Experimental realization of universal geometric quantum gates with solid-state spins

Abstract

Experimental realization of a universal set of quantum logic gates is the central requirement for the implementation of a quantum computer. In an 'all-geometric' approach to quantum computation, the quantum gates are implemented using Berry phases and their non-Abelian extensions, holonomies, from geometric transformation of quantum states in the Hilbert space. Apart from its fundamental interest and rich mathematical structure, the geometric approach has some built-in noise-resilience features. On the experimental side, geometric phases and holonomies have been observed in thermal ensembles of liquid molecules using nuclear magnetic resonance; however, such systems are known to be non-scalable for the purposes of quantum computing. There are proposals to implement geometric quantum computation in scalable experimental platforms such as trapped ions, superconducting quantum bits and quantum dots, and a recent experiment has realized geometric single-bit gates in a superconducting system. Here we report the experimental realization of a universal set of geometric quantum gates using the solid-state spins of diamond nitrogen-vacancy centres. These diamond defects provide a scalable experimental platform with the potential for room-temperature quantum computing, which has attracted strong interest in recent years. Our experiment shows that all-geometric and potentially robust quantum computation can be realized with solid-state spin quantum bits, making use of recent advances in the coherent control of this system.

Non-Markovianity-assisted high-fidelity Deutsch–Jozsa algorithm in diamond

“…17,[22][23][24] Many techniques have been developed to address this issue, including decoherence-free subspaces, 25 dynamical decoupling (DD) 13,26 and the geometric approach. 27 However, actively utilizing the environmental interactions would represent a significant achievement, compared with passively shielding them.…”

“…17,[22][23][24] Many techniques have been developed to address this issue, including decoherence-free subspaces, 25 dynamical decoupling (DD) 13,26 and the geometric approach. 27 However, actively utilizing the environmental interactions would represent a significant achievement, compared with passively shielding them.Usually, the interaction of an open quantum system with a noisy environment exhibits memory-less dynamics with an irreversible loss of quantum coherence, that can be described by the Born-Markov approximation. 28 However, because of strong system-environment couplings, structured or finite reservoirs, low temperatures, or large initial system-environment correlations, the dynamics of an open quantum system may deviate substantially from the Born-Markov approximation and follow a non-Markovian process.…”

Composite nonadiabatic holonomic quantum computation

“…See, for example, the Hamiltonians in Refs. [3,14]. Although both physical systems and controlling methods are different in these researches, the Hamiltonians can be uniformly written as H(t) = Ω jk e iφ jk | jk a| + Ω lm e iφ lm |lm a| + h.c.,…”

“…So far, many schemes of realizing nonadiabatic holonomic gates have been put forward for various physical systems . Particularly, nonadiabatic holonomic quantum computation has been experimentally demonstrated with circuit QED, NMR, and nitrogen-vacancy (NV) center in diamond [5,6,13,14].…”

Exact magnetic field control of nitrogen-vacancy center spin for realizing fast quantum logic gates

“…Additionally, one needs accurate timing to track the relative phase between the |0 and | + 1 (or | + 1 ) states due to the zero-field splitting effect. Recently, the NV center spin was used to experimentally realize geometric quantum gates with high fidelity 14,15 . In this approach, the | + 1 and | − 1 states are used to encode the qubit.…”