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We study the generation of two-qudit entangling quantum logic gates using two techniques in quantum optimal control. We take advantage of both continuous, Lie-algebraic control and digital, Lie-group control. In both cases, the key is access to a time-dependent Hamiltonian which can generate an arbitrary unitary matrix in the group SU($d^2$). We find efficient protocols for creating high-fidelity entangling gates. As a test of our theory, we study the case of qudits robustly encoded in nuclear spins of alkaline earth atoms and manipulated with magnetic and optical fields, with entangling interactions arising from the well-known Rydberg blockade. We applied this in a case study based on a $d=10$ dimensional qudit encoded in the $I=9/2$ nuclear spin in $^{87}$Sr, controlled through a combination of nuclear spin-resonance, a tensor AC-Stark shift, and Rydberg dressing, which allows us to generate an arbitrary symmetric entangling two-qudit gate such as CPhase. Our techniques can be used to implement qudit entangling gates for any $2\le d \le10$ encoded in the nuclear spin. We also studied how decoherence due to the finite lifetime of the Rydberg states affects the creation of the CPhase gate and found, through numerical optimization, a fidelity of $0.9985$, $0.9980$, $0.9942$, and $0.9800$ for $d=2$, $d=3$, $d=5$, and $d=7$ respectively. This provides a powerful platform to explore the various applications of quantum information processing of qudits including metrological enhancement with qudits, quantum simulation, universal quantum computation, and quantum error correction., Comment: Included more details and figures

We show that the lowest quantum Cramér-Rao bound achievable in interferometry with a one-axis twisted spin coherent state is saturated by the asymptotic method of moments error of a protocol that uses one call to the one-axis twisting, one call to time-reversed one-axis twisting, and a final total spin measurement (i.e., a twist-untwist protocol). The result is derived by first showing that the metrological phase diagram for one-axis twisting is asymptotically characterized by a single QFI value $N(N+1)/2$ for all times, then constructing a twist-untwist protocol having a method of moments error that saturates this value. The case of finite-range one-axis twisting is similarly analyzed, and a simple functional form for the metrological phase diagram is found in both the short-range and long-range interaction regimes. Numerical evidence suggests that the finite-range analogues of twist-untwist protocols can exhibit a method of moments error that asymptotically saturates the lowest quantum Cramér-Rao bound achievable in interferometry with finite-range one-axis twisted spin coherent states for all interaction times., 17 pages, 4 figures

Plagiarism in introductory programming courses is an enormous challenge for both students and institutions. For students, relying on the work of others too early in their academic development can make it impossible to acquire necessary skills for independent success in the future. For institutions, widespread student cheating can dilute the quality of the educational experience being offered. Currently available solutions consider only pairwise comparisons between student submissions and focus on punitive deterrence. Our approach instead relies on a class-wide statistical characterization that can be clearly and securely shared with students via an intuitive new p-value representing independence of student effort. A pairwise, compression-based similarity detection algorithm captures relationships between assignments more accurately. An automated deterrence system is used to warn students that their behavior is being closely monitored. High-confidence instances are made directly available for instructor review using our open-source toolkit. An unbiased scoring system aids students and the instructor in understanding true independence of effort. Preliminary results indicate that the system can provide meaningful measurements of independence from week one, improving the efficacy of technical education.

Twist-untwist protocols for quantum metrology consist of a serial application of: 1. unitary nonlinear dynamics (e.g., spin squeezing or Kerr nonlinearity), 2. parameterized dynamics $U(\phi)$ (e.g., a collective rotation or phase space displacement), 3. time reversed application of step 1. Such protocols are known to produce states that allow Heisenberg scaling for experimentally accessible estimators of $\phi$ even when the nonlinearities are applied for times much shorter than required to produce Schr\"{o}dinger cat states. In this work, we prove that twist-untwist protocols provide the lowest estimation error among quantum metrology protocols that utilize two calls to a weakly nonlinear evolution and a readout involving only measurement of a spin operator $\vec{n}\cdot \vec{J}$, asymptotically in the number of particles. We consider the following physical settings: all-to-all interactions generated by one-axis twisting $J_{z}^{2}$ (e.g., interacting Bose gases), constant finite range spin-spin interactions of distinguishable or bosonic atoms (e.g., trapped ions or Rydberg atoms, or lattice bosons). In these settings, we further show that the optimal twist-untwist protocols asymptotically achieve $85\%$ and $92\%$ of the respective quantum Cram\'{e}r-Rao bounds. We show that the error of a twist-untwist protocol can be decreased by a factor of $L$ without an increase in the noise of the spin measurement if the twist-untwist protocol can be noiselessly iterated as an $L$ layer quantum alternating operator ansatz., Comment: 8 pages, 2 figures

Neutral atoms are building blocks of ground-up quantum many-body systems. Well-controlled and high-fidelity entangling gates are an essential component for realizing complex neutral atom architectures for quantum computing, quantum simulation, and measurement with precision better than the standard quantum limit. In this Letter we report the realization of a M��lmer-S��rensen unitary between two neutral atoms, based on adiabatic single-photon dressing to Rydberg levels. We show that this technique is highly robust to noise sources and experimental imperfections that have limited the fidelity of other approaches to neutral atom gates., 7 pages, 4 figures

The Rydberg blockade mechanism is now routinely considered for entangling qubits encoded in clock states of neutral atoms. Challenges towards implementing entangling gates with high fidelity include errors due to thermal motion of atoms, laser amplitude inhomogeneities, and imperfect Rydberg blockade. We show that adiabatic rapid passage by Rydberg dressing provides a mechanism for implementing two-qubit entangling gates by accumulating phases that are robust to these imperfections. We find that the typical error in implementing a two-qubit gate, such as the controlled phase gate, is dominated by errors in the single atom light shift, and that this can be easily corrected using adiabatic dressing interleaved with a simple spin echo sequence. This results in a two-qubit M��lmer-S��renson gate. A gate fidelity $\sim 0.995$ is achieveable with modest experimental parameters and a path to higher fidelities is possible for Rydberg states in atoms with a stronger blockade, longer lifetimes, and larger Rabi frequencies.

Supplemental material, Supplementary_Table_2 for Pilot study of bevacizumab in combination with docetaxel and cyclophosphamide as adjuvant treatment for patients with early stage HER-2 negative breast cancer, including analysis of candidate circulating markers of cardiac toxicity: ICORG 08–10 trial by Giuseppe Gullo, Alex J. Eustace, Alexandra Canonici, Denis M. Collins, Michael J. Kennedy, Liam Grogan, Oscar Breathhnach, John McCaffrey, Maccon Keane, Michael J. Martin, Rajnish Gupta, Gregory Leonard, Miriam O’Connor, Paula M. Calvert, Paul Donnellan, Janice Walshe, Enda McDermott, Kathleen Scott, Andres Hernando, Imelda Parker, David W. Murray, Alice C. O’Farrell, Ashwini Maratha, Patrick Dicker, Mairin Rafferty, Verena Murphy, Norma O’Donovan, William M. Gallagher, Bonnie Ky, Dimitrios Tryfonopoulos, Brian Moulton, Annette T. Byrne and John Crown in Therapeutic Advances in Medical Oncology

Supplemental material, Supplementary_Table_1 for Pilot study of bevacizumab in combination with docetaxel and cyclophosphamide as adjuvant treatment for patients with early stage HER-2 negative breast cancer, including analysis of candidate circulating markers of cardiac toxicity: ICORG 08–10 trial by Giuseppe Gullo, Alex J. Eustace, Alexandra Canonici, Denis M. Collins, Michael J. Kennedy, Liam Grogan, Oscar Breathhnach, John McCaffrey, Maccon Keane, Michael J. Martin, Rajnish Gupta, Gregory Leonard, Miriam O’Connor, Paula M. Calvert, Paul Donnellan, Janice Walshe, Enda McDermott, Kathleen Scott, Andres Hernando, Imelda Parker, David W. Murray, Alice C. O’Farrell, Ashwini Maratha, Patrick Dicker, Mairin Rafferty, Verena Murphy, Norma O’Donovan, William M. Gallagher, Bonnie Ky, Dimitrios Tryfonopoulos, Brian Moulton, Annette T. Byrne and John Crown in Therapeutic Advances in Medical Oncology

Supplemental material, Supplementary_Table_3 for Pilot study of bevacizumab in combination with docetaxel and cyclophosphamide as adjuvant treatment for patients with early stage HER-2 negative breast cancer, including analysis of candidate circulating markers of cardiac toxicity: ICORG 08–10 trial by Giuseppe Gullo, Alex J. Eustace, Alexandra Canonici, Denis M. Collins, Michael J. Kennedy, Liam Grogan, Oscar Breathhnach, John McCaffrey, Maccon Keane, Michael J. Martin, Rajnish Gupta, Gregory Leonard, Miriam O’Connor, Paula M. Calvert, Paul Donnellan, Janice Walshe, Enda McDermott, Kathleen Scott, Andres Hernando, Imelda Parker, David W. Murray, Alice C. O’Farrell, Ashwini Maratha, Patrick Dicker, Mairin Rafferty, Verena Murphy, Norma O’Donovan, William M. Gallagher, Bonnie Ky, Dimitrios Tryfonopoulos, Brian Moulton, Annette T. Byrne and John Crown in Therapeutic Advances in Medical Oncology

Supplemental material, Supplementary_Table_3 for Pilot study of bevacizumab in combination with docetaxel and cyclophosphamide as adjuvant treatment for patients with early stage HER-2 negative breast cancer, including analysis of candidate circulating markers of cardiac toxicity: ICORG 08–10 trial by Giuseppe Gullo, Alex J. Eustace, Alexandra Canonici, Denis M. Collins, Michael J. Kennedy, Liam Grogan, Oscar Breathhnach, John McCaffrey, Maccon Keane, Michael J. Martin, Rajnish Gupta, Gregory Leonard, Miriam O’Connor, Paula M. Calvert, Paul Donnellan, Janice Walshe, Enda McDermott, Kathleen Scott, Andres Hernando, Imelda Parker, David W. Murray, Alice C. O’Farrell, Ashwini Maratha, Patrick Dicker, Mairin Rafferty, Verena Murphy, Norma O’Donovan, William M. Gallagher, Bonnie Ky, Dimitrios Tryfonopoulos, Brian Moulton, Annette T. Byrne and John Crown in Therapeutic Advances in Medical Oncology

Supplemental material, Supplementary_Table_1 for Pilot study of bevacizumab in combination with docetaxel and cyclophosphamide as adjuvant treatment for patients with early stage HER-2 negative breast cancer, including analysis of candidate circulating markers of cardiac toxicity: ICORG 08–10 trial by Giuseppe Gullo, Alex J. Eustace, Alexandra Canonici, Denis M. Collins, Michael J. Kennedy, Liam Grogan, Oscar Breathhnach, John McCaffrey, Maccon Keane, Michael J. Martin, Rajnish Gupta, Gregory Leonard, Miriam O’Connor, Paula M. Calvert, Paul Donnellan, Janice Walshe, Enda McDermott, Kathleen Scott, Andres Hernando, Imelda Parker, David W. Murray, Alice C. O’Farrell, Ashwini Maratha, Patrick Dicker, Mairin Rafferty, Verena Murphy, Norma O’Donovan, William M. Gallagher, Bonnie Ky, Dimitrios Tryfonopoulos, Brian Moulton, Annette T. Byrne and John Crown in Therapeutic Advances in Medical Oncology

Supplemental material, Supplementary_Methods for Pilot study of bevacizumab in combination with docetaxel and cyclophosphamide as adjuvant treatment for patients with early stage HER-2 negative breast cancer, including analysis of candidate circulating markers of cardiac toxicity: ICORG 08–10 trial by Giuseppe Gullo, Alex J. Eustace, Alexandra Canonici, Denis M. Collins, Michael J. Kennedy, Liam Grogan, Oscar Breathhnach, John McCaffrey, Maccon Keane, Michael J. Martin, Rajnish Gupta, Gregory Leonard, Miriam O’Connor, Paula M. Calvert, Paul Donnellan, Janice Walshe, Enda McDermott, Kathleen Scott, Andres Hernando, Imelda Parker, David W. Murray, Alice C. O’Farrell, Ashwini Maratha, Patrick Dicker, Mairin Rafferty, Verena Murphy, Norma O’Donovan, William M. Gallagher, Bonnie Ky, Dimitrios Tryfonopoulos, Brian Moulton, Annette T. Byrne and John Crown in Therapeutic Advances in Medical Oncology

Supplemental material, Supplementary_Table_2 for Pilot study of bevacizumab in combination with docetaxel and cyclophosphamide as adjuvant treatment for patients with early stage HER-2 negative breast cancer, including analysis of candidate circulating markers of cardiac toxicity: ICORG 08–10 trial by Giuseppe Gullo, Alex J. Eustace, Alexandra Canonici, Denis M. Collins, Michael J. Kennedy, Liam Grogan, Oscar Breathhnach, John McCaffrey, Maccon Keane, Michael J. Martin, Rajnish Gupta, Gregory Leonard, Miriam O’Connor, Paula M. Calvert, Paul Donnellan, Janice Walshe, Enda McDermott, Kathleen Scott, Andres Hernando, Imelda Parker, David W. Murray, Alice C. O’Farrell, Ashwini Maratha, Patrick Dicker, Mairin Rafferty, Verena Murphy, Norma O’Donovan, William M. Gallagher, Bonnie Ky, Dimitrios Tryfonopoulos, Brian Moulton, Annette T. Byrne and John Crown in Therapeutic Advances in Medical Oncology

Supplemental material, Supplementary_Methods for Pilot study of bevacizumab in combination with docetaxel and cyclophosphamide as adjuvant treatment for patients with early stage HER-2 negative breast cancer, including analysis of candidate circulating markers of cardiac toxicity: ICORG 08–10 trial by Giuseppe Gullo, Alex J. Eustace, Alexandra Canonici, Denis M. Collins, Michael J. Kennedy, Liam Grogan, Oscar Breathhnach, John McCaffrey, Maccon Keane, Michael J. Martin, Rajnish Gupta, Gregory Leonard, Miriam O’Connor, Paula M. Calvert, Paul Donnellan, Janice Walshe, Enda McDermott, Kathleen Scott, Andres Hernando, Imelda Parker, David W. Murray, Alice C. O’Farrell, Ashwini Maratha, Patrick Dicker, Mairin Rafferty, Verena Murphy, Norma O’Donovan, William M. Gallagher, Bonnie Ky, Dimitrios Tryfonopoulos, Brian Moulton, Annette T. Byrne and John Crown in Therapeutic Advances in Medical Oncology