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Frontiers in Optics

Finding excited states of physical Hamiltonians on a silicon quantum photonic device

Raffaele Santagati, J. Wang, Antonio A. Gentile, Stefano Paesani, Nathan Wiebe, Jarrod R. McClean, Damien Bonneau, Joshua W. Silverstone, Sam Morley-Short, Peter Shadbolt, David P. Tew, X. Zhou, Jeremy L. O’Brien, Mark G. Thompson

Published Jan 1, 2017• 2 citations
Publisher

Abstract

We introduce the concept of eigenstate-witness to implement a new protocol for finding excited-states of physical Hamiltonians. We experimentally demonstrate it on a silicon quantum photonic device embedding arbitrary controlled unitary operations.
DOI
10.1364/fio.2017.fm4e.2

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The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. We introduce the concept of an "eigenstate witness" and, through it, provide a new quantum approach that combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32 bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress toward quantum chemistry on quantum computers.
The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. Here, we introduce the concept of an eigenstate witness and through it provide a new quantum approach which combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled-unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32-bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress towards quantum chemistry on quantum computers.
Physical Unclonable Functions (PUFs) are hardware security primitives whose inherent physical complexity can be exploited for secure authentication and cryptographic key generation. Silicon photonic devices, owing to their suitability for quantum and artificial intelligence applications alongside standard CMOS fabrication processes, constitute a highly promising substrate for integrated multifunctional PUFs. Despite the advanced security guarantees offered by quantum cryptographic protocols and the central role of silicon photonics in quantum technologies, quantum readout strategies based on single-photon states for photonic PUFs remain largely unexplored. In this work, we experimentally demonstrate a silicon nitride (SiN) programmable photonic Mach Zehnder interferometer mesh that implements a unitary transformation and operates as a PUF, whose secret physical signature arises from uncontrollable waveguide variations during fabrication. Using experimentally derived parameters from the SiN integrated mesh, we further introduce and numerically evaluate a quantum readout protocol that combines single-photon states with PUFs. Maximally mixed quantum states are employed to conceal the underlying unitary transformation from passive eavesdropping. Security against adversaries possessing devices fabricated under similar conditions is assessed, with authentication performance quantified through Monte Carlo analysis of the false acceptance and false rejection rates as a function of the number of detected events and corrected errors. The results indicate exceptional performance with equal error rates as low as 10 to the minus 14, highlighting the potential of quantum secure PUFs for high security authentication applications.
An integrated silicon quantum photonic device, capable of implementing non-compiled controlled unitary operations (CUs), is performing a new variational protocol for searching the ground state of an exciton-transfer Hamiltonian in chlorophyll. This protocol only requires single-qubit measurements ―amenable for scalable quantum photonic approaches ― independently from the dimension of the Hamiltonian system. A maximally path-entangled state, |0>C|0>T +|1>C|0>T, is created on chip through the SFWM effect in silicon waveguides. Then, the target qubit state (with subscript “T”) is expanded into a four-dimensional space and evolved according to two separate unitary operations, i.e. I (identity) and an arbitrary U∈SU(2), ended with a path-information erasure process. This yields a non-compiled “CU” operation, controlled by the control qubit (with subscript “C”) as |0>C ⊗I|φ>T +|1>C⊗U|φ>T. In this experiment, an exciton-transfer Hamiltonian in chlorophyll is properly mapped as U onto our circuit’s parameters. Both state preparation and CU operations are implemented using thermo-optic phase shifting heaters. Our new protocol draws on the eigenstate-generation features of the Iterative Phase Estimation Algorithm (IPEA), and relies on 1-qubit state-tomography performed on the C-qubit alone, to infer properties of the Hamiltonian. The protocol proposes a variational search of the ground state in the Hilbert space spanned by U’s eigenstates, combining quantum measurements and a classical update scheme for the trial T-states that are prepared and evolved in the quantum circuit at each step of the algorithm. The search is guided by effectively minimizing an objective function Fobj=-αP+βE. Only when the input T-qubit is an eigenstate of U, the purity (P) of the output C-qubit |0> + eiφ|1>is 1, and in this case, eigenphase φprovides an estimator for |φ>T's eigenvalue (E). The on-chip implementation granted a robust, reconfigurable setup for our variational search algorithm: within less than 10 steps, we were able to achieve 99.8% fidelity of the final T-state with the ground-state of the implemented Hamiltonian. Under reasonable assumptions, these preliminary results may pave the way towards a scalable quantum-simulation approach for the ground-state problem.