Seminar

Improving the Fidelity of CNOT Circuits on NISQ Hardware

Quantum-Nano Centre, 200 University Ave West, Room QNC 1201 Waterloo, ON CA N2L 3G1

We introduce an improved CNOT synthesis algorithm that considers nearest-neighbour interactions and CNOT gate error rates in noisy intermediate-scale quantum (NISQ) hardware. Our contribution is twofold. First, we define a \Cost function by approximating the average gate fidelity Favg. According to the simulation results, \Cost fits the error probability of a noisy CNOT circuit, Prob = 1 - Favg, much tighter than the commonly used cost functions. On IBM's fake Nairobi backend, it fits Prob with an error at most 10^(-3). On other backends, it fits Prob with an error at most 10^(-1). \Cost accounts for the machine calibration data, and thus accurately quantifies the dynamic error characteristics of a NISQ-executable CNOT circuit. Moreover, it circumvents the computation complexity of calculating Favg and shows remarkable scalability. 

Second, we propose an architecture-aware CNOT synthesis algorithm, NAPermRowCol, by adapting the leading Steiner-tree-based synthesis algorithms. A weighted edge is used to encode a CNOT gate error rate and \Cost-instructed heuristics are applied to each reduction step. Compared to IBM's Qiskit compiler, it reduces \Cost by a factor of 2 on average (and up to a factor of 8.8). It lowers the synthesized CNOT count by a factor of 13 on average (up to a factor of 162). Compared with algorithms that are noise-agnostic, it is effective and scalable to improve the fidelity of CNOT circuits. Depending on the benchmark circuit and the IBM backend selected, it lowers the synthesized CNOT count up to 56.95% compared to ROWCOL and up to 21.62% compared to PermRowCol. It reduces the synthesis \Cost up to 25.71% compared to ROWCOL and up to 9.12% compared to PermRowCol. NAPermRowCol improves the fidelity and execution time of a synthesized CNOT circuit across varied NISQ hardware. It does not use ancillary qubits and is not restricted to certain initial qubit maps. It could be generalized to route a more complicated quantum circuit, and eventually boost the overall efficiency and accuracy of quantum computing on NISQ devices. 

Joint-work with: Dohun Kim, Minyoung Kim, and Michele Mosca

The Clifford theory of the n-qubit Clifford group

Quantum-Nano Centre, 200 University Ave West, Room QNC 1201 Waterloo, ON CA N2L 3G1

The n-qubit Pauli group and its normalizer the n-qubit Clifford group have applications in quantum error correction and device characterization. Recent applications have made use of the representation theory of the Clifford group. We apply the tools of (the coincidentally named) Clifford theory to examine the representation theory of the Clifford group using the much simpler representation theory of the Pauli group. We find an unexpected correspondence between irreducible characters of the n-qubit Clifford group and those of the (n + 1)-qubit Clifford group. This talk will rely on the explanation of Clifford theory given last week.

A quick introduction to Clifford theory

Quantum-Nano Centre, 200 University Ave West, Room QNC 1201 Waterloo, ON CA N2L 3G1

Clifford theory studies the connection between representations of a group and those of its normal subgroups. In recent work, I examined the Clifford theory of the Clifford group to determine parts of its character table for future applications. The goal of this talk is to introduce the representation theory and Clifford theory of finite groups sufficiently to understand next week's talk when I will explain the Clifford theory of the n-qubit Clifford group. Note that these are two distinct Cliffords. I may also briefly discuss the applications of Clifford theory in quantum error correction, time permitting.

Research Advancement Centre, 475 Wes Graham Way, Room RAC 2009, Waterloo, ON, CA N2L 6R2

Unruh phenomena and thermalization for qudit detectors

Quantum-Nano Centre, 200 University Ave West, Room QNC 1201 Waterloo, ON CA N2L 3G1

The Unruh effect is the flat space analogue to Hawking radiation, describing how an observer in flat spacetime perceives the quantum vacuum state to be in a thermal state when moving along a constantly accelerated trajectory. This effect is often described operationally using the qubit-based Unruh-DeWitt detector.

We study Unruh phenomena for more general qudit detectors coupled to a quantized scalar field, noting the limitations to the utility of the detailed balance condition as an indicator for Unruh thermality of higher-dimensional qudit detector models. We illustrate these limitations using two types of qutrit detector models based on the spin-1 representations of SU(2) and the non-Hermitian generalization of the Pauli observables (the Heisenberg-Weyl operators).

[2309.04598] Unruh phenomena and thermalization for qudit detectors (arxiv.org)

Tight bounds for Pauli channel learning with and without entanglement

Quantum Nano Centre, 200 University Ave West, Room QNC 1201
Waterloo, ON CA N2L 3G1

Quantum entanglement is a crucial resource for learning properties from nature, but a precise characterization of its advantage can be challenging. In this work, we consider learning algorithms without entanglement as those that only utilize separable states, measurements, and operations between the main system of interest and an ancillary system. Interestingly, these algorithms are equivalent to those that apply quantum circuits on the main system interleaved with mid-circuit measurements and classical feedforward. Within this setting, we prove a tight lower bound for Pauli channel learning without entanglement that closes the gap between the best-known upper bound. In particular, we show that Θ(n^2/ε^2) rounds of measurements are required to estimate each eigenvalue of an n-qubit Pauli channel to ε error with high probability when learning without entanglement. In contrast, a learning algorithm with entanglement only needs Θ(1/ε^2) copies of the Pauli channel. Our results strengthen the foundation for an entanglement-enabled advantage for Pauli noise characterization. We will talk about ongoing experimental progress in this direction.

Reference: Mainly based on [arXiv: 2309.13461]

Quantum Nano Centre, 200 University Ave West, Room QNC 1201
Waterloo, ON CA N2L 3G1

Two randomly selected audience members will get the opportunity to present their work on the whiteboard for 20-minutes each.

IQC Seminar - Jong-Souk Yeo, Yonsei University

Quantum Nano Centre, 200 University Ave West, Room QNC 0101
Waterloo, ON, CA N2L 3G1

Biomimetic or nature-Inspired technologies are referring to the emerging fields where innovations are strongly inspired by the wisdom from nature or biological systems. Multiple levels of approaches are feasible from nature-inspiration – adaptation of how nature works, adoption of what nature provides, or replication of natural processes and functionalities for eco-friendly, sustainable, and highly efficient technologies. In this talk, nature-inspired approaches will be introduced for the nano-bio and nano-IT convergence research in the areas of nanostructure-cell interactions [1], nano-bio sensorics [2], biomimetic optical nanostructures [3], stretchable electronics [4], quantum plasmonics [5], and neuromorphic semiconductor technologies. Along with the research, recent efforts at Yonsei University will be introduced about the School of Integrated Technology where research and education are organically integrated for the technology convergence, and Yonsei Science Park where innovation ecosystem is established for IT-Bio Cluster Hub hosting Global Bio Campus and IBM quantum computer. This research was supported by the MSIT (Ministry of Science and ICT), Korea, under the ICT Consilience Creative program (IITP-2019-2017-0-01015) supervised by the IITP (Institute for Information & communications Technology Planning & Evaluation), the Ministry of trade, Industry and Energy (MOTIE) and Korea Institute for Advancement of Technology (KIAT) through the International Cooperative R&D program (Project No. P0019630) and by the Human Frontier Science Program (RGP0047/2019).

Tracial embedded strategy: lifting MIP* tricks to MIPco

Quantum Nano Centre, 200 University Ave West, Room QNC 1201
Waterloo, ON CA N2L 3G1

Quantum non-local games have been an important object of study for the operator algebra and computer science community due to the recent ground-breaking result MIP*=RE. Although the majority of the study has been focused on the tensor product model in the non-local games literature recently, the commuting operator model is another model that is also considered in the non-local literature, and the difference between these two models forms the basis for disproving the famous Connes embeddings conjecture. In this talk, I will introduce a new set of strategies for the commuting operator model, the tracial embedded strategy, and sketch the proof that every strategy in the commuting operator model can be approximated by this set of strategies. Using this new characterization, I will present some similarities between the tensor product model and the commuting operator model in the complexity theory realm. This talk is based on the paper "Almost synchronous correlation in the commuting operator model".

Computational Entanglement Theory

Quantum Nano Centre, 200 University Ave W, Room QNC 1201
Waterloo, ON, CA N2L 3G1

Quantum entanglement is an important resource that contributes to the potential of quantum computers over classical computers. It turns out to be an interesting idea to quantify entanglement in states, and there are different approaches to this. We can, for example, consider the number of Bell states that are required to approximately produce a given state or the number of Bell states that can be produced from the state - these correspond to the 'entanglement cost’ and ‘distillable entanglement' respectively. Throughout this, we bear in mind a picture where Alice (A) and Bob (B) own a shared state, and are only able to perform LOCC operations on their respective systems. In practice, however, computational complexity must be taken into account. I will explain some recent developments towards taking computational complexity into account for these operational measures, as well as introducing pseudo-entanglement, and hopefully some quantum cryptography.

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