RESEARCH PROJECTS
Below is a mix of research projects in quantum computing that I've worked on, listed in reverse chronological order.
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Surface-code inspired compilations
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Clifford Synthesis
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General Toffoli Synthesis
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QIP with NMR
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Bosonic Gaussian Quantum Channel
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Numerical Method for Schrödinger Equation
SURFACE-CODE INSPIRED COMPILATIONS
Models and novel compilation techniques via GHZ-state injection
"Willers" Yang, Patrick Rall
IBM Quantum, Feb 2023
Abstract: In superconducting architectures, limited connectivity remains a significant challenge for the synthesis and compilation of quantum circuits. We consider models of entanglement-assisted computation where long-range operations are achieved through injections of large GHZ states. These are prepared using ancillary qubits acting as an “entanglement bus,” unlocking global operation primitives such as multi-qubit Pauli rotations and fan out gates. We derive bounds on the circuit size for several well-studied problems, such as CZ circuit, CX circuit, and Clifford circuit synthesis. In particular, in an architecture using one such entanglement bus, we give an O(n³)-complexity synthesis scheme for arbitrary Clifford operations requiring at most 2n+1 layers of entangled-state-injections. In a square-lattice architecture with two entanglement buses, we show that a graph state can be synthesized using at most n/2 +O(1) layers of GHZ state injections, and Clifford operations require only 3n/2 + O(√n) layers of GHZ state injections.
CLIFFORD SYNTHESIS
State-of-the-art synthesis algorithms for Hadamard-free Clifford transformations
Dmitri Maslov, "Willers" Yang
IBM Quantum, Oct. 2022
Abstract: A Hadamard-free Clifford transformation is a circuit composed of quantum Phase P, CZ, and CNOT gates. It is known that such a circuit can be written as a three-stage computation, -P-CZ-CNOT-, where each stage consists only of gates of the specified type.
We show that a Hadamard-free Clifford operation can be implemented over the linear nearest neighbor achitecture with 2-qubit-gate-depth 5n, i.e., in the same depth as the -CNOT- stage alone. This implies the ability to implement arbitrary Clifford transformation over LNN in depth no more than 7n+2, improving the best previous upper bound of 9n. We also report heuristic evidence that on average a random uniformly distributed Hadamard-free Clifford transformation over n>6 qubits can be implemented with only a tiny additive constant overhead over all-to-all connected architecture compared to the best-known depth-optimized implementation of the -CNOT- stage alone. This suggests the reduction of the depth of Clifford circuits from 2n+O(log(n)) to 1.5n + O(log(n)) over unrestricted architectures.
GENERAL TOFFOLI SYNTHESIS
Practical synthesis of multiply-controlled-Toffoli gates achieving gate count and depth reduction with limited space.
"Willers" Muye Yang, Xinjie He, Drew Gao, James Woodcock
Research in Industrial Projects for Students (RIPS), Summer 2021
Abstract: Multiple control Toffoli gate (MCX) is a family of quantum gates that compute the bitwise product of n-1 control qubits and write the result to a target qubit. They function as an important computation primitive for quantum algorithms and arithmetics. There exist good synthesis algorithms using relative Toffoli gates; however, they also require at least ⌊(n−3)/2⌋ancillae.
We focus on optimizing Clifford + T implementations of MCX with respect to the number of controlled-not (CNOT) gates and T gates, as they are the most difficult to implement. We show 2n-2 and 3(n-1)/2 lower bounds for the CNOT cost of relative phase Toffoli gates (RTOFn, a set of gates phase equivalent to MCX). These will be the first set of lower bounds known for the CNOT cost of RTOFn. We also provide proof showing that the known implementation of RTOF4 is CNOT-optimal. Finally, we provide a systematic construction of TOFn which improves the current best-known implementations of TOFn in terms of CNOT-cost, T-cost, and Ancilla-count when access to ancillae is limited.
Paper (RIPS Final Report) Presentation (JMM 2022)
QIP WITH NMR
Experimental Demonstration of Quantum Advantage on Query Complexity
"Willers" Muye Yang
MIT Experimental Physics Laboratory, Fall 2021
Abstract: In this experiment, we demonstrated quantum advantage with respect to query complexity through the Deutch-Jozsa algorithm and Grover's search algorithm on a two-qubit quantum computer implemented using liquid-state NMR techniques. Specifically, we show that certain problems can be solved using one query to an unknown function on our quantum computer, whereas any classical algorithms require two queries in the worst case.
BOSONIC GAUSSIAN QUANTUM CHANNEL
Numerical Evidence to the Minimum Output Entropy
"Willers" Muye Yang, Giacomo De Palma
MIT RLE, funded under the MIT Undergraduate Research Opportunity Program, Summer 2020
We set out to develop a numerical algorithm to find possible counter-examples to the constrained minimum output conjecture for quantum gaussian broadcast channels. The conjecture states that for any natural number n, quantum Gaussian input states minimize the output entropy of the n-mode Gaussian quantum attenuators and amplifiers among all the input states with a given entropy. The conjecture is proven for the one-mode case. We implement a new algorithm to minimize the output entropy of a quantum channel with a constraint on the input entropy which has some interesting convergence behaviors that show evidence in support of the conjecture.
Paper in preparation
NUMERICAL METHOD FOR SCHRÖDINGER EQUATION
Solving Time Independent Schrödinger Equation with Airy’s Function and Numerov Method
"Willers" Muye Yang
Course Project for 18.303, Linear PDE, Analytics and Numerics, Spring 2019
Abstract: We give a numerical method to find solutions to the Time-Independent Schrödinger Equation (TISE) with arbitrary, non-decreasing potential well using its linear function approximation. We call this method the Airy Function's Approximation. The TISE can be solved piece-wisely using Airy functions and the Numerov integration scheme and is “stitched” together, producing a continuous and differentiable approximate solution.