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Register a new userSingle qubit gates in frequency-crowded transmon systems
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Recent experimental work on superconducting transmon qubits in 3D cavities show that their coherence times are increased by an order of magnitude compared to their 2D 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 leakage transition of qubits are close to computational transitions in other. Here it is shown that fast pulses are possible which address single qubits using two quadrature control of the pulse envelope while the DRAG method 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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We present a few-parameter ansatz for pulses to implement a broad set of simultaneous single-qubit rotations in frequency-crowded multilevel systems. Specifically, we consider a system of two qutrits whose working and leakage transitions suffer from spectral crowding (detuned by $delta$). In order to achieve precise controllability, we make use of two driving fields (each having two quadratures) at two different tones to implement arbitrary simultaneous rotations. Expanding the waveforms in terms of Hanning windows, we show how analytic pulses containing smooth and composite-pulse features can easily achieve gate errors less than $10^{-4}$ and considerably outperform known adiabatic techniques. Moreover, we find a generalization of the WahWah method by Schutjens et al. [Phys. Rev. A 88, 052330 (2013)] that allows precise separate single-qubit rotations for all gate times beyond a quantum speed limit. We find in all cases a quantum speed limit slightly below $2pi/delta$ for the gate time and show that our pulses are robust against variations in system parameters and filtering due to transfer functions, making them suitable for experimental implementations.
Composite pulses are an efficient tool for robust quantum control. In this work, we derive the form of the composite pulse sequence to implement robust single-qubit gates in a three-level system, where two low-energy levels act as a qubit. The composite pulses can efficiently cancel the systematic errors up to a certain order. We find that the three-pulse sequence cannot completely eliminate the first order of systematic errors, but still availably makes the fidelity resistant to variations in a specific direction. When employing more pulses in the sequence ($N>3$), the fidelity can be insensitive to the variations in all directions and the robustness region becomes much wider. Finally we demonstrate the applications of composite pulses in quantum information processing, e.g., robust quantum information transfer between two qubits.
We consider the effects of plane-wave states scattering off finite graphs, as an approach to implementing single-qubit unitary operations within the continuous-time quantum walk framework of universal quantum computation. Four semi-infinite tails are attached at arbitrary points of a given graph, representing the input and output registers of a single qubit. For a range of momentum eigenstates, we enumerate all of the graphs with up to $n=9$ vertices for which the scattering implements a single-qubit gate. As $n$ increases, the number of new unitary operations increases exponentially, and for $n>6$ the majority correspond to rotations about axes distributed roughly uniformly across the Bloch sphere. Rotations by both rational and irrational multiples of $pi$ are found.
We experimentally demonstrate the underlying physical mechanism of the recently proposed protocol for superreplication of quantum phase gates [W. Dur, P. Sekatski, and M. Skotiniotis, Phys. Rev. Lett. 114, 120503 (2015)], which allows to produce up to $N^2$ high-fidelity replicas from N input copies in the limit of large N. Our implementation of 1->2 replication of the single-qubit phase gates is based on linear optics and qubits encoded into states of single photons. We employ the quantum Toffoli gate to imprint information about the structure of an input two-qubit state onto an auxiliary qubit, apply the replicated operation to the auxiliary qubit, and then disentangle the auxiliary qubit from the other qubits by a suitable quantum measurement. We characterize the replication protocol by full quantum process tomography and observe good agreement of the experimental results with theory.
Coherent operations constitutive for the implementation of single and multi-qubit quantum gates with trapped ions are demonstrated that are robust against variations in experimental parameters and intrinsically indeterministic system parameters. In particular, pulses developed using optimal control theory are demonstrated for the first time with trapped ions. Their performance as a function of error parameters is systematically investigated and compared to composite pulses.
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