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Coupled superconducting flux qubits

J. H. Plantenberg

Published Oct 5, 2007• 0 citations
OpenAlex

Abstract

This thesis presents results of theoretical and experimental work on superconducting persistent-current quantum bits. These qubits offer an attractive route towards scalable solid-state quantum computing. The focus of this work is on the gradiometer flux qubit which has a special geometric design, that both provides a stable phase bias and improved immunity to global flux noise, and which enables the implementation of qubit registers. The realization of the simplest quantum register consisting for two such qubits, allowed for the experimental execution of the complete set of four controlled-NOT quantum gates.

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This thesis presents results of theoretical and experimental work on superconducting persistent-current flux quantum bits. These qubits are promising candidates for the implementation of scalable quantum information processing. This work focuses on the study of one dimensional chains of inductively coupled flux qubits and on qubits with a tunable energy gap. Chains of flux qubits can be used as models of quantum spin chains, one of the most basic systems in many-body physics that has been extensively studied theoretically. The ability to design and tune the qubit and coupling parameters enables exploration of different phase regimes during measurements, in parameter regimes that are not accessible with magnetic materials. The study of the dynamics of quantum waves in an artificial spin chain can also be used to explore novel quantum phenomena with possible applications in quantum computing. Tunability of the minimal energy splitting (the gap) enables one to rapidly bring the flux qubit in and out of resonance with other quantum systems, including a harmonic oscillator. With tunable qubits it also becomes possible to create inter-qubit couplings of different vector nature, using magnetic fluxes. This permits the design of various interaction Hamiltonians for multiple qubit systems. These operations can be performed at the degeneracy point of the qubit, where coherence properties are optimal. Therefore the tunable flux qubit provides an attractive component for the implementation of scalable quantum computation.

•Jun 18, 2009•4 citations

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In this thesis measurements on single and coupled Josephson persistent current qubits are presented. The Josephson persistent current qubit consists of a superconducting loop intersected by three Josephson junctions. When half a flux quantum is applied to the loop this system acts as a quantum two state system. The two states are associated with a clock or anti clockwise current flowing in the loop and can be measured using a SQUID magnetometer. The research presented in this thesis aimed at achieving coupling between two Josephson persistent current qubits and to show conditional gate operations in such a coupled qubit system. Also it was tried to improve the coherence properties of a single qubit by using a gradiometer type configuration to minimize influence from fluxnoise which would cause a disturbance of the energy bias of the qubit system. The basic principles of the Josephson persistent current qubit are discussed, as well as design criteria to minimize decoherence due to the environment seen by the squid or microwave lines. Spectroscopy measurements have been performed on coupled qubit systems mapping out the energy level structure of these systems. For two coupled qubits the origin and magnitude of the coupling J is derived for coupling via the geometrical inductance between the qubits. Also it is shown that coupling via a shared junction or a shared line acts the same as the geometrical coupling. Spectroscopy measurements show coupling for qubits which are mainly geometrical coupled and spectroscopy measurements on an other sample show a coupling for qubits coupled via a large shared Josephson junction. Using such a shared junction allows for the coupling to be designed within a large range. For the coupled qubit system with coupling via a large junction spectroscopy measurements from both the ground state to higher states as well as from the partially populated first excited state to higher states have been performed and the level structure of this system is mapped out. The energy level structure is in good agreement with the 4 level approximation for two coupled qubits. Coherent Rabi oscillations between two states flipping either qubit of this system have been performed with an oscillation decay time of up to 70ns. Also conditional spectroscopy has been performed by first going coherently from the ground state to a higher state and then incoherently pumping the system to other states. Spectroscopy measurements on a gradiometer type Josephson persistent current qubit show trapped fluxoid biasing can be used to create a phase bias of pi over the qubit junctions. The results of this thesis show that coupling between Josephson persistent current qubits can be achieved and designed within the wanted range. Superpositions between the ground state and higher states in such a coupled qubit system have been created by performing Rabi oscillations. Also conditional spectroscopy has been performed.

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Superconducting qubits have in recent years become a promising candidate for the implementation of a quantum computer due to their design flexibility, good protection from decohering elementary excitations, and availability of well developed fabrication and measurement techniques. Superconducting flux qubits, for which the effect of offset charge noise is reduced due to the fact that the Josephson energy dominates over the charging energy, correspond to one of the proposed means of designing a superconducting qubit. A nonlinear dispersive readout scheme of flux qubits involving a DC SQUID magnetometer that avoids the effects of on-chip dissipation can be readily implemented, yielding high contrast output for single qubit readout. Coupling schemes via nonlinear Josephson elements have also been realized. On the other hand, while the means of isolating superconducting qubits from external noise sources has been found, the mechanisms by which they undergo relaxation and decoherence due to intrinsic noise sources in the junctions themselves are not very well understood, and the question of how to deal with these noise sources remains unanswered in the general case. Other questions deal with the problem of experimentally observing entanglement in an array of coupled superconducting qubits, and finding the means by which the existence of entanglement in a typical laboratory setup may to some extent be verified by measurements on a global scale. Following a brief introductory review, we will first investigate the influence of a Two-Level Fluctuator on a DC SQUID driven by a finite current bias. Then we introduce a directly measurable signature of multiqubit entanglement for a large system of qubits and show that it is compatible to a recently introduced measure of global entanglement.

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Solid-State Qubits with Current-Controlled Coupling

T. Hime, P. A. Reichardt, B. L. T. Plourde +4 more

The ability to switch the coupling between quantum bits (qubits) on and off is essential for implementing many quantum-computing algorithms. We demonstrated such control with two flux qubits coupled together through their mutual inductances and through the dc superconducting quantum interference device (SQUID) that reads out their magnetic flux states. A bias current applied to the SQUID in the zero-voltage state induced a change in the dynamic inductance, reducing the coupling energy controllably to zero and reversing its sign.

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Frederick W. Strauch

The theory of superconducting phase qubits---also known as current-biased Josephson junctions---is presented. In the first part of this thesis, I introduce quantum computation, quantum simulation, and their deep connection with symplectic integration. I then consider the fundamental many-body theory of superconductivity and Josephson junctions and show how the quantum dynamics of a single macroscopic degree of freedom, the gauge invariant phase difference, emerges. A complete study of the Hilbert space structure of such a variable is performed for the current-biased junction. The resulting resonance structure is studied in detail, using various formalisms including the WKB approximation, instanton methods, the complex scaling transformation, basis set stabilization, numerical integration, and dynamical simulation using Lie algebraic wave-packet propagation. The second part of this thesis explores how the current-biased junction can be used as an element of a quantum computer---a quantum bit (qubit). Single qubit operations are studied, followed by the presentation of the theory of coupled qubit devices. My key result is the design and optimization of quantum logic gates with high fidelity (F ~ 0.9999) for capacitively coupled phase qubits with short gate times (~ 10 ns). Finally, I examine an advanced qubit-coupling scheme, a resonant coupling method utilizing a harmonic oscillator as the auxiliary degree of freedom. The models and methods presented here have been developed in direct collaboration with an experimental program. These experiments are the first to show spectroscopic evidence for entanglement between two and three macroscopic degrees of freedom in a superconducting circuit.

•Nov 24, 2004•6 citations
This thesis presents results of theoretical and experimental work on superconducting persistent-current quantum bits. These qubits offer an attractive route towards scalable solid-state quantum computing. The focus of this work is on the gradiometer flux qubit which has a special geometric design, that both provides a stable phase bias and improved immunity to global flux noise, and which enables the implementation of qubit registers. The realization of the simplest quantum register consisting for two such qubits, allowed for the experimental execution of the complete set of four controlled-NOT quantum gates.
This thesis presents results of theoretical and experimental work on superconducting persistent-current flux quantum bits. These qubits are promising candidates for the implementation of scalable quantum information processing. This work focuses on the study of one dimensional chains of inductively coupled flux qubits and on qubits with a tunable energy gap. Chains of flux qubits can be used as models of quantum spin chains, one of the most basic systems in many-body physics that has been extensively studied theoretically. The ability to design and tune the qubit and coupling parameters enables exploration of different phase regimes during measurements, in parameter regimes that are not accessible with magnetic materials. The study of the dynamics of quantum waves in an artificial spin chain can also be used to explore novel quantum phenomena with possible applications in quantum computing. Tunability of the minimal energy splitting (the gap) enables one to rapidly bring the flux qubit in and out of resonance with other quantum systems, including a harmonic oscillator. With tunable qubits it also becomes possible to create inter-qubit couplings of different vector nature, using magnetic fluxes. This permits the design of various interaction Hamiltonians for multiple qubit systems. These operations can be performed at the degeneracy point of the qubit, where coherence properties are optimal. Therefore the tunable flux qubit provides an attractive component for the implementation of scalable quantum computation.
In this thesis measurements on single and coupled Josephson persistent current qubits are presented. The Josephson persistent current qubit consists of a superconducting loop intersected by three Josephson junctions. When half a flux quantum is applied to the loop this system acts as a quantum two state system. The two states are associated with a clock or anti clockwise current flowing in the loop and can be measured using a SQUID magnetometer. The research presented in this thesis aimed at achieving coupling between two Josephson persistent current qubits and to show conditional gate operations in such a coupled qubit system. Also it was tried to improve the coherence properties of a single qubit by using a gradiometer type configuration to minimize influence from fluxnoise which would cause a disturbance of the energy bias of the qubit system. The basic principles of the Josephson persistent current qubit are discussed, as well as design criteria to minimize decoherence due to the environment seen by the squid or microwave lines. Spectroscopy measurements have been performed on coupled qubit systems mapping out the energy level structure of these systems. For two coupled qubits the origin and magnitude of the coupling J is derived for coupling via the geometrical inductance between the qubits. Also it is shown that coupling via a shared junction or a shared line acts the same as the geometrical coupling. Spectroscopy measurements show coupling for qubits which are mainly geometrical coupled and spectroscopy measurements on an other sample show a coupling for qubits coupled via a large shared Josephson junction. Using such a shared junction allows for the coupling to be designed within a large range. For the coupled qubit system with coupling via a large junction spectroscopy measurements from both the ground state to higher states as well as from the partially populated first excited state to higher states have been performed and the level structure of this system is mapped out. The energy level structure is in good agreement with the 4 level approximation for two coupled qubits. Coherent Rabi oscillations between two states flipping either qubit of this system have been performed with an oscillation decay time of up to 70ns. Also conditional spectroscopy has been performed by first going coherently from the ground state to a higher state and then incoherently pumping the system to other states. Spectroscopy measurements on a gradiometer type Josephson persistent current qubit show trapped fluxoid biasing can be used to create a phase bias of pi over the qubit junctions. The results of this thesis show that coupling between Josephson persistent current qubits can be achieved and designed within the wanted range. Superpositions between the ground state and higher states in such a coupled qubit system have been created by performing Rabi oscillations. Also conditional spectroscopy has been performed.
Superconducting qubits have in recent years become a promising candidate for the implementation of a quantum computer due to their design flexibility, good protection from decohering elementary excitations, and availability of well developed fabrication and measurement techniques. Superconducting flux qubits, for which the effect of offset charge noise is reduced due to the fact that the Josephson energy dominates over the charging energy, correspond to one of the proposed means of designing a superconducting qubit. A nonlinear dispersive readout scheme of flux qubits involving a DC SQUID magnetometer that avoids the effects of on-chip dissipation can be readily implemented, yielding high contrast output for single qubit readout. Coupling schemes via nonlinear Josephson elements have also been realized. On the other hand, while the means of isolating superconducting qubits from external noise sources has been found, the mechanisms by which they undergo relaxation and decoherence due to intrinsic noise sources in the junctions themselves are not very well understood, and the question of how to deal with these noise sources remains unanswered in the general case. Other questions deal with the problem of experimentally observing entanglement in an array of coupled superconducting qubits, and finding the means by which the existence of entanglement in a typical laboratory setup may to some extent be verified by measurements on a global scale. Following a brief introductory review, we will first investigate the influence of a Two-Level Fluctuator on a DC SQUID driven by a finite current bias. Then we introduce a directly measurable signature of multiqubit entanglement for a large system of qubits and show that it is compatible to a recently introduced measure of global entanglement.
The concept of a quantum computer was invented in the beginning of the 1980s as a quantum generalization of the reversible classical computer. After discoveries in the middle of the 1990s of quantum algorithms, which wouldsolve some problems considered intractable for classical computers, the field of quantum computing has developed rapidly. A wide range of quantum systems are investigated for their possible ability to implement quantum algorithms in practice. The most promising solid state implementations are superconducting electrical circuits based on the Josephson effect, and the Coulomb blockade effect. Superconducting circuits are macroscopic quantum systems which can be fabricated using standard lithography technologies. Superconducting qubits - basic building blocks of a quantum computer - have been developed at several research laboratories, among others the MC2 here at Chalmers. This thesis presents a theoretical investigation of controllable coupling of superconducting qubits based on the single Cooper-pair box. Two coupling schemes are investigated in detail: current-controlled coupling via large Josephson junctions, and coupling via a superconducting stripline cavity. Both coupling designs are scalable and suitable for the charge regime of the single Cooper-pair box, as well as for the charge-phase regime where the qubit is better protected from environmental noise. Quantum gate protocols which are relevant for these physical couplings are discussed. The investigations show that, for both considered designs, the simplest two-qubit gate is the conditional phase-shift gate. This gate is universal for quantum computing, and it can create maximallyentangled qubit pairs in only one run. The investigation combines methods from electrical engineering, quantum mechanics and quantum computer science.
The ability to switch the coupling between quantum bits (qubits) on and off is essential for implementing many quantum-computing algorithms. We demonstrated such control with two flux qubits coupled together through their mutual inductances and through the dc superconducting quantum interference device (SQUID) that reads out their magnetic flux states. A bias current applied to the SQUID in the zero-voltage state induced a change in the dynamic inductance, reducing the coupling energy controllably to zero and reversing its sign.
The theory of superconducting phase qubits---also known as current-biased Josephson junctions---is presented. In the first part of this thesis, I introduce quantum computation, quantum simulation, and their deep connection with symplectic integration. I then consider the fundamental many-body theory of superconductivity and Josephson junctions and show how the quantum dynamics of a single macroscopic degree of freedom, the gauge invariant phase difference, emerges. A complete study of the Hilbert space structure of such a variable is performed for the current-biased junction. The resulting resonance structure is studied in detail, using various formalisms including the WKB approximation, instanton methods, the complex scaling transformation, basis set stabilization, numerical integration, and dynamical simulation using Lie algebraic wave-packet propagation. The second part of this thesis explores how the current-biased junction can be used as an element of a quantum computer---a quantum bit (qubit). Single qubit operations are studied, followed by the presentation of the theory of coupled qubit devices. My key result is the design and optimization of quantum logic gates with high fidelity (F ~ 0.9999) for capacitively coupled phase qubits with short gate times (~ 10 ns). Finally, I examine an advanced qubit-coupling scheme, a resonant coupling method utilizing a harmonic oscillator as the auxiliary degree of freedom. The models and methods presented here have been developed in direct collaboration with an experimental program. These experiments are the first to show spectroscopic evidence for entanglement between two and three macroscopic degrees of freedom in a superconducting circuit.