Unitary Fund

A key concept of quantum information theory is that accessing information encoded in a quantum system requires us to discriminate between several possible states the system could be in. A natural generalization of this problem, namely, quantum sequence discrimination, appears in various quantum information processing tasks, the objective being to determine the state of a finite sequence of quantum states. Since such a sequence is a composite quantum system, the fundamental question is whether an optimal measurement is local, i.e., comprising measurements on the individual members, or collective, i.e., requiring joint measurement(s). In some known instances of this problem, the optimal measurement is local, whereas in others, it is collective. But, so far, a definite prescription based solely on the problem description has been lacking. In this paper, we prove that if the members of a given sequence are secretly and independently drawn from an ensemble or even from different ensembles, the optimum success probability is achievable by fixed local measurements on the individual members of the sequence, and no collective measurement is necessary. This holds for both minimum-error and unambiguous state discrimination paradigms.

The authors present an error-mitigation scheme in which the noise from different layers of a quantum circuit can be amplified and then extrapolated to the zero-noise limit independently. In doing this they enhance the traditional Richardson extrapolation protocol with the flexibility of layerwise unitary folding schemes.

We show that counting the number of collisions (re-sampled bitstrings) when measuring a random quantum circuit provides a practical benchmark for the quality of a quantum computer and a quantitative noise characterization method. We analytically estimate the difference in the expected number of collisions when sampling bitstrings from a pure random state and when sampling from the classical uniform distribution. We show that this quantity, if properly normalized, can be used as a collision anomaly benchmark or as a collision volume test, which is similar to the well-known quantum volume test, with advantages (no classical computing cost) and disadvantages (high sampling cost). We also propose to count the number of cross-collisions between two independent quantum computers running the same random circuit in order to obtain a cross-validation test of the two devices. Finally, we quantify the sampling cost of quantum collision experiments. We find that the sampling cost for running a collision volume test on state-of-the-art processors (e.g., 20 effective clean qubits) is quite small: less than 105 shots. For large-scale experiments in the quantum supremacy regime, the required number of shots for observing a quantum signal in the observed number of collisions is currently infeasible (>1012), but not completely out of reach for near-future technology.

We apply quantum error mitigation techniques to a variety of benchmark problems and quantum computers to evaluate the performance of quantum error mitigation in practice. To do so, we define an empirically motivated, resource-normalized metric of the improvement of error mitigation which we call the improvement factor, and calculate this metric for each experiment we perform. The experiments we perform consist of zero-noise extrapolation and probabilistic error cancellation applied to two benchmark problems run on IBM, IonQ, and Rigetti quantum computers, as well as noisy quantum computer simulators. Our results show that error mitigation is on average more beneficial than no error mitigation -even when normalized by the additional resources usedbut also emphasize that the performance of quantum error mitigation depends on the underlying computer.

For a large class of variational quantum circuits, we show how\narbitrary-order derivatives can be analytically evaluated in terms of simple\nparameter-shift rules, i.e., by running the same circuit with different shifts\nof the parameters. As particular cases, we obtain parameter-shift rules for the\nHessian of an expectation value and for the metric tensor of a variational\nstate, both of which can be efficiently used to analytically implement\nsecond-order optimization algorithms on a quantum computer. We also consider\nthe impact of statistical noise by studying the mean squared error of different\nderivative estimators. In the second part of this work, some of the theoretical\ntechniques for evaluating quantum derivatives are applied to their typical use\ncase: the implementation of quantum optimizers. We find that the performance of\ndifferent estimators and optimizers is intertwined with the values of different\nhyperparameters, such as a step size or a number of shots. Our findings are\nsupported by several numerical and hardware experiments, including an\nexperimental estimation of the Hessian of a simple variational circuit and an\nimplementation of the Newton optimizer.\n

We have previously constructed a chimeric version of KC4G3, a murine antibody that reacts with several human epithelial cancers and binds to the human breast epithelial mucin. We have now successfully humanized KC4G3 using positional consensus data, previously compiled after examining several other antibody structures, listing residues in the VH and V kappa frameworks that could influence antigen binding. We have previously showed that a fraction of the kappa chains of murine and chimeric KC4G3 migrates abnormally on SDS-PAGE most likely due to N-linked glycosylation in V kappa. The glycosylation signal has now been removed from V kappa, as a consequence of humanization. As expected, the humanized kappa chain migrates normally on SDS-PAGE. We detected no significant differences either in the affinities (1.6 x 10(9) M-1 vs. 1.4 x 10(9) M-1, respectively) or in the ability to compete for antigen binding, between the murine and the humanized antibodies. The humanized version is an IgG1, kappa immunoglobulin produced by mouse myeloma SP2/0-Ag14 cells and is designated HuKC4v2. The HuKC4v2 frameworks conform to the V kappa II and VHIII human consensus in all but six positions in V kappa and three positions in VH.