Josephson junctions in the flux qubit. Applying a voltage allows qubit rotations about the yyy axis, in addition to pure xxx and zzz rotations obtained in the absence of applied voltages. The orientation and magnitude of the rotation axis on the Bloch sphere can be tuned by the gate voltages, the external magnetic flux, and the ratio \ensuremathα\ensuremath{\alpha}\ensuremathα between the Josephson energies of the junctions via a flux-tunable junction. We compare the single-qubit control in the known regime \ensuremathα<1\ensuremath{\alpha}<1\ensuremathα<1 with the unexplored range \ensuremathα>1\ensuremath{\alpha}>1\ensuremathα>1 and estimate the decoherence due to voltage fluctuations.
Parity-protected superconducting qubits offer intrinsically long coherence, but many current implementations require magnetic-flux biasing, which introduces flux noise, control overhead, and limited scalability. Here we propose a parity-protected qubit based on a gate-tunable superconductor-altermagnet-superconductor Josephson junction. Altermagnets are compensated magnets with momentum-dependent spin splitting and zero net magnetization, providing spin-dependent functionality without external magnetic fields. In the proposed junction, the two spin sectors acquire opposite phase shifts, generating two Josephson channels whose interference is controlled electrically by the chemical potential. At the tuned 000-πππ transition, the first Josephson harmonic is strongly suppressed while the second harmonic dominates, yielding a double-well potential with two nearly degenerate states of opposite Cooper-pair parity. For realistic gatemon-compatible parameters, we estimate coherence times of up to tens of milliseconds while maintaining fully gate-controlled qubit operations. These results establish altermagnetic Josephson junctions as a promising route toward protected superconducting qubits with local, scalable, and all-electrical control.
Abstract Superconducting circuits represent a versatile playground to explore novel quantum phenomena and a platform to realize quantum bits (qubits). Superconducting qubits hinge on the coherent tunneling of Cooper pairs across the insulating barrier of a Josephson junction. This qubit implementation is, however, plagued with the variability of the fabricated junction, along with the need for magnetic tunability of the qubit transition frequency. Alternatively, a dual to the Josephson effect—referred to as quantum phase slips—allows for a coherent coupling of flux states and has been used to build phase-slip qubits. In this paper, we propose coupling flux states of a superconducting ring using a bias voltage. By solving the time-dependent Ginzburg–Landau equations, we demonstrate that the bias voltage locally suppresses the density of Cooper pairs, thereby forming a weak link where phase slips occur. Moreover, we show that a voltage-biased superconducting ring serves as an electrically-controlled magnetic memory. The work presented in this paper is an important step towards realizing electrically-tunable superconducting devices, such as qubits and SQUIDs.
Quantum state on Bloch sphere for superconducting charge qubit, phase qubit and flux qubit for all time in absence of external drive is stable to initial state. By driving the qubits, approximation of charge and flux Hamiltonian lead to quantum state rotation in Bloch sphere around an axis completely differ from rotation vector of exact Hamiltonian. The trajectory of quantum state for phase qubit for approximated and exact Hamiltonian is the same but the expectation of quantum observable has considerable errors as two other qubits. microwave drive control is designed for approximated Hamiltonian and exerted on actual systems and shows completely different trajectory with respect to desired trajectory. Finally a nonlinear control with external μμμV voltage control and nA current control is designed for general qubit which completely stabilizes quantum state toward a desired state.
Abstract Quantum state on Bloch sphere for superconducting charge qubit, phase qubit and flux qubit for all time in absence of external drive is stable to initial state. By driving the qubits, approximation of charge and flux Hamiltonian lead to quantum state rotation in Bloch sphere around an axis completely differ from rotation vector of exact Hamiltonian. The trajectory of quantum state for phase qubit for approximated and exact Hamiltonian is the same but the expectation of quantum observable has considerable errors as two other qubits. microwave drive control is designed for approximated Hamiltonian and exerted on actual systems and shows completely different trajectory with respect to desired trajectory. Finally a nonlinear control with external µV voltage control and nA current control is designed for general qubit which completely stabilizes quantum state toward a desired state.
Leveraging the higher harmonics content of the Josephson potential in a superconducting circuit offers a promising route in the search for new qubits with increased protection against decoherence. In this work, we demonstrate how the flux tunability of a hybrid semiconductor-superconductor Josephson junction based on a single full-shell nanowire enables this possibility. Near one flux quantum, Φ≈Φ0=h/2eΦ\approx Φ_0=h/2eΦ≈Φ0​=h/2e, we find that the qubit system can be tuned from a gatemon regime to a parity-protected regime with qubit eigenstates localized in phase space in the 000 and πππ minima of the Josephson potential (cos⁡2φ0\cos 2φ_0cos2φ0​). Estimates of qubit coherence and relaxation times due to different noise sources are presented.
We have realized controllable coupling between two three-junction flux qubits by inserting an additional coupler loop between them, containing three Josephson junctions. Two of these are shared with the qubit loops, providing strong qubit-coupler interaction. The third junction gives the coupler a nontrivial current-flux relation; its derivative (i.e., the susceptibility) determines the coupling strength J, which thus is tunable in situ via the coupler's flux bias. In the qubit regime, J was varied from approximately 45 (antiferromagnetic) to approximately -55 mK (ferromagnetic); in particular, J vanishes for an intermediate coupler bias. Measurements on a second sample illuminate the relation between two-qubit tunable coupling and three-qubit behavior.