Simple Pulses for Elimination of Leakage in Weakly Nonlinear Qubits

Motzoi, Felix; Gambetta, Jay; Rebentrost, Patrick; Wilhelm, Frank K.

doi:10.1103/physrevlett.103.110501

Cited by 692 publications

(674 citation statements)

References 28 publications

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“…All single-qubit gates are 40-ns Gaussian-shaped microwave pulses (Gaussian width s ¼ 10 ns) resonant with the transition frequencies of the qubits, with scaled derivative-of-Gaussian shapes applied on the quadrature channel to minimize leakage effects 30 . The gates are all autonomously calibrated with a set of repeated pulse experiments, correcting for: amplitude of X 90 and X gates, amplitude imbalance between X-and Y-rotations, mixer skew and derivative-of-Gaussian-shape parameter.…”

Section: Arrangement)mentioning

confidence: 99%

Implementing a strand of a scalable fault-tolerant quantum computing fabric

et al. 2014

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With favourable error thresholds and requiring only nearest-neighbour interactions on a lattice, the surface code is an error-correcting code that has garnered considerable attention. At the heart of this code is the ability to perform a low-weight parity measurement of local code qubits. Here we demonstrate high-fidelity parity detection of two code qubits via measurement of a third syndrome qubit. With high-fidelity gates, we generate entanglement distributed across three superconducting qubits in a lattice where each code qubit is coupled to two bus resonators. Via high-fidelity measurement of the syndrome qubit, we deterministically entangle the code qubits in either an even or odd parity Bell state, conditioned on the syndrome qubit state. Finally, to fully characterize this parity readout, we develop a measurement tomography protocol. The lattice presented naturally extends to larger networks of qubits, outlining a path towards fault-tolerant quantum computing.

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Section: Arrangement)mentioning

confidence: 99%

Implementing a strand of a scalable fault-tolerant quantum computing fabric

et al. 2014

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“…Optimized superconducting qubits such as 3D transmons are well described by weakly anharmonic oscillators [19,22]. A realistic model of the qubit has to take at least one extra noncomputational level (a leakage level) into account [23][24][25].…”

Section: Systemmentioning

confidence: 99%

“…The DRAG method [19,20,28] strongly reduces leakage to the |2 state with a two-quadrature drive. Here, we show that this method does not provide a sizable improvement over a single Gaussian envelope.…”

Section: Applying Dragmentioning

confidence: 99%

“…Although high-fidelity gates have been demonstrated with single-junction transmons in the 2D architecture [18], spectral crowding will limit the gate fidelity in 3D architectures. In order to mitigate spectral overlap, the derivative removal by adiabatic gate (DRAG) technique has been developed [19,20]. We will apply this technique to the problem at hand and show that on its own it is of limited success.…”

Section: Introductionmentioning

confidence: 99%

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Single-qubit gates in frequency-crowded transmon systems

et al. 2013

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Recent experimental work on superconducting transmon qubits in three-dimensional (3D) cavities shows that their coherence times are increased by an order of magnitude compared to their two-dimensional cavity counterparts. However, to take advantage of these coherence times while scaling up the number of qubits it is advantageous to address individual qubits which are all coupled to the same 3D cavity fields. The challenge in controlling this system comes from spectral crowding, where the leakage transition of qubits is close to computational transitions in other qubits. Here, it is shown that fast pulses are possible which address single qubits using two-quadrature control of the pulse envelope, while the derivative removal by adiabatic gate method of Motzoi et al. [Phys. Rev. Lett. 103, 110501 (2009)] alone only gives marginal improvements over the conventional Gaussian pulse shape. On the other hand, a first-order result using the Magnus expansion gives a fast analytical pulse shape which gives a high-fidelity gate for a specific gate time, up to a phase factor on the second qubit. Further numerical analysis corroborates these results and yields to even faster gates, showing that leakage-state anharmonicity does not provide a fundamental quantum speed limit.

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“…To implement these rotations, the AWG shapes a 100 MHz sinewave with a 6σ long Gaussian envelope having σ = 12 ns and DRAG correction 38,39 . The output of the IQ mixers ( This substantially higher fidelity than the maximum fidelity to the Bell-state we estimate in the main text, leads us to believe that systematic errors in the tomography do not significantly alter the maximum measured fidelity of 77 % to |φ − .…”

Section: Calibration Of Systematic Errors In Tomographymentioning

confidence: 99%

Autonomously stabilized entanglement between two superconducting quantum bits

Shankar¹,

Hatridge²,

Leghtas³

et al. 2013

Nature

338

344

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Quantum error-correction codes would protect an arbitrary state of a multi-qubit register against decoherence-induced errors 1 , but their implementation is an outstanding challenge for the development of large-scale quantum computers. A first step is to stabilize a nonequilibrium state of a simple quantum system such as a qubit or a cavity mode in the presence of decoherence. Several groups have recently accomplished this goal using measurementbased feedback schemes [2][3][4][5] . A next step is to prepare and stabilize a state of a composite system [6][7][8] . Here we demonstrate the stabilization of an entangled Bell state of a quantum register of two superconducting qubits for an arbitrary time. Our result is achieved by an autonomous feedback scheme which combines continuous drives along with a specifically engineered coupling between the two-qubit register and a dissipative reservoir. Similar autonomous feedback techniques have recently been used for qubit reset 9 and the stabilization of a single qubit state 10 , as well as for creating 11 and stabilizing 6 states of multipartite quantum systems. Unlike conventional, measurement-based schemes, an autonomous approach counter-intuitively uses engineered dissipation to fight decoherence [12][13][14][15] , obviating the need 1 arXiv:1307.4349v3 [quant-ph] 23 Oct 2013 for a complicated external feedback loop to correct errors, simplifying implementation. Instead the feedback loop is built into the Hamiltonian such that the steady state of the system in the presence of drives and dissipation is a Bell state, an essential building-block state for quantum information processing. Such autonomous schemes, broadly applicable to a variety of physical systems as demonstrated by a concurrent publication with trapped ion qubits 16 , will be an essential tool for the implementation of quantum-error correction.Here we implement a proposal 17 , tailored to the circuit Quantum Electrodynamics (cQED) architecture 18 , for stabilizing entanglement between two superconducting transmon qubits 19 . The qubits are dispersively coupled to an open cavity which acts as the dissipative reservoir. The cavity in our implementation is furthermore engineered to preferentially decay into a 50 Ω transmission line that we can monitor on demand. We show, using two-qubit quantum state tomography and high-fidelity single-shot readout, that the steady-state of the system reaches the target Bell state with a fidelity of 67 %, well above the 50 % threshold that witnesses entanglement. As discussed in Ref. 17, the fidelity can be further improved by monitoring the cavity output and performing conditional tomography when the output indicates that the two qubits are in the Bell state. We implemented this protocol via post-selection and demonstrated that the fidelity increased to ∼ 77 %.Our cQED setup, outlined schematically in Fig. 1a, consists of two individually addressable qubits, Alice and Bob, coupled dispersively to a three-dimensional (3D) rectangular copper cavity.The setup is described by...

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Simple Pulses for Elimination of Leakage in Weakly Nonlinear Qubits

Cited by 692 publications

References 28 publications

Implementing a strand of a scalable fault-tolerant quantum computing fabric

Implementing a strand of a scalable fault-tolerant quantum computing fabric

Single-qubit gates in frequency-crowded transmon systems

Autonomously stabilized entanglement between two superconducting quantum bits

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