Welcome to the Institute for Quantum Computing

Math/CS Seminar - Joseph Slote, Caltech

ZOOM ONLY

An important challenge in quantum computing is to develop quantum circuit lower bound techniques beyond lightcone arguments. Towards this goal, we examine a circuit model formed from a shallow quantum circuit composed with a classical AC0 circuit and ask whether this model can compute parity. We then bridge ideas from Fourier analysis, info-theoretic cryptography, and nonlocal games to settle this question in several cases. We'll also discuss implications for a search-decision dichotomy in unstructured quantum advantage, a phenomenon that was recently understood in the context of query complexity: for unstructured (promise-free) query problems, exponential quantum advantage can exist for search problems but never for decision problems.

Based on https://arxiv.org/abs/2311.13679.

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.

IQC Seminar - Sarah Meng Li - University of Amsterdam, Centrum Wiskunde & Informatica (CWI)

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.