Yu, Xi; Wilhelm, Benjamin; Holmes, Danielle; Vaartjes, Arjen; Schwienbacher, Daniel; Nurizzo, Martin; Kringhoj, Anders; Van Blankenstein, Mark R.; Jakob, Alexander M.; Gupta, Pragati; Hudson, Fay E.; Itoh, Kohei M.; Murray, Riley J.; Blume-Kohout, Robin; Ladd, Thaddeus D.; Dzurak, Andrew S.; Sanders, Barry C.; Jamieson, David N.; Morello, Andrea
High-dimensional quantum systems are a valuable resource for quantum information processing. They can be used to encode error-correctable logical qubits, which has been demonstrated using continuous-variable states in microwave cavities or the motional modes of trapped ions. For example, high-dimensional systems can be used to realize ‘Schrödinger cat’ states, which are superpositions of widely displaced coherent states that can be used to illustrate quantum effects at large scales. Recent proposals have suggested encoding qubits in high-spin atomic nuclei, which are finite-dimensional systems that can host hardware-efficient versions of continuous-variable codes. Here we demonstrate the creation and manipulation of Schrödinger cat states using the spin-7/2 nucleus of an antimony atom embedded in a silicon nanoelectronic device. We use a multi-frequency control scheme to produce spin rotations that preserve the symmetry of the qudit, and we constitute logical Pauli operations for qubits encoded in the Schrödinger cat states. Our work demonstrates the ability to prepare and control non-classical resource states, which is a prerequisite for applications in quantum information processing and quantum error correction, using our scalable, manufacturable semiconductor platform.
Ostrove, Corey I.; Rudinger, Kenneth M.; Blume-Kohout, Robin; Young, Kevin; Stemp, Holly G.; Asaad, Serwan; Van Blankenstein, Mark R.; Vaartjes, Arjen; Johnson, Mark A.I.; Madzik, Mateusz T.; Heskes, Amber J.A.; Firgau, Hannes R.; Su, Rocky Y.; Yang, Chih H.; Laucht, Arne; Hudson, Fay E.; Dzurak, Andrew S.; Itoh, Kohei M.; Jakob, Alexander M.; Johnson, Brett C.; Jamieson, David N.; Morello, Andrea
Scalable quantum processors require high-fidelity universal quantum logic operations in a manufacturable physical platform. Donors in silicon provide atomic size, excellent quantum coherence and compatibility with standard semiconductor processing, but no entanglement between donor-bound electron spins has been demonstrated to date. Here we present the experimental demonstration and tomography of universal one- and two-qubit gates in a system of two weakly exchange-coupled electrons, bound to single phosphorus donors introduced in silicon by ion implantation. We observe that the exchange interaction has no effect on the qubit coherence. We quantify the fidelity of the quantum operations using gate set tomography (GST), and we use the universal gate set to create entangled Bell states of the electrons spins, with fidelity 91.3 ± 3.0%, and concurrence 0.87 ± 0.05. These results form the necessary basis for scaling up donor-based quantum computers.
Errors in quantum logic gates are usually modeled by quantum process matrices (CPTP maps). But process matrices can be opaque and unwieldy. We show how to transform the process matrix of a gate into an error generator that represents the same information more usefully. We construct a basis of simple and physically intuitive elementary error generators, classify them, and show how to represent the error generator of any gate as a mixture of elementary error generators with various rates. Finally, we show how to build a large variety of reduced models for gate errors by combining elementary error generators and/or entire subsectors of generator space. We conclude with a few examples of reduced models, including one with just 9N2 parameters that describes almost all commonly predicted errors on an N-qubit processor.