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Abstract
Error-detection and correction are necessary prerequisites for any scalable quantum computing architecture. Given the inevitability of unwanted physical noise in quantum systems and the propensity for errors to spread as computations proceed, computational outcomes can become substantially corrupted. This observation applies regardless of the choice of physical implementation. In the context of photonic quantum information processing, there has recently been much interest inpassivelinear optics quantum computing, which includes boson-sampling, as this model eliminates the highly-challenging requirements for feed-forward via fast, active control. That is, these systems arepassiveby definition. In usual scenarios, error detection and correction techniques are inherentlyactive, making them incompatible with this model, arousing suspicion that physical error processes may be an insurmountable obstacle. Here we explore a photonic error-detection technique, based on W-state encoding of photonic qubits, which is entirely passive, based on post-selection, and compatible with these near-term photonic architectures of interest. We show that this W-state redundant encoding techniques enables the suppression of dephasing noise on photonic qubits via simple fan-out style operations, implemented by optical Fourier transform networks, which can be readily realised today. The protocol effectively maps dephasing noise into heralding failures, with zero failure probability in the ideal no-noise limit. We present our scheme in the context of a single photonic qubit passing through a noisy communication or quantum memory channel, which has not been generalised to the more general context of full quantum computation.
Highlights
Error rates [20, 21, 31]
There is currently a pursuit to find utility for achievable near-term devices with post-classical capabilities, even if not universal [12, 18]. This has lead to the alternative target where universality is discarded as a requirement and the sole purpose is demonstrating some form of quantum computational advantage with pragmatically reasonable resources
Devices requiring higher photon numbers could be accommodated by parallel combinations of single photon interferometers. This is distinct from the considerations of [4] for errors within unitary networks as there it was assumed that there was no redundancy utilizing additional resources. We extend this result by considering single photon encoding that involve W-state path entanglement encoding of photonic qubits encoded in dual-rail form
Summary
The worst-case scenario is the GHZ state, a maximally-entangled n-qubit state of the form,. Measurement of any one (in the computational Z-basis), reveals the equivalent measurement outcome of all others. This directly implies that losing access to this information implies loss of knowledge of the others. Loss or dephasing directly correspond to such loss of information. For this reason, dephasing a single qubit, or losing it outright, implies complete decoherence of the entire n-qubit state. Partial tracing out a single qubit from a GHZ state leaves behind the hopelessly mixed stated, Tri(|GHZn. + 1 |1 ⊗n−1 1|⊗n−1 , (2) 2 where the partial trace is performed upon any qubit i
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