Current graduate students
Exploring Wigner Negativity of Pure Spin States on a Spherical Phase Space
The past two decades have largely vindicated the long-held belief that Wigner negativity is an indicator of genuine nonclassicality in quantum systems. Here we will discuss how Wigner negativity manifests in pure spin-j systems using the spherical Wigner function. Common symmetric multi-qubit states are studied and compared, including Bell, W and GHZ states. Spin coherent states are shown to never have vanishing Wigner negativity, in contrast to other phase spaces. Pure states that maximize negativity are determined and analyzed using the Majorana stellar representation. Time permitting, these results will be contrasted with similar works on symmetric state entanglement and other forms of phase-space nonclassicality.
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Wigner negativity on the sphere
The rise of quantum information theory has largely vindicated the long-held belief that Wigner negativity is an indicator of genuine nonclassicality in quantum systems. This thesis explores its manifestation in spin-j systems using the spherical Wigner function. Common symmetric multi-qubit states are studied and compared. Spin coherent states are shown to never have vanishing Wigner negativity. Pure states that maximize negativity are determined and analyzed using the Majorana stellar representation. The relationship between negativity and state mixedness is discussed, and polytopes characterizing unitary orbits of lower-bounded Wigner functions are studied. Results throughout are contrasted with similar works on symmetric state entanglement and other forms of phase-space nonclassicality.
Math/CS Seminar - Atsuya Hasegawa (University of Tokyo)
Recently, Chia, Chung and Lai (JACM 2023) and Coudron and Menda (STOC 2020) have shown that there exists an oracle $\mathcal{O}$ such that $\mathsf{BQP}^\mathcal{O} \neq (\mathsf{BPP^{BQNC}})^\mathcal{O} \cup (\mathsf{BQNC^{BPP}})^\mathcal{O}$. In fact, Chia et al. proved a stronger statement: for any depth parameter $d$, there exists an oracle that separates quantum depth $d$ and $2d+1$, when polynomial-time classical computation is allowed.
Preserving a Qubit During Adjacent Measurements at a Few Micrometers Distance
Abstract:
Protecting a quantum object against irreversible accidental measurements from its surroundings is necessary for controlled quantum operations. This becomes especially challenging or unfeasible if one must simultaneously measure or reset a nearby object's quantum state, such as in quantum error correction.
In atomic systems - among the most established quantum information processing platforms - current attempts to preserve qubits against resonant laser-driven adjacent measurements, waste valuable experimental resources such as coherence time or extra qubits and introduce additional errors. We preserve the quantum state of an 'asset' ion qubit with high fidelity, while a neighbouring qubit at a few microns distance is reset/measured. We achieve < 1 x 10-3 probability of accidental measurement of the asset qubit during a neighbouring qubit reset and < 4 x 10-3 while applying a detection beam on the same neighbour, for 11 μs, at a distance of 6 μm or 4 times the addressing Gaussian beam waist (permitted by the numerical aperture).
These low probabilities correspond to the preservation of the quantum state of the qubit with fidelities above 99.90% (state-reset) and 99.6% (state-measurement). Our results are enabled by precise wavefront control of the addressing optical beams, while utilizing a single ion as a quantum sensor of optical aberrations.
Our work demonstrates the feasibility of in-situ state-reset and measurement operations, building towards enhancements in the speed and capabilities of quantum processors such as in simulating measurement-driven quantum phases and realizing quantum error correction.
Math/CS Seminar - Featuring Olivier Lalonde Université de Montréal
Quantum communication complexity, which concerns itself with determining how much communication is required by two participants having access to quantum resources to compute a boolean function of their inputs, has long been a lively subfield of quantum information science. The topic of this talk will be the power of shared prior entanglement relative to quantum communication without prior entanglement, which, despite having been studied for more twenty years, remains rather mysterious. After a quick review of the bare bones of classical communication complexity, I will proceed to discuss the model of entanglement-assisted communication complexity.
En français
The inaugural networking conference brought together over 150 quantum professionals from government, industry and academic sectors to foster collaborations and create connections over two days. Quantum Connections attendees critically examined the challenges we face as a country within the landscape of quantum and had proactive conversations considering Canada’s quantum future.
Graphical CSS Code Transformation Using ZX Calculus
Abstract:
In this work, we present a generic approach to transform CSS codes by building upon their equivalence to phase-free ZX diagrams. Using the ZX calculus, we demonstrate diagrammatic transformations between encoding maps associated with different codes. As a motivating example, we give explicit transformations between the Steane code and the quantum Reed-Muller code, since by switching between these two codes, one can obtain a fault-tolerant universal gate set. To this end, we propose a bidirectional rewrite rule to find a (not necessarily transversal) physical implementation for any logical ZX diagram in any CSS code.
Then we focus on two code transformation techniques: code morphing, a procedure that transforms a code while retaining its fault-tolerant gates, and gauge fixing, where complimentary codes (such as the Steane and quantum Reed-Muller codes) can be obtained from a common subsystem code. We provide explicit graphical derivations for these techniques and show how ZX and graphical encoder maps relate several equivalent perspectives on these code transforming operations.
CS/Math seminar - Igor Klep, University of Ljubljana
The talk will discuss state polynomials, i.e., polynomials in noncommuting variables and formal states of their products. The motivation behind this theory arises from the study of correlations in quantum networks. We will give a state analog of Artin's solution to Hilbert's 17th problem showing that state polynomials, positive over all matrices and matricial states, are sums of squares with denominators.
13-level Qudit Measurement Demonstrated in Trapped Ions
Abstract: Qudits are an interesting alternative to qubits for a number of algorithmic reasons, but for trapped ions they could be a path for scaling. Ion traps are running into limitations on the number of qubits they can confine in a single trap, and using more of the computational space available in the ions to make qudits is an attractive solution. We have proposed using trapped ion qudits in a previous paper, developing all of the necessary quantum information protocols for their implementation. Here, we present an experimental result of a 13-level qudit measurement with a fidelity of 91.3%. The protocol can be used to measure up to a 25-level qudit in barium. The error scaling is not inherent to the dimension of the qudit, so we can envision going to higher dimensions without a significant increase in error.
En français
This winter term, the Institute for Quantum Computing (IQC) welcomed seventeen elementary school classes to our Institute to learn about quantum information science and technology, as well as ion trapping.