Analytical modeling of parametrically modulated transmon qubits

Didier, Nicolas; Sete, Eyob A.; Silva, Marcus; Rigetti, Chad

doi:10.1103/physreva.97.022330

Cited by 80 publications

(98 citation statements)

References 41 publications

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“…Moreover, the quest for useful quantum computations before full quantum error correction becomes available may be assisted by efficient, short-depth gate sequences based on two-or multi-qubit gates [14,15] with versatile types of interactions. In particular, parametric schemes based on tunable couplers have been proposed and recently realized as a means to achieve fast gates with high fidelities [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”

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confidence: 99%

Analysis of a parametrically driven exchange-type gate and a two-photon excitation gate between superconducting qubits

et al. 2017

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A current bottleneck for quantum computation is the realization of high-fidelity two-qubit quantum operations between two and more quantum bits in arrays of coupled qubits. Gates based on parametrically driven tunable couplers offer a convenient method to entangle multiple qubits by selectively activating different interaction terms in the effective Hamiltonian. Here, we study theoretically and experimentally a superconducting qubit setup with two transmon qubits connected via a capacitively coupled tunable bus. We develop a time-dependent Schrieffer-Wolff transformation and derive analytic expressions for exchange-interaction gates swapping excitations between the qubits (iSWAP) and for two-photon gates creating and annihilating simultaneous two-qubit excitations (bSWAP). We find that the bSWAP gate is generally slower than the more commonly used iSWAP gate, but features favorable scalability properties with less severe frequency crowding effects, which typically degrade the fidelity in multi-qubit setups. Our theoretical results are backed by experimental measurements as well as exact numerical simulations including the effects of higher transmon levels and dissipation.Quantum computation is based on accurate and precise control of quantum bits and their interactions to create multi-qubit superpositions and entanglement. With superconducting circuits, single qubit quantum gates can be carried out with fidelities approaching 99.99% [1-4], while errors in two-qubit operations are typically higher with record fidelities around 99% [3,5]. However, the realization of qubit operations with even higher fidelity is required both for reaching the error threshold for quantum computation [6-9] and for carrying out reliable quantum simulations and optimizations in large arrays of coupled qubits [10][11][12][13]. Moreover, the quest for useful quantum computations before full quantum error correction becomes available may be assisted by efficient, short-depth gate sequences based on two-or multi-qubit gates [14,15] with versatile types of interactions. In particular, parametric schemes based on tunable couplers have been proposed and recently realized as a means to achieve fast gates with high fidelities [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].In this context, effective interactions were engineered in Ref.[26] between two transmon qubits mediated by a third, ancilla transmon device (bus), which couples dispersively to both qubits and whose frequency is modulated by an external magnetic flux. Such a flux-modulation scheme provides frequency-selectivity and allows to use fixed-frequency computational qubits, thereby minimizing the sensitvity of the device with respect to magnetic flux noise and disorder effects. For example, modulating at the (fixed) difference frequency of the qubits brings these qubits effectively into resonance in a co-rotating frame such that a single excitation can be swapped efficiently (iSWAP). The effective Hamiltonian in this case is H iSWAP ∝ XX + YY. With this method gate ...

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confidence: 99%

Analysis of a parametrically driven exchange-type gate and a two-photon excitation gate between superconducting qubits

et al. 2017

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“…The two-qubit gates available in the transmonlike superconducting qubit architecture can roughly be split into two broad families as outlined previously: one group requiring local magnetic fields to tune the transition frequency of qubits and one group consisting of all-microwave control. There exist several hybrid schemes that combine various aspects of these two categories and, in particular, the notions of tunable coupling and parametric driving are proving to be important ingredients in modern superconducting qubit processors 63,67,89,103,106,[207][208][209][210][211][212][213] . In this section, however, we start by introducing the iSWAP gate, and then review the CPHASE (controlled-phase) in Section IV F and the CR (cross-resonance) in Section IV G. We briefly review a few other two-qubit gates and discuss their merits in Sections IV G 4 and IV H.…”

Section: E the Iswap Two-qubit Gate In Tunable Qubitsmentioning

confidence: 99%

“…A hybrid approach, in which a combination of tunable and fixed-frequency qubits is used, was recently demonstrated for both iSWAP and CPHASE gates 67,105,211 . This scheme has no added tunable qubits (or resonators) acting as the coupling element, but rather, relies solely on an always-on capacitive coupling between the qubits, and the effective coupling is roughly half that of the always-on coupling.…”

Section: H Gate Implementations With Tunable Couplingmentioning

confidence: 99%

A quantum engineer's guide to superconducting qubits

Krantz

Kjærgaard

Yan

et al. 2019

Applied Physics Reviews

1,454

962

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The aim of this review is to provide quantum engineers with an introductory guide to the central concepts and challenges in the rapidly accelerating field of superconducting quantum circuits. Over the past twenty years, the field has matured from a predominantly basic research endeavor to one that increasingly explores the engineering of larger-scale superconducting quantum systems. Here, we review several foundational elements -qubit design, noise properties, qubit control, and readout techniques -developed during this period, bridging fundamental concepts in circuit quantum electrodynamics (cQED) and contemporary, stateof-the-art applications in gate-model quantum computation.

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“…Our chosen entangling gate is a parametrically activated controlled-Z (CZ) gate, which has the unitary representation U = diag(1, 1, 1, −1). This gate is native to our architecture, as shown by the first harmonic terms of the Hamiltonian of a capacitively coupled fixed and tunable transmon under flux modulation in the interaction picture [27] H int = g 20 e i(2ωp−[∆+η F ])t e iβ20 |11 20| (4)…”

Section: Cross Tomographymentioning

confidence: 99%

“…In order to operate high-fidelity gates simultaneously, we would like to know whether there are certain operating points that are more resilient to crosstalk. In previous work, the concept of an "AC sweet spot" for parametrically activated entangling gates has been discussed [27]. This AC sweet spot is located at the point of maximal detuning of the tunable qubit from its parking frequency.…”

Section: Cross Tomographymentioning

confidence: 99%

Methods for Measuring Magnetic Flux Crosstalk between Tunable Transmons

et al. 2019

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In the gate model of quantum computing, a program is typically decomposed into a sequence of 1and 2-qubit gates that are realized as control pulses acting on the system. A key requirement for a scalable control system is that the qubits are addressable -that control pulses act only on the targeted qubits. The presence of control crosstalk makes this addressability requirement difficult to meet. In order to provide metrics that can drive requirements for decreasing crosstalk, we present three measurements that directly quantify the DC and AC flux crosstalk present between tunable transmons, with sensitivities as fine as 0.001%. We develop the theory to connect AC flux crosstalk measures to the infidelity of a parametrically activated two-qubit gate. We employ quantum process tomography in the presence of crosstalk to provide an empirical study of the effects of crosstalk on two-qubit gate fidelity.

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Analytical modeling of parametrically modulated transmon qubits

Cited by 80 publications

References 41 publications

Analysis of a parametrically driven exchange-type gate and a two-photon excitation gate between superconducting qubits

Analysis of a parametrically driven exchange-type gate and a two-photon excitation gate between superconducting qubits

A quantum engineer's guide to superconducting qubits

Methods for Measuring Magnetic Flux Crosstalk between Tunable Transmons

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