The standard approach to universal fault-tolerant quantum computing is to develop a general-purpose quantum error correction mechanism that can implement a universal set of logical gates fault-tolerantly. Given such a scheme, any quantum algorithm can be realized fault-tolerantly by composing the relevant logical gates from this set. However, we know that quantum computers provide a significant quantum advantage only for specific quantum algorithms. Hence, a universal quantum computer can likely gain from compiling such specific algorithms using tailored quantum error correction schemes. In this work, we take the first steps towards such algorithm-tailored quantum fault-tolerance. We consider Trotter circuits in quantum simulation, which is an important application of quantum computing. We develop a solve-and-stitch algorithm to systematically synthesize physical realizations of Clifford Trotter circuits on the well-known [[n,n−2,2]] error-detecting code family. Our analysis shows that this family implements Trotter circuits with optimal depth, thereby serving as an illuminating example of tailored quantum error correction. We achieve fault-tolerance for these circuits using flag gadgets, which add minimal overhead. The solve-and-stitch algorithm has the potential to scale beyond this specific example and hence provide a principled approach to tailored fault-tolerance in quantum computing.
The paper is available at: https://arxiv.org/abs/2404.11953. It is closely related to my prior work on the Logical Clifford Synthesis (LCS) algorithm: https://arxiv.org/abs/1907.00310, whose implementation is available at: https://github.com/nrenga/symplectic-arxiv18a.
*We strongly encourage attendees to use their full name (and if possible, their UMD credentials) to join the zoom session.*
Join Zoom Meeting
https://umd.zoom.us/j/9893676372?pwd=VVNOd2xNZ3FCblk4aFdTMjkzTllvQT09&om...
Meeting ID: 989 367 6372
Passcode: abc123
---
One tap mobile
+19294362866,,9893676372# US (New York)
+12532050468,,9893676372# US
---
Dial by your location
• +1 929 436 2866 US (New York)
• +1 253 205 0468 US
• +1 253 215 8782 US (Tacoma)
• +1 301 715 8592 US (Washington DC)
• +1 305 224 1968 US
• +1 309 205 3325 US
• +1 312 626 6799 US (Chicago)
• +1 346 248 7799 US (Houston)
• +1 360 209 5623 US
• +1 386 347 5053 US
• +1 507 473 4847 US
• +1 564 217 2000 US
• +1 646 931 3860 US
• +1 669 444 9171 US
• +1 669 900 6833 US (San Jose)
• +1 689 278 1000 US
• +1 719 359 4580 US
Meeting ID: 989 367 6372
Find your local number: https://umd.zoom.us/u/abF3cNNZ0B
---
Join by SIP
• [email protected]
---
Join by H.323
• 162.255.37.11 (US West)
• 162.255.36.11 (US East)
• 115.114.131.7 (India Mumbai)
• 115.114.115.7 (India Hyderabad)
• 213.19.144.110 (Amsterdam Netherlands)
• 213.244.140.110 (Germany)
• 103.122.166.55 (Australia Sydney)
• 103.122.167.55 (Australia Melbourne)
• 149.137.40.110 (Singapore)
• 64.211.144.160 (Brazil)
• 149.137.68.253 (Mexico)
• 69.174.57.160 (Canada Toronto)
• 65.39.152.160 (Canada Vancouver)
• 207.226.132.110 (Japan Tokyo)
• 149.137.24.110 (Japan Osaka)
Meeting ID: 989 367 6372
Passcode: 578842