Advice on Schools to Target//Applied Math

[RadioactiveMonkey]

Hi,

I am currently considering doing a PhD or masters degree in applied math (or pure math or physics, whatever program I can get into that deals with quantum computing). It's rather difficult to get a grasp on what schools to target, as the profiles of applicants seem all over the board.  I'm particularly interested in doing work on quantum computing, although I also know many universities house this research in their physics departments.  

Target Programs: Waterloo, Cambridge, UT Austin, Cal, UCSB, Oxford (are these too much of reach)?

Undergraduate Institution: Large State School

Major: Applied Mathematics

GPA: 3.8

Type of Student: Domestic white Male

Graduate Institution: N/A

GRE Score: 
163V/170Q/5.0W 

Subject: no locations available to take it until April

Relevant Classes:

I have low grades in Diff Eq and Linear Algebra 1 due to shirking homework assignments when I wasn't a mathematics major (I was frequently preoccupied with CS assignments).  The Quantum grade is low because of covid; I was on track for a high A prior to moving online.  

Cal III (A), Two years of CS courses (A's), Linear Algebra (B), Differnetial Equations (B), Probabilty /MathStat1 (A), Mathematical Statistics 2 (A), Honors Real Analysis 1 (A), Topology (A), Combinatorics (A), Honors Linear Algebra II (A), Honors Quantum Computing and Information Theory (B), Graduate Abstract Algebra (Fall), Graduate Analysis of Algorithms (Fall), Honors Real Analysis 2 (Fall, may see if I can take the graduate version), Differential Geometry (Fall).  

Research Experience: 

Not math research, but I've done some research on radiation effects on microprocessors as part of an internship with NASA for two summers.  May be seen as slightly relevant for quantum computing, as radiation is a source of decoherence that is difficult to isolate.

Work Experience: 

Undergrad teaching fellowship for the basic E&M course.

NASA

Letters: 

Average - Above Average?

I can get two good letters from professors at the top of their fields, one who publishes papers in QC.  I can also get a good letter from my mentor at NASA, although I'm not sure how good of an idea this would be for a math program.  He has an undergraduate degree in math and physics, and a PhD in physics, and he's shared several of my ideas with his collaborators in Brazil to work on.

 

Am I being too ambitious with the schools I'm looking at?  Is it hopeless to get into a PhD program if I can't take the math subject test?  Any suggestions on programs to apply to, or general advice would be greatly appreciated.