Events

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]

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)

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

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.

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.

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

IQC Seminar - Ashutosh Marwah, University of Montreal

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

For a state $\rho_{A_1^n B}$, we call a sequence of states $(\sigma_{A_1^k B}^{(k)})_{k=1}^n$ an approximation chain if for every $1 \leq k \leq n$, $\rho_{A_1^k B} \approx_\epsilon \sigma_{A_1^k B}^{(k)}$. In general, it is not possible to lower bound the smooth min-entropy of such a $\rho_{A_1^n B}$, in terms of the entropies of $\sigma_{A_1^k B}^{(k)}$ without incurring very large penalty factors. In this paper, we study such approximation chains under additional assumptions. We begin by proving a simple entropic triangle inequality, which allows us to bound the smooth min-entropy of a state in terms of the R\'enyi entropy of an arbitrary auxiliary state while taking into account the smooth max-relative entropy between the two. Using this triangle inequality, we create lower bounds for the smooth min-entropy of a state in terms of the entropies of its approximation chain in various scenarios. In particular, utilising this approach, we prove approximate versions of the asymptotic equipartition property and entropy accumulation. In a companion paper, we show that the techniques developed in this paper can be used to prove the security of quantum key distribution in the presence of source correlations.

IQC Seminar - Jameson O'Reilly, Duke University

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

Trapped atomic ions are a leading candidate platform for quantum simulation and computing but system sizes are limited by motional mode crowding and transport overhead. Multiple reasonably-sized, well-controlled modules can be connected into one universal system using photonic interconnects, in which photons entangled with ions in each trap are collected into and detected in a Bell-state analyzer. The speed of these interconnects has heretofore been limited by the use of 0.6 NA objectives and the need to periodically pause entanglement attempts for recooling. In this work, we use a system with two in-vacuo 0.8 NA lenses on either side of an ion trap to collect 493 nm photons from barium ions and demonstrate the most efficient free-space ion trap photonic interconnect to date. In addition, we introduce an ytterbium ion as a sympathetic coolant during the entangling attempts cycle to remove the need for recooling, enabling a record photon-mediated entanglement rate between two trapped ions. The major remaining error source is imperfections in the photon polarization encoding, so we also develop a new protocol for remotely entangling two ions using time-bin encoded photons and present preliminary results of an experimental implementation. Finally, we prepare the first remote entangled state involving two barium ions in separate vacuum chambers.

Overparameterization and Expressivity of Realistic Quantum Systems

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

Quantum computing devices require exceptional control of their experimental parameters to prepare quantum states and simulate other quantum systems, in particular while subject to noise. Of interest here are notions of trainability, how difficult is it to classically optimize parameterized, realistic quantum systems to represent target states or operators of interest, and expressivity, how much of a desired set of these targets is our parameterized ansatze even capable of representing? We observe that overparameterization phenomena, where systems are adequately parameterized, are resilient in noisy settings at short times and optimization can converge exponentially with circuit depth. However fidelities decay to zero past a critical depth due to accumulation of either quantum or classical noise. To help explain these noise-induced phenomena, we introduce the notion of expressivity of non-unitary, trace preserving operations, and highlight differences in average behaviours of unitary versus non-unitary ensembles. We rigorously prove that highly-expressive noisy quantum circuits will suffer from barren plateaus, thus generalizing reasons behind noise-induced phenomena. Our results demonstrate that appropriately parameterized ansatze can mitigate entropic effects from their environment, and care must be taken when selecting ansatze of channels.

CS/Math Seminar - Yu Tong, Caltech

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

In the last few years a number of works have proposed and improved provably efficient algorithms for learning the Hamiltonian from real-time dynamics. In this talk, I will first provide an overview of these developments, and then discuss how the Heisenberg limit, the fundamental precision limit imposed by quantum mechanics, can be reached for this task. I will demonstrate how the Heisenberg limit requires techniques that are fundamentally different from previous ones, and the important roles played by quantum control and thermalization. I will also discuss open problems that are crucial to making these algorithms implementable on current devices.