Quantum computing has attracted much attention over the past sesquidecade because it makes integer-factoring easy, even though that has been a historically (if not provably) hard mathematical problem . Another major interest is the exponential speedup of quantum simulations . The physical implementation of nontrivial quantum computing is an exciting, if daunting, experimental challenge, epitomized by the issues of decoherence and scalability of the quantum registers and processors. In this talk, I will present a novel scheme for realizing a scalable quantum register of potentially very large size, entangled in a "cluster" state, in a remarkably compact physical system: the optical frequency comb (OFC) defined by the eigenmodes of a single optical resonator. The classical OFC is well known as implemented by the femtosecond, carrier-envelope-phase- and mode-locked lasers which have redefined time/frequency metrology and ultraprecise measurements in recent years [3,4]. The quantum version of the OFC is then a set of harmonic oscillators, or "Qmodes," whose amplitude and phase are analogues of the position and momentum mechanical observables. The quantum manipulation of these continuous variables for one or two Qmodes is a mature field. Recently, we have shown theoretically that the nonlinear optical medium of a single optical parametric oscillator (OPO) can be engineered, in a sophisticated but already demonstrated manner, so as to entangle, in constant time, the OPO's OFC into a cluster state of arbitrary size, suitable for one-way quantum computing over continuous variables [5,6]. I will describe the mathematical proof of this result and report on our progress towards its experimental implementation at the University of Virginia.
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