Accurate control of Josephson phase qubits

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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“…(9) of the gate with the control sequence from Eq. (24). It is by these phases that the qubits or the subsequent gates need to be corrected.…”

Section: B Phase Correctionmentioning

confidence: 99%

“…A realistic model of the qubit has to take at least one extra noncomputational level (a leakage level) into account [23][24][25]. This is reflected in the following Hamiltonian for two superconducting transmon qubits in a common 3D cavity: …”

Section: Systemmentioning

confidence: 99%

Single-qubit gates in frequency-crowded transmon systems

et al. 2013

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“…A natural solution to this constraint is using smooth waveforms, which also seems to be a good strategy in terms of controlling many qubits, achieving low crosstalk, and simplifying the requirements of control electronics and their system calibration. We thus rule out pulse and refocussing type protocols common in nuclear magnetic resonance (NMR) [15,16], but welcome any theory making this a practical solution.…”

Section: Introductionmentioning

confidence: 99%

Fast adiabatic qubit gates using onlyσzcontrol

2014

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A controlled-phase gate was demonstrated in superconducting Xmon transmon qubits with fidelity reaching 99.4%, relying on the adiabatic interaction between the |11 and |02 states. Here we explain the theoretical concepts behind this protocol that achieves fast gate times with only σz control of the Hamiltonian, based on a theory of non-linear mapping of state errors to a power spectral density and use of optimal window functions. With a solution given in the Fourier basis, optimization is shown to be straightforward for practical cases of an arbitrary state change and finite bandwidth of control signals. We find that errors below 10 −4 are readily achievable for realistic control waveforms.

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“…A device that behaves similarly to the optical lattice in the context of superconducting qubits [35,36] is the charge qubit [37][38][39][40]. The effective Hamiltonian of this system takes the form…”

Section: Relation To the Charge Qubitmentioning

confidence: 99%

“…The controls we have at our disposal are collective controls of the lattice. The challenge is to control an ensemble of particles in parallel even though they each undergo a different quantum evolution, which mathematically is identical to the problem of robust control [13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

High-fidelity quantum gates in the presence of dispersion

et al. 2012

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We numerically demonstrate the control of motional degrees of freedom of an ensemble of neutral atoms in an optical lattice with a shallow trapping potential. Taking into account the range of quasimomenta across different Brillouin zones results in an ensemble whose members effectively have inhomogeneous control fields as well as spectrally distinct control Hamiltonians. We present an ensemble-averaged optimal control technique that yields high fidelity control pulses, irrespective of quasimomentum, with average fidelities above 98%. The resulting controls show a broadband spectrum with gate times in the order of several free oscillations to optimize gates with up to 13.2% dispersion in the energies from the band structure. This can be seen as a model system for the prospects of robust quantum control. This result explores the limits of discretizing a continuous ensemble for control theory.

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Accurate control of Josephson phase qubits

Cited by 122 publications

References 20 publications

Single-qubit gates in frequency-crowded transmon systems

Single-qubit gates in frequency-crowded transmon systems

Fast adiabatic qubit gates using onlyσzcontrol

High-fidelity quantum gates in the presence of dispersion

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