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Gottesman-Kitaev-Preskill state preparation by photon catalysis

Miller Eaton, Rajveer Nehra, Olivier Pfister

Published Mar 5, 2019• 5 citations
OpenAlex

Abstract

Continuous-variable quantum-computing (CVQC) is the most scalable implementation of QC to date but requires non-Gaussian resources to allow exponential speedup and quantum correction, using error encoding such as Gottesman-Kitaev-Preskill (GKP) states. However, GKP state generation is still an experimental challenge. We show theoretically that photon catalysis, the interference of coherent states with single-photon states followed by photon-number-resolved detection, is a powerful enabler for non-Gaussian quantum state engineering such as exactly displaced single-photon states and $M$-symmetric superpositions of squeezed vacuum (SSV), including squeezed cat states ($M=2$). By including photon-counting based state breeding, we demonstrate the potential to enlarge SSV states and produce GKP states.

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Continuous-variable quantum-computing (CVQC) is the most scalable implementation of QC to date but requires non-Gaussian resources to allow exponential speedup and quantum correction, using error encoding such as Gottesman-Kitaev-Preskill (GKP) states. However, GKP state generation is still an experimental challenge. We show theoretically that photon catalysis, the interference of coherent states with single-photon states followed by photon-number-resolved detection, is a powerful enabler for non-Gaussian quantum state engineering such as exactly displaced single-photon states and MMM-symmetric superpositions of squeezed vacuum (SSV), including squeezed cat states (M=2M=2M=2). By including photon-counting based state breeding, we demonstrate the potential to enlarge SSV states and produce GKP states.
Abstract Continuous-variable quantum-computing is the most scalable implementation of QC to date but requires non-Gaussian resources to allow exponential speedup and quantum correction, using error encoding such as Gottesman–Kitaev–Preskill (GKP) states. However, GKP state generation is still an experimental challenge. We show theoretically that photon catalysis, the interference of coherent states with single-photon states followed by photon-number-resolved detection, is a powerful enabler for non-Gaussian quantum state engineering such as exactly displaced single-photon states and M -symmetric superpositions of squeezed vacuum (SSV), including squeezed cat states ( M = 2). By including photon-counting based state breeding, we demonstrate the potential to enlarge SSV states and produce GKP states.
Gottesman-Kitaev-Preskill (GKP) qubits, known for their exceptional error-correction capabilities, are highly coveted in quantum computing. However, generating optical GKP qubits has been a significant challenge. Measurement-based methods, where a portion of entangled squeezed vacuum modes are measured with photon number resolving detectors heralding a desired state in the undetected modes, have emerged as leading candidates for optical GKP qubit generation due their minimal resource requirements. While the current measurement-based methods can produce high-quality GKP qubits, they suffer from low success probabilities limiting experimental realization. The heart of the problem lies in the duality of photon number resolving measurements, being both the source of nonlinearity needed to generate quality GKP qubits and the component driving down their probability of successful production. Our method, breeding approximate squeezed coherent state superpositions created by generalized photon subtraction, overcomes this problem by supplementing two photon number resolving measurements with a single high success probability homodyne measurement. This scheme achieves success probabilities $\ensuremath{\ge}{10}^{\ensuremath{-}5}$, two orders of magnitude higher than strictly photon number resolving measurement based methods, while still producing states with high fidelity, possessing error-correction capabilities equivalent to up to a 10 dB squeezed GKP qubit. This breakthrough significantly advances the practical use of the optical GKP qubit encoding.
Gottesman-Kitaev-Preskill (GKP) states are a central resource for fault-tolerant optical continuous-variable quantum computing and communication. However, their realization in the optical domain remains to be demonstrated. Here we propose a method for preparing GKP states using a cavity QED system as the only non-Gaussian element. This system can be realized in several platforms such as trapped atoms, quantum dots or diamond color centers. We simulate the protocol with finite-cooperativity systems to evaluate the achievable quality of the produced GKP states in realistic noisy systems. We further combine the protocol with the previously proposed breeding protocol by Vasconcelos et al. to relax the demands on the quality of the QED system. We find that GKP states with more than 10 dB squeezing could be achieved in near-future experiments. Additionally, the approach can be made fully deterministic, thus providing a more scalable and hardware-efficient approach compared to probabilistic approaches based on photon counting.
Large-amplitude squeezed cat states and high-quality Gottesman-Kitaev-Preskill (GKP) states are essential for effective quantum error correction, yet their optical preparation has been hindered by challenges such as low success probabilities, small amplitudes, and insufficient squeezing. Addressing these limitations, our research introduces scalable optical schemes for the deterministic preparation of large-amplitude squeezed cat states from photon-number states. Fock states have the benefit of producing consistent cat states across all measurement outcomes and intrinsically provides a degree of squeezing. Notably, these squeezed cat states facilitate the deterministic generation of high-quality approximate GKP states via "breeding," showing that GKP error correction in optics is technically feasible in near-term experiments. Our schemes allow fault-tolerant quantum computation through the use of GKP error correction.
Continuous-variable quantum computing (CVQC) boasts, by way of quantum optics, one of the largest scalability potentials of all quantum computing platforms. In order to enable universal CVQC, i.e., exponential speedup as well as fault tolerance, one requires quantum resources (states and/or gates) with a non-Gaussian Wigner function. We present several state preparation techniques, using photon-number-resolving detection, that enable the generation of resource states such as GKP or binomial error encodings.