ABSTRACT
Quantum computing technology may soon deliver revolutionary improvements in algorithmic performance, but it is useful only if computed answers are correct. While hardware-level decoherence errors have garnered significant attention, a less recognized obstacle to correctness is that of human programming errors-"bugs." Techniques familiar to most programmers from the classical domain for avoiding, discovering, and diagnosing bugs do not easily transfer, at scale, to the quantum domain because of its unique characteristics. To address this problem, we have been working to adapt formal methods to quantum programming. With such methods, a programmer writes a mathematical specification alongside the program and semiautomatically proves the program correct with respect to it. The proof's validity is automatically confirmed-certified-by a "proof assistant." Formal methods have successfully yielded high-assurance classical software artifacts, and the underlying technology has produced certified proofs of major mathematical theorems. As a demonstration of the feasibility of applying formal methods to quantum programming, we present a formally certified end-to-end implementation of Shor's prime factorization algorithm, developed as part of a framework for applying the certified approach to general applications. By leveraging our framework, one can significantly reduce the effects of human errors and obtain a high-assurance implementation of large-scale quantum applications in a principled way.
ABSTRACT
PURPOSE: This was an open-label, dose-escalation trial of intratumoral administration of IL-4 Pseudomonas exotoxin (NBI-3001) in patients with recurrent malignant glioma. PATIENTS AND METHODS: A total of 31 patients with histologically verified supratentorial grades 3 and 4 astrocytoma were studied. Of these, 25 patients were diagnosed with glioblastoma multiforme (GBM) while six were diagnosed with anaplastic astrocytoma. Patients were over 18 years of age and had Karnofsky performance scores > or = 60. Patients were assigned to one of four dose groups in a dose-escalation fashion: 6 microg/ml x 40 ml, 9 microg/ml x 40 ml, 15 microg/ml x 40 ml, or 9 microg/ml x 100 ml of NBI-3001 administered via convection-enhanced delivery intratumorally using stereotactically placed catheters. Patients were followed with serial MRI scans and clinical assessments every four weeks for the first 16 weeks and then every eight weeks until week 26. RESULTS: No drug-related systemic toxicity, as evident by lack of hematological or serum chemical changes, was apparent in any patients; treatment-related adverse effects were limited to the central nervous system. No deaths were attributable to treatment. Drug-related grade 3 or 4 toxicity was seen in 39% of patients in all dose groups and 22% of patients at the maximum tolerated dose of 6 microg/ml x 40 ml. The overall median survival was 8.2 months with a median survival of 5.8 months for the GBM patients. Six-month survival was 52% and 48%, respectively. Gadolinium-enhanced magnetic resonance imaging of the brain showed areas of decreased signal intensity within the tumor consistent with tumor necrosis following treatment in many patients. CONCLUSIONS: NBI-3001 appears to have an acceptable safety and toxicity profile when administered intratumorally in patients with recurrent malignant glioma.
