In order to achieve the high-fidelity quantum control needed for a broad range of quantum information technologies, reducing the effects of noise and system inhomogeneities is an essential task. It is well known that a system can be decoupled from noise or made insensitive to inhomogeneous dephasing dynamically by using carefully designed pulse sequences based on square or delta-function waveforms such as Hahn spin echo or CPMG. However, such ideal pulses are often challenging to implement experimentally with high fidelity. Here, we uncover a new geometrical framework for visualizing all possible driving fields, which enables one to generate an unlimited number of smooth, experimentally feasible pulses that perform dynamical decoupling or dynamically corrected gates to arbitrarily high order. We demonstrate that this scheme can significantly enhance the fidelity of singlequbit operations in the presence of noise and when realistic limitations on pulse rise times and amplitudes are taken into account.In recent years, the prospect of enhanced technologies that exploit the principles of quantum mechanics has attracted great interest from many fields in physics and beyond. These efforts are geared toward several envisioned applications, including information processing [1-6], secure communications [7,8], and sensing [9][10][11], and enormous progress has been made in engineering and optimizing coherent quantum systems for these purposes. However, decoherence caused by the environment or other factors remains a primary impediment to realizing quantum technologies [12][13][14][15]; overcoming this challenge requires improvements not only in system engineering [16][17][18], but also in how such systems are controlled.It has been known since the early days of nuclear magnetic resonance that it is possible to design driving fields that suppress adverse effects caused by fluctuations in the system Hamiltonian or in the driving field itself. The simplest example is the Hahn spin echo [19], in which a fast (δ-function) π-pulse is applied halfway through the evolution of a precessing spin, guaranteeing that the spin returns to its initial state at the end of the evolution regardless of the precession rate. This has long been a standard technique to combat inhomogeneous dephasing -the loss of coherence due to variations in precession frequency in spin ensembles. Spin echo and related multipulse sequences [20][21][22][23][24][25][26][27] have also been widely employed to mitigate other types of decoherence such as environmental noise fluctuations [28][29][30]. Much work has been done to extend dynamical decoupling to not only preserve the state of the system, but to also cancel errors while performing operations on the system (dynamical gate correction) [31][32][33][34][35][36][37][38][39][40][41][42][43].Although these dynamical decoupling methods have been broadly successful, there are many systems, especially in the context of quantum information technologies, where they exhibit substantial drawbacks. This is because the hig...

Implementing high-fidelity two-qubit gates in single-electron spin qubits in silicon double quantum dots is still a major challenge. In this work, we employ analytical methods to design control pulses that generate high-fidelity entangling gates for quantum computers based on this platform. Using realistic parameters and initially assuming a noise-free environment, we present simple control pulses that generate cnot, cphase, and cz gates with average fidelities greater than 99.99% and gate times as short as 45ns. Moreover, using the local invariants of the system's evolution operator, we show that a simple square pulse generates a cnot gate in less than 27 ns and with a fidelity greater than 99.99%. Last, we use the same analytical methods to generate two-qubit gates locally equivalent to √ cnot and √ cz that are used to implement simple two-piece pulse sequences that produce high-fidelity cnot and cz gates in the presence of low-frequency noise.

Superconducting transmon qubits comprise one of the most promising platforms for quantum information processing due to their long coherence times and to their scalability into larger qubit networks. However, their weakly anharmonic spectrum leads to spectral crowding in multiqubit systems, making it challenging to implement fast, high-fidelity gates while avoiding leakage errors. To address this challenge, we use a protocol known as SWIPHT [Phys. Rev. B 91, 161405(R) (2015)], which yields smooth, simple microwave pulses designed to suppress leakage without sacrificing gate speed through spectral selectivity. Here, we determine the parameter regimes in which SWIPHT is effective and demonstrate that in these regimes it systematically produces two-qubit gate fidelities for cavity-coupled transmons in the range 99.6%-99.9% with gate times as fast as 23 ns. Our results are obtained from full numerical simulations that include current experimental levels of relaxation and dephasing. These high fidelities persist over a wide range of system parameters that encompass many current experimental setups and are insensitive to small parameter variations and pulse imperfections.

We study a superconducting circuit that can act as a toolbox to generate various Bogoliubov-linear and nonlinear quantum operations on the microwave photon modes of superconducting resonators within one single circuit. The quantum operations are generated by exploring dispersive four-wave mixing (FWM) processes involving the resonator modes. Different FWM geometries can be realized by adjusting the circuit parameters and by applying appropriate microwave drivings. We illustrate this scheme using a circuit made of two superconducting qubits that couple with each other. Each qubit couples with one superconducting resonator. We also discuss main quantum errors in this scheme and study the fidelity of the quantum operations by numerical simulation. Our scheme provides a practical approach to realize quantum information protocols on superconducting resonators.Comment: 9 pages, 6 figures, accepted version, new simulation and reference adde

Via explicit examples we show that the pre-existing entanglement can really enhance ͑not only behave as an assistance for͒ the efficiency of the quantum error-correcting codes ͑QECCs͒ in a single block of encoding or decoding as well as help in beating the quantum Hamming bound. A systematic approach to constructing entanglement-assisted ͑or enhanced͒ quantum error-correcting codes ͑EAQECCs͒ via graph states is also presented, and an infinite family of entanglement-enhanced codes has been constructed. Furthermore we generalize the EAQECCs to the case of not-so-perfectly protected qubit and introduce the quantity infidelity as a figure of merit and show that the EAQECCs also outperform the ordinary QECCs.