Current undergraduate students

Designing a precision gravitational experiment and budgeting uncertainties

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

Neutrons have a long history at the forefront of precision metrology. Following in the footsteps of the first experiment that measured the effect of gravity on a quantum particle (the C.O.W. experiment), we aim to generate structured neutron momentum profiles and apply these states to measure the gravitational constant, big-G. The significant discrepancy between modern big-G experimental results underscores the need for new experiments whose systematic uncertainties can be decoupled from existing techniques. Previously, perfect-crystal neutron interferometers were used to measure local gravitational acceleration, little-g, unfortunately, the low neutron flux (a few neutrons per second) of these devices makes them impractical for precision measurements of big-G. The recently demonstrated Phase-Grating Moiré Interferometer (PGMI) offers an increase in neutron flux of several orders of magnitude while preserving the large interferometer area, and thus the sensitivity, of a perfect-crystal interferometer. This device possesses a set of systematic uncertainties that are independent from those in existing techniques that measure big-G. In this talk, I will discuss the feasibility of measuring big-G using a neutron PGMI apparatus with a test mass on the order of 1 tonne. Further, I will address how we can optimize this setup to maximize the phase shift from a 1-tonne mass and quantify the various sources of uncertainty in the proposed experiment.

Stable and Localized Emission from Ambipolar Dopant-Free Lateral p-n Junctions

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

Combining the architectures of a dopant-free lateral p-n junction and a single-electron pump in a GaAs/AlGaAs heterostructure material system could yield high-rate, electrically-driven quantum emitters with performances surpassing the competition in quantum sensing, communication and cryptography. Observed drawbacks of the dopant-free p-n junctions are a rapid decay in electroluminescence during operation, as well as delocalized emission that lowers the measured quantum efficiency. This talk details novel measurement protocols and gate architectures implemented by us to overcome these challenges.

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

Clifford gates are ubiquitous in quantum computing. We consider the multiqudit analog for arbitrary d>1, which for example, includes the qudit Fourier transform. In this talk, we discuss the structure of the multiqudit projective Clifford group and give a high-level overview of a Clifford-based functional programming language whose underlying type system incorporates the resulting encoding scheme for projective Cliffords. This is joint work with Jennifer Paykin.

Fermionic encodings: BK Superfast, ternary trees, and even fermionic encodings

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

We give an introduction to fermionic encoding schemes applicable in the context of quantum simulation of fermionic systems in condensed matter physics, lattice gauge theories, and in quantum chemistry.
 
For this we will focus on the circuit depth overhead for a variety of constructions of fermionic encodings, more precisely in terms of their weight given by the choice of encoding within the Pauli group, and as such also in terms of their circuit depth due to multi-qubit rotation gates.
 
In particular we will introduce the Fenwick tree encoding due to Bravyi and Kitaev, as well as an optimal all-to-all encoding scheme in terms of ternary trees due to Jiang et al, and put those in perspective with the well-known fermionic encoding given by the Jordan-Wigner transformation. Such encoding schemes of fermionic systems with all-to-all connectivity become relevant especially in the context of molecular simulation in quantum chemistry.
 
We then further discuss the encoding of the algebra of even fermionic operators, which becomes particularly handy in the estimation of ground state energies for complex materials and their phase transitions in condensed matter physics.
 
In particular, we will introduce here the so-called Bravyi--Kitaev superfast encoding for the algebra of even fermionic operators, as well as the compact encoding due to Klassen and Derby as a particular variant thereof. These encoding schemes require the further use of stabilizer subspaces and so of fault-tolerant encoding schemes for their practical implementation for the purpose of quantum simulation. We then finish with a further improvement, the so-called supercompact encoding, due to Chen and Xu. In particular, we will focus here on its code parameters (more precisely its encoding rate and code distance) and put those in perspective with the previous compact encoding due to Klassen and Derby.
 
This talk is meant as an expository talk on available encoding schemes for fermionic systems, together with their best practices for the purpose of quantum simulations.

Entangled photon source for a long-distance quantum key distribution

Remote

Variational methods for quantum sensing

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

The precise estimation of unknown physical quantities is foundational across science and technology. Excitingly, by harnessing carefully-prepared quantum correlations, we can design and implement sensing protocols that surpass the intrinsic precision limits imposed on classical approaches. Applications of quantum sensing are myriad, including gravitational wave detection, imaging and microscopy, geoscience, and atomic clocks, among others.

However, current and near-term quantum devices have limitations that make it challenging to capture this quantum advantage for sensing technologies, including noise processes, hardware constraints, and finite sampling rates. Further, these non-idealities can propagate and accumulate through a sensing protocol, degrading the overall performance and requiring one to study protocols in their entirety.

In recent work [1], we develop an end-to-end variational framework for quantum sensing protocols. Using parameterized quantum circuits and neural networks as adaptive ansätze of the sensing dynamics and classical estimation, respectively, we study and design variational sensing protocols under realistic and hardware-relevant constraints. This seminar will review the fundamentals of quantum metrology, cover common sensing applications and protocols, introduce and benchmark our end-to-end variational approach, and conclude with perspectives on future research.

[1] https://arxiv.org/abs/2403.02394

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.

Rajibul Islam
Faculty, Institute for Quantum Computing
Associate Professor, Department of Physics and Astronomy, University of Waterloo
Co-founder, Open Quantum Design

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

Quantum computing promises to advance our computational abilities significantly in many high-impact research areas. In this period of rapid development, the experimental capabilities needed to build quantum computing devices and prototypes are highly specialized and often difficult to access. In this public talk, we'll discuss how to build quantum computing devices one atom a time using the ion-trap approach. We'll show how we build quantum bits out of individually isolated atoms, explore how we use them to simulate other complex systems, and showcase how we're building open-access hardware to advance research in this exciting field.

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.