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Currently Playing: How to Generalize Qubit Circuits to Qudits | Qiskit Seminar Series with Lia Yeh

How to Generalize Qubit Circuits to Qudits Qiskit Seminar Series with Lia Yeh Your formal invite to weekly Qiskit videos ► https://ibm.biz/q-subscribe This week on the 8th March was International Women's Day! Check out the Qiskit Quantum Women Invited Talk Series here: http://qisk.it/q-women. Speaker: Lia Yeh Host: Maria Violaris Slides: https://www.dropbox.com/s/b32kvzwi7ppasbx/Lia%20Yeh%20Slides.pdf?dl=0 References: https://arxiv.org/abs/2303.03163 https://arxiv.org/abs/2012.13966 https://www.cambridge.org/core/books/picturing-quantum-processes/1119568B3101F3A685BE832FEEC53E52 Abstract: For many qubit circuit decompositions, it is not obvious if a similar technique can be applied to qudits. For continuous parameter quantum circuits, there are many more parameters involved as qudit dimension increases. On the other hand, discrete gate sets have very different properties depending on the qudit dimension. We show a number of qudit circuit decompositions, of both continuous parameter and discrete gate sets, that build upon a pre-existing qubit decomposition. These include multiple-controlled Toffolis and other classical reversible gates, W states, and the generalization of a class of continuous parameter diagonal gates called phase gadgets or phase polynomials. In particular, we identify a novel qudit gate which we call the Z^(1/d) gate. This is an alternate generalization of the qutrit T gate to any odd prime dimension d, in the dth level of the Clifford hierarchy; for d = 3, Clifford+Z^(1/d) coincides with Clifford+T. We present an explicit construction of any d-ary (for d prime) classical reversible gate on n qudits in the Clifford+Z^(1/d) gate set; moreover, we show that this converges asymptotically to within a log(n) factor of the minimum gate count necessary. Finally, we discuss how if a conjecture by de Silva holds that all single-qudit gates in any level of the Clifford hierarchy can be implemented efficiently fault-tolerantly, then our results immediately resolve the open problem of fault-tolerant realization of qudit Toffoli gates. Bio: Lia Yeh is a computer science PhD student in the Quantum Group at the University of Oxford, where her primary research focus is on using and developing ZX-calculus and related quantum graphical calculi as a useful language for qudit circuit synthesis and quantum error correction. She has bachelor’s degrees in physics and computing at the College of Creative Studies of the University of California, Santa Barbara where she designed microwave spectroscopy algorithms to determine molecular structure. She currently works part-time at Quantinuum, volunteers for IEEE Quantum Education as a steering committee member of the IEEE Quantum Initiative, and volunteers for the Quantum Universal Education not-for-profit community. Previously, she worked part-time at IBM Quantum Education developing a tutorial as an introduction to quantum computing through ZX-calculus diagrams. Prior to that, she worked part-time teaching high school students for The Coding School non-profit's free yearlong quantum computing course taken by more than 8,000 students.