Rafael N. Alexander

Noise analysis of single-mode Gaussian operations using continuous-variable cluster states

We consider measurement-based quantum computation that uses scalable continuous-variable cluster states with a one-dimensional topology. The physical resource, known here as the dual-rail quantum wire, can be generated using temporally multiplexed offline squeezing and linear optics or by using a single optical parametric oscillator. We focus on an important class of quantum gates, specifically Gaussian unitaries that act on single quantum modes (qumodes), which gives universal quantum computation when supplemented with multi-qumode operations and photon-counting measurements. The dual-rail wire supports two routes for applying single-qumode Gaussian unitaries: The first is to use traditional one-dimensional quantum-wire cluster-state measurement protocols. The second takes advantage of the dual-rail quantum wire in order to apply unitaries by measuring pairs of qumodes called macronodes. We analyze and compare these methods in terms of the suitability for implementing single-qumode Gaussian measurement-based quantum computation.

Measurement-Based Linear Optics

A major challenge in optical quantum processing is implementing large, stable interferometers. We offer a novel approach: virtual, measurement-based interferometers that are programed on the fly solely by the choice of homodyne measurement angles. The effects of finite squeezing are captured as uniform amplitude damping. We compare our proposal to existing (physical) interferometers and consider its performance for BosonSampling, which could demonstrate postclassical computational power in the near future. We prove its efficiency in time and squeezing (energy) in this setting.

Flexible quantum circuits using scalable continuous-variable cluster states

We show that measurement-based quantum computation on scalable continuous-variable (CV) cluster states admits more quantum-circuit flexibility and compactness than similar protocols for standard square-lattice CV cluster states. This advantage is a direct result of themacronode structure of these states-that is, a lattice structure in which each graph node actually consists of several physical modes. These extra modes provide additional measurement degrees of freedom at each graph location, which can be used to manipulate the flow and processing of quantum information more robustly and with additional flexibility that is not available on an ordinary lattice.

One-way quantum computing with arbitrarily large time-frequency continuous-variable cluster states from a single optical parametric oscillator

One-way quantum computing is experimentally appealing because it requires only local measurements on an entangled resource called a cluster state. Record-size, but nonuniversal, continuous-variable cluster states were recently demonstrated separately in the time and frequency domains. We propose to combine these approaches into a scalable architecture in which a single optical parametric oscillator and simple interferometer entangle up to (3×103 frequencies) × (unlimited number of temporal modes) into a computationally universal continuous-variable cluster state. We introduce a generalized measurement protocol to enable improved computational performance on this entanglement resource.

Randomized benchmarking in measurement-based quantum computing

Randomized benchmarking is routinely used as an efficient method for characterizing the performance of sets of elementary logic gates in small quantum devices. In the measurement-based model of quantum computation, logic gates are implemented via single-site measurements on a fixed universal resource state. Here we adapt the randomized benchmarking protocol for a single qubit to a linear cluster state computation, which provides partial, yet efficient characterization of the noise associated with the target gate set. Applying randomized benchmarking to measurement-based quantum computation exhibits an interesting interplay between the inherent randomness associated with logic gates in the measurement-based model and the random gate sequences used in benchmarking. We consider two different approaches: the first makes use of the standard single-qubit Clifford group, while the second uses recently introduced (non-Clifford) measurement-based 2-designs, which harness inherent randomness to implement gate sequences.