MC, 200 University Ave West, Room MC 5417
Waterloo, ON CA N2L 3G1
Supervisors: Thomas Jennewein and Norbert Lütkenhaus
Quantum-Nano Centre, 200 University Ave West, Waterloo, ON CA N2L 3G1 ZOOM ONLY
Quantum data access and quantum processing can make certain classically intractable learning tasks feasible. However, quantum capabilities will only be available to a select few in the near future. Thus, reliable schemes that allow classical clients to delegate learning to untrusted quantum servers are required to facilitate widespread access to quantum learning advantages. Building on a recently introduced framework of interactive proof systems for classical machine learning, we develop a framework for classical verification of quantum learning. We exhibit learning problems that a classical learner cannot efficiently solve on their own, but that they can efficiently and reliably solve when interacting with an untrusted quantum prover. Concretely, we consider the problems of agnostic learning parities and Fourier-sparse functions with respect to distributions with uniform input marginal. We propose a new quantum data access model that we call "mixture-of-superpositions" quantum examples, based on which we give efficient quantum learning algorithms for these tasks. Moreover, we prove that agnostic quantum parity and Fourier-sparse learning can be efficiently verified by a classical verifier with only random example or statistical query access. Finally, we showcase two general scenarios in learning and verification in which quantum mixture-of-superpositions examples do not lead to sample complexity improvements over classical data. Our results demonstrate that the potential power of quantum data for learning tasks, while not unlimited, can be utilized by classical agents through interaction with untrusted quantum entities.
Quantum-Nano Centre, 200 University Ave West, Room QNC 1201 Waterloo, ON CA N2L 3G1
In this talk, I will describe the use of entropic uncertainty relations in QKD security proofs. I will show how this proof method requires a bound on the classical statistics of the underlying quantum state, and thus ultimately reduces to a sampling problem. I will then describe how the sampling problem is addressed in the literature under certain unphysical assumptions on the QKD hardware. Finally, I will describe how these assumptions can be removed, thereby rendering this proof technique applicable to practical scenarios.
Quantum-Nano Centre, 200 University Ave West, Room QNC 0101 Waterloo, ON CA N2L 3G1
: Quantum compiling translates a quantum algorithm into a sequence of elementary operations. There exists a correspondence between certain quantum circuits and matrices over some number rings. This number-theoretic perspective reveals important properties of gate sets and leads to improved quantum compiling protocols. Here, we demonstrate several algebraic methods in quantum circuit characterization and optimization, based on my master’s research at IQC.
First, we design two improved synthesis algorithms for Toffoli-Hadamard circuits, achieving an exponential reduction in circuit size. Second, we define a unique normal form for qutrit Clifford operators. This allows us to find a set of relations that suffice to rewrite any qutrit Clifford circuit to its normal form, adding to the family of number-theoretic characterization of quantum operators.
Quantum-Nano Centre, 200 University Ave West, Room QNC 1201 + ZOOM Waterloo, ON CA N2L 3G1
We define a map from an arbitrary quantum circuit to a local Hamiltonian whose ground state encodes the quantum computation. All previous maps relied on the Feynman-Kitaev construction, which introduces an ancillary ‘clock register’ to track the computational steps. Our construction, on the other hand, relies on injective tensor networks with associated parent Hamiltonians, avoiding the introduction of a clock register. This comes at the cost of the ground state containing only a noisy version of the quantum computation, with independent stochastic noise. We can remedy this - making our construction robust - by using quantum fault tolerance. In addition to the stochastic noise, we show that any state with energy density exponentially small in the circuit depth encodes a noisy version of the quantum computation with adversarial noise. We also show that any ‘combinatorial state’ with energy density polynomially small in depth encodes the quantum computation with adversarial noise. This serves as evidence that any state with energy density polynomially small in depth has a similar property. As an application, we give a new proof of the QMA-completeness of the local Hamiltonian problem (with logarithmic locality) and show that contracting injective tensor networks to additive error is BQP- hard. We also discuss the implication of our construction to the quantum PCP conjecture, combining with an observation that QMA verification can be done in logarithmic depth.
Based on joint work with Anurag Anshu and Nikolas P. Breuckmann. (https://arxiv.org/abs/2309.16475)
Quantum-Nano Centre, 200 University Ave West, Room QNC 1201 Waterloo, ON CA N2L 3G1
The entanglement structure of quantum fields is of central importance in various aspects of the connection between spacetime geometry and quantum field theory. However, it is challenging to quantify entanglement between complementary regions of a quantum field theory due to the formally infinite amount of entanglement present at short distances. We present an operationally motivated way of analyzing entanglement in a QFT by considering the entanglement which can be transferred to a set of local probes coupled to the field. In particular, using a lattice approximation to the field theory, we show how to optimize the coupling of the local probes with the field in a given region to most accurately capture the original entanglement present between that region and its complement. This coupling prescription establishes a bound on the entanglement between complementary regions that can be extracted to probes with finitely many degrees of freedom.
Based on: J. High Energ. Phys. 2023, 58 (2023), arXiv:2301.08775
Research Advancement Center, 485 Wes Graham Way, Room 2009 Waterloo, ON N2L 6R2
Single-photon sources (SPSs) are an elementary building block for quantum technologies. An ideal SPS is deterministic, on-demand and produces exactly one photon per pulse. Additionally, desirable features include a high repetition rate, an all-electrical driving mechanism and compatibility with semiconductor manufacturing techniques. Despite great advances in the field of single photon emitters, an SPS with all the features outlined above remains elusive. In this talk, we will present our proposed SPS, consisting of a single-electron pump integrated in proximity to a lateral PN-junction, which would allow our SPS to meet all the criteria listed above. We discuss progress towards our goal, and also discuss an unconventional electroluminescence mechanism observed during recent experiments.
QNC building, 200 University Ave. Room QNC 1201 Waterloo
Understanding the dynamics of quantum many-body systems is one of the fundamental objectives of physics. The existence of an efficient quantum algorithm for simulating these dynamics with reasonable resource requirements suggests that this problem might be among the first practically relevant tasks quantum computers can tackle. Although an efficient classical algorithm for simulating such dynamics is not generally expected, the classical hardness of many-body dynamics has been rigorously proven only for certain commuting Hamiltonians. In this talk, I will show that computing the output distribution of quantum many-body dynamics is classically difficult, classified as #P-hard, also for a large class of non-commuting many-body spin Hamiltonians. Our proof leverages the robust polynomial estimation technique and the #P-hardness of computing the permanent of a matrix. By combining this with the anticoncentration conjecture of the output distribution, I will argue that sampling from the output distribution generated by the dynamics of a large class of spin Hamiltonians is classically infeasible. Our findings can significantly reduce the number of qubits required to demonstrate quantum advantage using analog quantum simulators.
QNC building, 200 University Ave. Room 1201, Waterloo
We use numerical optimal-control-theory methods to determine the minimum number of two-qubit CNOT gates needed to perform quantum state preparation and unitary operator synthesis for few-qubit systems. In the first set of calculations, we consider all possible gate configurations for a given number of qubits and a given number of CNOT gates, and we determine the maximum achievable fidelity for the specified parameters. This information allows us to identify the minimum number of gates needed to perform a specific target operation. It also allows us to enumerate the different gate configurations that can be used for a perfect implementation of the target operation. We find that there are a large number of configurations that all produce the desired result, even at the minimum number of gates. This last result motivates the second set of calculations, in which we consider only a small fraction of the super-exponentially large number of possible gate configurations for an increasing number of qubits. We find that the fraction of gate configurations that allow us to achieve the desired target operation increases rapidly as soon as the number of gates exceeds the theoretical lower bound for the required number of gates. As a result, a random search can be a highly efficient approach for quantum circuit synthesis. Our results demonstrate the important role that numerical optimal control theory can play in the development of quantum compilers.
Quantum key distribution (QKD) is on the verge of becoming a robust security solution, backed by security proofs that closely model practical implementations. As QKD matures, a crucial requirement for its widespread adoption is establishing standards for evaluating and certifying practical implementations, particularly against side-channel attacks resulting from device imperfections that can undermine security claims. Today, QKD is at a stage where the development of such standards is increasingly prioritized. This works aims to address some of the challenges associated with this task by focusing on the process of preparing an in-house QKD system for evaluation. We first present a consolidated and accessible baseline security proof for the one-decoy state BB84 protocol with finite-keys, expressed in a unified language. Building upon this security proof, we identify and tackle some of the most critical side-channel attacks by characterizing and implementing countermeasures both in the QKD system and within the security proof. In this process, we iteratively evaluate the risk of the individual attacks and re-assess the security of the system. Evaluating the security of QKD systems additionally involves performing attacks to potentially identify new loopholes. Thus, we also aim to perform the first real-time Trojan horse attack on a decoy state BB84 system, further highlighting the need for robust countermeasures. By providing a critical evaluation of our QKD system and incorporating robust countermeasures against side-channel attacks, our research contributes to advancing the practical implementation and evaluation of QKD as a trusted security solution.