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Register a new userRobust single-qubit gates by composite pulses in three-level systems
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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.
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We present a new method of constructing a fully robust qubit in a three-level system. By the application of continuous driving fields, robustness to both external and controller noise is achieved. Specifically, magnetic noise and power fluctuations do not operate within the robust qubit subspace. Whereas all the continuous driving based constructions of such a fully robust qubit considered so far have required at least four levels, we show that in fact only three levels are necessary. This paves the way for simple constructions of a fully robust qubit in many atomic and solid state systems that are controlled by either microwave or optical fields. We focus on the NV-center in diamond and analyze the implementation of the scheme, by utilizing the electronic spin sub-levels of its ground state. In current state-of-the-art experimental setups the scheme leads to improvement of more than two orders of magnitude in coherence time, pushing it towards the lifetime limit. We show how the fully robust qubit can be used to implement quantum sensing, and in particular, the sensing of high frequency signals.
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.
It has been known since the early days of quantum mechanics that hyperbolic secant pulses possess the unique property that they can perform cyclic evolution on two-level quantum systems independently of the pulse detuning. More recently, it was realized that they induce detuning- controlled phases without changing state populations. Here, we experimentally demonstrate the properties of hyperbolic secant pulses on superconducting transmon qubits and contrast them with the more commonly used Gaussian and square waves. We further show that these properties can be exploited to implement phase gates, nominally without exiting the computational subspace. This enables us to demonstrate the first microwave-driven Z-gates with a single control parameter, the detuning.
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.
Realizing an arbitrary single-qubit gate is a precursor for many quantum computational tasks, including the conventional approach to universal quantum computing. For superconducting qubits, single-qubit gates are usually realized by microwave pulses along drive or flux lines. These pulses are calibrated to realize a particular single-qubit gate. However, it is clearly impractical to calibrate a pulse for every possible single-qubit gate in $SU(2)$. On the other hand, compiling arbitrary gates using a finite universal gate set will lead to unacceptably low fidelities. Here, we provide a compilation scheme for arbitrary single-qubit gates for which the three real parameters of the gate directly correspond to the phase shifts of microwave pulses, which can be made extremely accurate experimentally, that is also compatible with any two-qubit gate. Furthermore, we only require the calibration of the $X_pi$ and $X_{frac pi 2}$ pulses, gates that are already necessary for tasks such as Clifford-based randomized benchmarking as well as measuring the $T_1$ and $T_2$ decoherence parameters.
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