Seminar

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.

CS/MATH Seminar - Kieran Mastel from IQC ZOOM + IN PERSON

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

The recent MIP*=RE theorem of Ji, Natarajan, Vidick, Wright, and Yuen shows that the complexity class MIP* of multiprover proof systems with entangled provers contains all recursively enumerable languages. In prior work Grilo, Slofstra, and Yuen showed (via a technique called simulatable codes) that every language in MIP* has a perfect zero knowledge (PZK) MIP* protocol.  The MIP*=RE theorem uses two-prover one-round proof systems, and hence such systems are complete for MIP*. However, the construction in Grilo, Slofstra, and Yuen uses six provers, and there is no obvious way to get perfect zero knowledge with two provers via simulatable codes. This leads to a natural question: are there two-prover PZK-MIP* protocols for all of MIP*?

In this talk we answer the question in the affirmative. For the proof, we use a new method based on a key consequence of the MIP*=RE theorem, which is that every MIP* protocol can be turned into a family of boolean constraint system (BCS) nonlocal games. This makes it possible to work with MIP* protocols as boolean constraint systems, and in particular allows us to use a variant of a construction due to Dwork, Feige, Kilian, Naor, and Safra which gives a classical MIP protocol for 3SAT with perfect zero knowledge. To show quantum soundness of this classical construction, we develop a toolkit for analyzing quantum soundness of reductions between BCS games, which we expect to be useful more broadly. This talk is based on joint work with William Slofstra

IQC Seminar - Alexander George-Kennedy, Georgia Tech

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

Protecting quantum information against noise is a widespread goal in quantum computation. In addition to implementing quantum error correcting codes, classical pre-processing steps of circuit optimization and qubit routing can greatly increase the fidelity of the result of a quantum computation. Prior work has shown that neural networks and/or reinforcement learning can be used to discover quantum error correcting codes, perform qubit routing optimized for circuit depth, and find optimal points to insert dynamical decoupling pulse sequences in a quantum circuit. We extend prior work by creating a deep reinforcement learning directed transpiler. We treat the problem of qubit routing and circuit optimization together, and can regard it as a single-player “game,” where the objective is minimizing the output circuit's estimated noise, subject to the connectivity constraints of the architecture. The “moves” in this game available to the transpiler are selecting the qubit layout, introducing SWAP gates subject to architecture constraints, and rewriting the circuit according to equivalency rules (such as introducing dynamical decoupling sequences, or simply optimizing away repeated self-adjoint gates). We train a transpiler for a specific quantum device, in our experiments, each of the available 5-qubit IBM devices, crucially including the reported error rates per gate per qubit per device as part of the transpiler training data. Running the transpilers on a series of random circuits across different devices, we compare the transpiler output circuits with IBM's transpiler outputs. We find an average improvement of 17% reduction in output error rate compared to the IBM transpiler. This is an improvement on prior work that also uses a neural network as a noise-indicating objective function, but with no explicit loading of device error rates, a different vectorization of circuits, and a greedy circuit rewrite policy. Our work is ongoing, as we intend to extend the transpiler's capability in the vein of prior work to construct error correcting codes during optimization.

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.

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

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.

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.

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