Quantum superposition of a single microwave photon in two different "colour" states

The ability to coherently couple arbitrary harmonic oscillators in a fully-controlled way is an important tool to process quantum information. Coupling between quantum harmonic oscillators has previously been demonstrated in several physical systems by use of a two-level system as a mediating element. Direct interaction at the quantum level has only recently been realized by use of resonant coupling between trapped ions. Here we implement a tunable direct coupling between the microwave harmonics of a superconducting resonator by use of parametric frequency conversion. We accomplish this by coupling the mode currents of two harmonics through a superconducting quantum interference device (SQUID) and modulating its flux at the difference (~ 7 GHz) of the harmonic frequencies. We deterministically prepare a single-photon Fock state and coherently manipulate it between multiple modes, effectively controlling it in a superposition of two different "colours". This parametric interaction can be described as a beam-splitter-like operation that couples different frequency modes. As such, it could be used to implement linear optical quantum computing protocols on-chip.Comment: 21 pages, 10 figure

Accumulation of copy number alterations and clinical progression across advanced prostate cancer

Background: Genomic copy number alterations commonly occur in prostate cancer and are one measure of genomic instability. The clinical implication of copy number change in advanced prostate cancer, which defines a wide spectrum of disease from high-risk localised to metastatic, is unknown. Methods: We performed copy number profiling on 688 tumour regions from 300 patients, who presented with advanced prostate cancer prior to the start of long-term androgen deprivation therapy (ADT), in the control arm of the prospective randomised STAMPEDE trial. Patients were categorised into metastatic states as follows; high-risk non-metastatic with or without local lymph node involvement, or metastatic low/high volume. We followed up patients for a median of 7 years. Univariable and multivariable Cox survival models were fitted to estimate the association between the burden of copy number alteration as a continuous variable and the hazard of death or disease progression. Results: The burden of copy number alterations positively associated with radiologically evident distant metastases at diagnosis (P=0.00006) and showed a non-linear relationship with clinical outcome on univariable and multivariable analysis, characterised by a sharp increase in the relative risk of progression (P=0.003) and death (P=0.045) for each unit increase, stabilising into more modest increases with higher copy number burdens. This association between copy number burden and outcome was similar in each metastatic state. Copy number loss occurred significantly more frequently than gain at the lowest copy number burden quartile (q=4.1 × 10−6). Loss of segments in chromosome 5q21-22 and gains at 8q21-24, respectively including CHD1 and cMYC occurred more frequently in cases with higher copy number alteration (for either region: Kolmogorov–Smirnov distance, 0.5; adjusted P<0.0001). Copy number alterations showed variability across tumour regions in the same prostate. This variance associated with increased risk of distant metastases (Kruskal-Wallis test P=0.037). Conclusions: Copy number alteration in advanced prostate cancer associates with increased risk of metastases at diagnosis. Accumulation of a limited number of copy number alterations associates with most of the increased risk of disease progression and death. The increased likelihood of involvement of specific segments in high copy number alteration burden cancers may suggest an order underlying the accumulation of copy number changes