Quantum information processing using quasiclassical electromagnetic interactions between qubits and electrical resonators

Kerman, Andrew J.

doi:10.1088/1367-2630/15/12/123011

New J. Phys.

2013

DOI: 10.1088/1367-2630/15/12/123011

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Quantum information processing using quasiclassical electromagnetic interactions between qubits and electrical resonators

Andrew J. Kerman

Abstract: Abstract. Electrical resonators are widely used in quantum information processing, by engineering an electromagnetic interaction with qubits based on real or virtual exchange of microwave photons. This interaction relies on strong coupling between the qubits' transition dipole moments and the vacuum fluctuations of the resonator in the same manner as cavity quantum electrodynamics (QED), and has consequently come to be called 'circuit QED' (cQED). Great strides in the control of quantum information have alread… Show more

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Cited by 46 publications

(73 citation statements)

References 99 publications

(298 reference statements)

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“…This Chern number may be intuitively understood as counting the number of times an eigenstate wraps around a manifold in Hilbert space, and is precisely the topological invariant that yields, for example, quantization of the resistance in the integer quantum Hall effect [8][9][10]. The Berry phase has been investigated in a wide variety of systems [15][16][17][18], both as a fundamental property of quantum systems and as a practical method to manipulate quantum information [19,20]. In a breakthrough experiment, Leek et al first measured the Berry phase of a superconducting qubit [21][22][23].…”

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confidence: 99%

Measuring a Topological Transition in an Artificial Spin-1/2System

Schroer

Kolodrubetz²,

Kindel³

et al. 2014

Phys. Rev. Lett.

160

157

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We present measurements of a topological property, the Chern number (C1), of a closed manifold in the space of two-level system Hamiltonians, where the two-level system is formed from a superconducting qubit. We manipulate the parameters of the Hamiltonian of the superconducting qubit along paths in the manifold and extract C1 from the nonadiabitic response of the qubit. By adjusting the manifold such that a degeneracy in the Hamiltonian passes from inside to outside the manifold, we observe a topological transition C1 = 1 → 0. Our measurement of C1 is quantized to within 2 percent on either side of the transition.

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mentioning

confidence: 99%

Measuring a Topological Transition in an Artificial Spin-1/2System

Schroer

Kolodrubetz²,

Kindel³

et al. 2014

Phys. Rev. Lett.

160

157

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“…x To calculate the effective coupling energy J xx in equation (2), we expand the qubit energies around the points F A x and F B x , and then minimize the total energy with respect to the coupler current I C (following [64]), to obtain:…”

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confidence: 99%

Superconducting qubit circuit emulation of a vector spin-1/2

Kerman

2019

New J. Phys.

Self Cite

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We propose a superconducting qubit that fully emulates a quantum spin-1/2, with an effective vector dipole moment whose three components obey the commutation relations of an angular momentum in the computational subspace. Each of these components of the dipole moment also couples approximately linearly to an independently-controllable external bias, emulating the linear Zeeman effect due to a fictitious, vector magnetic field over a broad range of effective total fields around zero. This capability, combined with established techniques for qubit coupling, should enable for the first time the direct, controllable hardware emulation of nearly arbitrary, interacting quantum spin-1/2 systems, including the canonical Heisenberg model. Furthermore, it constitutes a crucial step both towards realizing the full potential of quantum annealing, as well as exploring important quantum information processing capabilities that have so far been inaccessible to available hardware, such as quantum error suppression, Hamiltonian and holonomic quantum computing, and adiabatic quantum chemistry.Quantum spin-1/2 models serve as basic paradigms for a wide variety of physical systems in quantum statistical mechanics and many-body physics, and are among the most highly studied in the context of quantum phase transitions and topological order [1][2][3][4]. In addition, since the spin-1/2 in a magnetic field is one of the simplest realizations of a qubit, many quantum information processing paradigms draw heavily on concepts which originated from or are closely related to quantum magnetism. For example, quantum spin-1/2 language is used to describe nearly all of the constructions underlying quantum error-correction [5-7] and error-suppression [8,9] methods. It is also the most commonly-used framework for specifying engineered Hamiltonians in many other quantum protocols such as quantum annealing [10,11], adiabatic topological quantum computing [12], quantum simulation [13-17], Hamiltonian and holonomic quantum computing [9,[18][19][20][21], and quantum chemistry [22][23][24].The conventional method for simulating vector spin-1/2 Hamiltonians is based on the 'gate-model' quantum simulation paradigm, and uses pulsed, high-speed sequences of discrete, non-commuting gate operations [25-27] to approximate time-evolution under a desired Hamiltonian [28,29]. In this paradigm, simulating a different Hamiltonian simply requires reprogramming the hardware with a different sequence of gates, a desirable property so long as the error introduced by the discretization can be kept sufficiently low. Unfortunately, this becomes increasingly difficult as the required spin interactions become stronger and/or more complex, since for a fixed gate duration 1 , the discretization error grows both with the strength of the spinspin interactions, and with the number of mutually-noncommuting terms they contain. In addition, gate-based implementation necessarily implies that the system occupies Hilbert space far above its ground state, and the resulting information ...

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“…Consequently, modulating the coupling at the oscillator frequency rapidly dephases the qubits. To keep dephasing to a minimum, we instead use an off-resonant modulation of g i (t) at a frequency ω m detuned from ω r by many oscillator linewidths κ: g i (t) = g i cos(ω m t), where g 1,2 are constant real amplitudes [10].The oscillator-mediated qubit-qubit interaction can be made more apparent by applying a polaron trans-with an appropriate choice of α i (t) (see supplemental material). Doing this, we find in the polaron frame the simple Hamiltonian…”

mentioning

confidence: 99%

“…Note that these conclusions remain unchanged if the oscillator is initially in a coherent state. As a result, there is no need for the oscillator to be empty at the start of the gate [10]. Based on the dephasing rate Γ and on the gate time t g , a simple estimate for the scaling of the gate infi-…”

mentioning

confidence: 99%

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Fast and high-fidelity entangling gate through parametrically modulated longitudinal coupling

Royer

Grimsmo

Didier

et al. 2017

Quantum

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We investigate an approach to universal quantum computation based on the modulation of longitudinal qubit-oscillator coupling. We show how to realize a controlled-phase gate by simultaneously modulating the longitudinal coupling of two qubits to a common oscillator mode. In contrast to the more familiar transversal qubitoscillator coupling, the magnitude of the effective qubit-qubit interaction does not rely on a small perturbative parameter. As a result, this effective interaction strength can be made large, leading to short gate times and high gate fidelities. We moreover show how the gate infidelity can be exponentially suppressed with squeezing and how the entangling gate can be generalized to qubits coupled to separate oscillators. Our proposal can be realized in multiple physical platforms for quantum computing, including superconducting and spin qubits.Introduction-A widespread strategy for quantum information processing is to couple the dipole moment of multiple qubits to common oscillator modes, the latter being used to measure the qubits and to mediate longrange interactions. Realizations of this idea are found in Rydberg atoms [1], superconducting qubits [2] and quantum dots [3] amongst others. With the dipole moment operator being off-diagonal in the qubit's eigenbasis, this type of transversal qubit-oscillator coupling leads to hybridization of the qubit and oscillator degrees of freedom. In turn, this results in qubit Purcell decay [4] and to qubit readout that is not truly quantum non-demolition (QND) [5]. To minimize these problems, the qubit can be operated at a frequency detuning from the oscillator that is large with respect to the transverse coupling strength g x . This interaction then only acts perturbatively, taking a dispersive character [1]. While it has advantages, this perturbative character also results in slow oscillator-mediated qubit entangling gates [6][7][8].Rather than relying on the standard transversal coupling,Since H z commutes with the qubit's bare Hamiltonian the qubit is not dressed by the oscillator. Purcell decay is therefore absent [10,11] and qubit readout is truly QND [13]. The absence of qubit dressing also allows for scaling up to a lattice of arbitrary size with strictly local interactions [11].By itself, longitudinal interaction however only leads to a vanishingly small qubit state-dependent displacement of the oscillator field of amplitude g z /ω r 1, with ω r the oscillator frequency. In Ref.[13], it was shown that modulating g z at the oscillator frequency ω r activates this interaction leading to a large qubit statedependent oscillator displacement and to fast QND qubit readout. In this paper, we show how the same approach can be used, together with single qubit rotations, for universal quantum computing by introducing a fast and high-fidelity controlled-phase gate based on longitudinal coupling. The two-qubit logical operation relies on parametric modulation of a longitudinal qubit-oscillator coupling, inducing an effectiveσ zσz interaction between qubits co...

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Quantum information processing using quasiclassical electromagnetic interactions between qubits and electrical resonators

Cited by 46 publications

References 99 publications

Measuring a Topological Transition in an Artificial Spin-1/2System

Measuring a Topological Transition in an Artificial Spin-1/2System

Superconducting qubit circuit emulation of a vector spin-1/2

Fast and high-fidelity entangling gate through parametrically modulated longitudinal coupling

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