Quantum simulation of partially distinguishable boson sampling

Boson Sampling is the problem of sampling from the same output probability distribution as a collection of indistinguishable single photons input into a linear interferometer. It has been shown that, subject to certain computational complexity conjectures, in general the problem is difficult to solve classically, motivating optical experiments aimed at demonstrating quantum computational "supremacy". There are a number of challenges faced by such experiments, including the generation of indistinguishable single photons. We provide a quantum circuit that simulates bosonic sampling with arbitrarily distinguishable particles. This makes clear how distinguishabililty leads to decoherence in the standard quantum circuit model, allowing insight to be gained. At the heart of the circuit is the quantum Schur transform, which follows from a representation theoretic approach to the physics of distinguishable particles in first quantisation. The techniques are quite general and have application beyond boson sampling.Comment: 25 pages, 4 figures, 2 algorithms, comments welcom

Classically simulating near-term partially-distinguishable and lossy boson sampling

Boson Sampling is the problem of sampling from the same distribution as indistinguishable single photons at the output of a linear optical interferometer. It is an example of a non-universal quantum computation which is believed to be feasible in the near term and cannot be simulated on a classical machine. Like all purported demonstrations of "quantum supremacy", this motivates optimizing classical simulation schemes for a realistic model of the problem, in this case Boson Sampling when the implementations experience lost or distinguishable photons. Although current simulation schemes for sufficiently imperfect boson sampling are classically efficient, in principle the polynomial runtime can be infeasibly large. In this work, we develop a scheme for classical simulation of Boson Sampling under uniform distinguishability and loss, based on the idea of sampling from distributions where at most k photons are indistinguishable. We show that asymptotically this scheme can provide a polynomial improvement in the runtime compared to classically simulating idealised Boson Sampling. More significantly, we show that in the regime considered experimentally relevant, our approach gives an substantial improvement in runtime over other classical simulation approaches.Comment: 15 pages, 5 figures, comments welcom

Neonatal Gram Negative and Candida Sepsis Survival and Neurodevelopmental Outcome at the Corrected Age of 24 Months

Objectives: To evaluate the long term neurodevelopmental outcome of premature infants exposed to either gram- negative sepsis (GNS) or neonatal Candida sepsis (NCS), and to compare their outcome with premature infants without sepsis. Methods: Historical cohort study in a population of infants born at <30 weeks gestation and admitted to the Neonatal Intensive Care Unit (NICU) of the Academic Medical Center in Amsterdam during the period 1997-2007. Outcome of infants exposed to GNS or NCS and 120 randomly chosen uncomplicated controls (UC) from the same NICU were compared. Clinical data during hospitalization and neurodevelopmental outcome data (clinical neurological status; Bayley -test results and vision/hearing test results) at the corrected age of 24 months were collected. An association model with sepsis as the central determinant of either good or adverse outcome (death or severe developmental delay) was made, corrected for confounders using multiple logistic regression analysis. Results: Of 1362 patients, 55 suffered from GNS and 29 suffered from NCS; cumulative incidence 4.2% and 2.2%, respectively. During the follow-up period the mortality rate was 34% for both GNS and NCS and 5% for UC. The adjusted Odds Ratio (OR) [95% CI] for adverse outcome in the GNS group compared to the NCS group was 1.4 [0.4-4.9]. The adjusted ORs [95% CI] for adverse outcome in the GNS and NCS groups compared to the UC group were 4.8 [1.5-15.9] and 3.2 [0.7-14.7], respectively. Conclusions: We found no statistically significant difference in outcome at the corrected age of 24 months between neonatal GNS and NCS cases. Suffering from either gram -negative or Candida sepsis increased the odds for adverse outcome compared with an uncomplicated neonatal period

Compilation of a simple chemistry application to quantum error correction primitives

A number of exciting recent results have been seen in the field of quantum error correction. These include initial demonstrations of error correction on current quantum hardware, and resource estimates which improve understanding of the requirements to run large-scale quantum algorithms for real-world applications. In this work, we bridge the gap between these two developments by performing careful estimation of the resources required to fault-tolerantly perform quantum phase estimation (QPE) on a minimal chemical example. Specifically, we describe a detailed compilation of the QPE circuit to lattice surgery operations for the rotated surface code, for a hydrogen molecule in a minimal basis set. We describe a number of optimisations at both the algorithmic and error correction levels. We find that implementing even a simple chemistry circuit requires 900 qubits and 2,300 quantum error correction rounds, emphasising the need for improved error correction techniques specifically targeting the early fault-tolerant regime.Comment: 22 pages, 23 figures, 1 table, source code available at https://github.com/riverlane/h2_compilation