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Low-frequency time-dependent noise is one of the main obstacles on the road towards a fully scalable quantum computer. The majority of solid-state qubit platforms, from superconducting circuits to spins in semiconductors, are greatly affected by $1/f$ noise. Among the different control techniques used to counteract noise effects on the system, dynamical decoupling sequences are one of the most effective. However, most dynamical decoupling sequences require unbounded and instantaneous pulses, which are unphysical and can only implement identity operations. Among methods that do restrict to bounded control fields, there remains a need for protocols that implement arbitrary gates with lab-ready control fields. In this work, we introduce a protocol to design bounded and continuous control fields that implement arbitrary single-axis rotations while shielding the system from low-frequency time-dependent noise perpendicular to the control axis. We show the versatility of our method by presenting a set of non-negative-only control pulses that are immediately applicable to quantum systems with constrained control, such as singlet-triplet spin qubits. Finally, we demonstrate the robustness of our control pulses against classical $1/f$ noise and noise modeled with a random quantum bath, showing that our pulses can even outperform ideal dynamical decoupling sequences., Comment: 11 pages, 4 figures

The Arecibo Observatory (AO) is a multidisciplinary research and education facility that is recognized worldwide as a leading facility in astronomy, planetary, and atmospheric and space sciences. AO's cornerstone research instrument was the 305-m William E. Gordon telescope. On December 1, 2020, the 305-m telescope collapsed and was irreparably damaged. In the three weeks following the collapse, AO's scientific and engineering staff and the AO users community initiated extensive discussions on the future of the observatory. The community is in overwhelming agreement that there is a need to build an enhanced, next-generation radar-radio telescope at the AO site. From these discussions, we established the set of science requirements the new facility should enable. These requirements can be summarized briefly as: 5 MW of continuous wave transmitter power at 2 - 6 GHz, 10 MW of peak transmitter power at 430 MHz (also at 220MHz under consideration), zenith angle coverage 0 to 48 deg, frequency coverage 0.2 to 30 GHz and increased Field-of-View. These requirements determine the unique specifications of the proposed new instrument. The telescope design concept we suggest consists of a compact array of fixed dishes on a tiltable, plate-like structure with a collecting area equivalent to a 300m dish. This concept, referred to as the Next Generation Arecibo Telescope (NGAT), meets all of the desired specifications and provides significant new science capabilities to all three research groups at AO. This whitepaper presents a sample of the wide variety of the science that can be achieved with the NGAT, the details of the telescope design concept and the need for the new telescope to be located at the AO site. We also discuss other AO science activities that interlock with the NGAT in the white paper., Comment: 82 pages (executive summary 10 pages), 21 figures, Arecibo observatory white paper (Updated with the complete author list and minor edits)

The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves combinatorial optimization problems. While there is evidence suggesting that the fixed form of the standard QAOA ansatz is not optimal, there is no systematic approach for finding better ans\"atze. We address this problem by developing an iterative version of QAOA that is problem-tailored, and which can also be adapted to specific hardware constraints. We simulate the algorithm on a class of Max-Cut graph problems and show that it converges much faster than the standard QAOA, while simultaneously reducing the required number of CNOT gates and optimization parameters. We provide evidence that this speedup is connected to the concept of shortcuts to adiabaticity., Comment: 11 pages, 7 figures; v3: additional analysis, analytical results, and simulations of larger systems

Color centers in solids, such as the nitrogen-vacancy center in diamond, offer well-protected and well-controlled localized electron spins that can be employed in various quantum technologies. Moreover, the long coherence time of the surrounding spinful nuclei can enable a robust quantum register controlled through the color center. We design pulse sequence protocols that drive the electron spin to generate robust entangling gates with these nuclear memory qubits. We find that compared to using Carr-Purcell-Meiboom-Gill (CPMG) alone, Uhrig decoupling sequence and hybrid protocols composed of CPMG and Uhrig sequences improve these entangling gates in terms of fidelity, spin control range, and spin selectivity. We provide analytical expressions for the sequence protocols and also show numerically the efficacy of our method on nitrogen-vacancy centers in diamond. Our results are broadly applicable to color centers weakly coupled to a small number of nuclear spin qubits., Comment: 22 pages, 15 figures

A high degree of controllability and long coherence time make the nuclear spin of a phosphorus donor in isotopically purified silicon a promising candidate for a quantum bit. However, long-distance two-qubit coupling and fast, robust gates remain outstanding challenges for these systems. Here, following recent proposals for long-distance coupling via dipole-dipole interactions, we present a simple method to implement fast, high-fidelity arbitrary single- and two-qubit gates in the absence of charge noise. Moreover, we provide a method to make the single-qubit gates robust to moderate levels of charge noise to well within an error bound of $10^{-3}$., Comment: 13 pages, 10 figures

Superconducting transmon qubits are of great interest for quantum computing and quantum simulation. A key component of quantum chemistry simulation algorithms is breaking up the evolution into small steps, which naturally leads to the need for non-maximally entangling, arbitrary CPHASE gates. Here we design such microwave-based gates using an analytically solvable approach leading to smooth, simple pulses. We use the local invariants of the evolution operator in $SU(4)$ to develop a method of constructing pulse protocols, which allows for the continuous tuning of the phase. We find CPHASE fidelities of more than $0.999$ and gate times as low as $100\text{ ns}$.

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 45 ns. 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 $\sqrt{\mathrm{CNOT}}$ and $\sqrt{\mathrm{CZ}}$ 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., Comment: 11 pages, 7 figures. Published version

It has been experimentally shown that negative exchange interactions can arise in a linear three-dot system when a two-electron double quantum dot is exchange coupled to a larger quantum dot containing on the order of one hundred electrons. The origin of this negative exchange can be traced to the larger quantum dot exhibiting a spin triplet-like rather than singlet-like ground state. Here, we show using a microscopic model based on the configuration interaction (CI) method that both triplet-like and singlet-like ground states are realized depending on the number of electrons. In the case of only four electrons, a full CI calculation reveals that triplet-like ground states occur for sufficiently large dots. These results hold for symmetric and asymmetric quantum dots in both Si and GaAs, showing that negative exchange interactions are robust in few-electron double quantum dots and do not require large numbers of electrons., Comment: 8 pages, 3 figures

Singlet-triplet qubits in lateral quantum dots in semiconductor heterostructures exhibit high-fidelity single-qubit gates via exchange interactions and magnetic field gradients. High-fidelity two-qubit entangling gates are challenging to generate since weak interqubit interactions result in slow gates that accumulate error in the presence of noise. However, the interqubit electrostatic interaction also produces a shift in the local double well detunings, effectively changing the dependence of exchange on the gate voltages. We consider an operating point where the effective exchange is first order insensitive to charge fluctuations while maintaining nonzero interactions. This "sweet spot" exists only in the presence of interactions. We show that working at the interacting sweet spot can directly produce maximally entangling gates and we simulate the gate evolution under realistic 1/f noise. We report theoretical two-qubit gate fidelities above 99% in GaAs and Si systems., Comment: 6 pages, 4 figures

We present an approximate analytical solution to the dynamic equation of two Ising-coupled qubits with oscillating classical control fields that are nonperpendicular to the static drift fields. This is a situation that has recently arisen in some solid-state experiments. With our solution we derive the analytical expressions for the local invariants as well as the local rotations needed to isolate a purely nonlocal gate. This determines the set of parameters that are required to generate any entangling gate. Moreover, we use our results to describe a recent experimental work on capacitively coupled singlet-triplet qubits in GaAs and discuss possible differences for a similar device in silicon., Comment: 6 pages, 3 figures

Using the experimental value for the rate $R^{LEP} _{exp}=\Gamma_{inv}/\Gamma_{l\bar l}=5.942\pm 0.016$, we derive constraints on the number of light neutrino species with the invisible width method in the framework of a left-right symmetric model (LRSM) and a $E_6$ superstring model as a function of their respective mixing angles for the neutral vector gauge bosons. Using the above LEP result we get the constraints $-1.6\times 10^{-3}\leq\phi \leq 1.1\times 10^{-3}$ and $-1.3\times 10^{-2}\leq\phi_{E_6} \leq 0.4\times 10^{-2}$, which are stronger than those obtained in previous studies of these models., Comment: 9 pages, 4 figures, Submit to Modern Physics Letter A

Using the experimental values for the rates $R^{LEP} _{exp}=\Gamma_{inv}/\Gamma_{l\bar l}=5.942\pm 0.016$, $R^{Giga-Z_1}=\Gamma_{inv}/\Gamma_{l\bar l}=5.942\pm 0.012$ (most conservative) and $R^{Giga-Z_1}=\Gamma_{inv}/\Gamma_{l\bar l}=5.942\pm 0.006$ (most optimistic) we derive constraints on the number of neutrinos light species $(N_\nu)_{LRSM}$ with the invisible width method in the framework of a left-right symmetric model (LRSM) as a function of the LR mixing angle $\phi$. Using the LEP result for $N_\nu$ we may place a bound on this angle, $-1.6\times 10^{-3}\leq\phi \leq 1.1\times 10^{-3}$, which is stronger than those obtained in previous studies of the LRSM., Comment: 8 pages, 3 figures