efficient circuit decompositions using intermediate qudits · fermilab quantum institute, april...
TRANSCRIPT
![Page 1: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/1.jpg)
Efficient Circuit Decompositions Using Intermediate QuditsJonathan M. Baker
University of Chicago
Fermilab Quantum Institute, April 24th 2020
![Page 2: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/2.jpg)
Fermilab Quantum Institute, April 24th 2020
Outline1. Basics of Multivalued Quantum Computing
2. Generalized Toffoli
3. Arithmetics Part 1
4. Qubit-Qudit Compression
5. Arithmetics Part 2
![Page 3: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/3.jpg)
Fermilab Quantum Institute, April 24th 2020
Outline1. Basics of Multivalued Quantum Computing
2. Generalized Toffoli
3. Arithmetics Part 1
4. Qubit-Qudit Compression
5. Arithmetics Part 2
![Page 4: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/4.jpg)
Fermilab Quantum Institute, April 24th 2020
From Qubits to QuditsClassically:
Bits - Trits -Dits -
![Page 5: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/5.jpg)
Fermilab Quantum Institute, April 24th 2020
From Qubits to QuditsClassically:
Bits - Trits -Dits -
Quantumly:Qubits - Qutrits - Qudits -
![Page 6: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/6.jpg)
Fermilab Quantum Institute, April 24th 2020
Logical Manipulation of Qudit StatesClassically Reversible Operations - Single Qudit Operators
![Page 7: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/7.jpg)
Fermilab Quantum Institute, April 24th 2020
Logical Manipulation of Qudit StatesClassically Reversible Operations - Single Qudit Operators
![Page 8: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/8.jpg)
Fermilab Quantum Institute, April 24th 2020
Logical Manipulation of Qudit StatesClassically Reversible Operations - Single Qudit Operators
![Page 9: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/9.jpg)
Fermilab Quantum Institute, April 24th 2020
Logical Manipulation of Qudit StatesClassically Reversible Operations - Controlled Qudit Operators
![Page 10: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/10.jpg)
Fermilab Quantum Institute, April 24th 2020
Logical Manipulation of Qudit StatesQutrit CSUM can be written using our set of gates
![Page 11: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/11.jpg)
Fermilab Quantum Institute, April 24th 2020
Outline1. Basics of Multivalued Quantum Computing
2. Generalized Toffoli
3. Arithmetics Part 1
4. Qubit-Qudit Compression
5. Arithmetics Part 2
![Page 12: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/12.jpg)
Fermilab Quantum Institute, April 24th 2020
2-Control Toffoli
Nielsen and Chuang Gokhale et al. (https://arxiv.org/abs/1905.10481)
![Page 13: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/13.jpg)
Fermilab Quantum Institute, April 24th 2020
Generalized Toffoli
Nielsen and Chuang Gokhale et al. (https://arxiv.org/abs/1905.10481)
=
![Page 14: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/14.jpg)
Fermilab Quantum Institute, April 24th 2020
Generalized Toffoli
Nielsen and Chuang Gokhale et al. (https://arxiv.org/abs/1905.10481)
=
![Page 15: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/15.jpg)
Fermilab Quantum Institute, April 24th 2020
Generalized Toffoli
Intermediate Qutrits
![Page 16: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/16.jpg)
Fermilab Quantum Institute, April 24th 2020
Generalized Toffoli
Number of Ancilla (30 Controls)
Bridging the gap:
https://arxiv.org/abs/1904.01671
![Page 17: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/17.jpg)
Fermilab Quantum Institute, April 24th 2020
Generalized Toffoli
Gokhale et al. (https://arxiv.org/abs/1905.10481)
![Page 18: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/18.jpg)
Fermilab Quantum Institute, April 24th 2020
Generalized Toffoli Use:
Gokhale et al. (https://arxiv.org/abs/1905.10481)
![Page 19: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/19.jpg)
Fermilab Quantum Institute, April 24th 2020
Outline1. Basics of Multivalued Quantum Computing
2. Generalized Toffoli
3. Arithmetics Part 1
4. Qubit-Qudit Compression
5. Arithmetics Part 2
![Page 20: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/20.jpg)
Fermilab Quantum Institute, April 24th 2020
Ripple Carry Adder
https://arxiv.org/abs/quant-ph/0410184
![Page 21: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/21.jpg)
Fermilab Quantum Institute, April 24th 2020
Ripple Carry Adder - w/ Qutrits
![Page 22: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/22.jpg)
Fermilab Quantum Institute, April 24th 2020
Adder with Temp. Qutrits
![Page 23: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/23.jpg)
Fermilab Quantum Institute, April 24th 2020
Adder with Temp. Qutrits
![Page 24: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/24.jpg)
Fermilab Quantum Institute, April 24th 2020
Problem: With only two bits, irreversible
![Page 25: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/25.jpg)
Fermilab Quantum Institute, April 24th 2020
Fix: Use Temp. Qutrits
![Page 26: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/26.jpg)
Fermilab Quantum Institute, April 24th 2020
Fix: Use Temp. Qutrits
![Page 27: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/27.jpg)
Fermilab Quantum Institute, April 24th 2020
Fix: Use Temp. Qutrits
![Page 28: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/28.jpg)
Fermilab Quantum Institute, April 24th 2020
Adder with Temp. Qutrits
![Page 29: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/29.jpg)
Fermilab Quantum Institute, April 24th 2020
Outline1. Basics of Multivalued Quantum Computing
2. Generalized Toffoli
3. Arithmetics Part 1
4. Qubit-Qudit Compression
5. Arithmetics Part 2
![Page 30: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/30.jpg)
Fermilab Quantum Institute, April 24th 2020
Qubit-Qudit Compression
https://arxiv.org/pdf/2002.10592.pdf
![Page 31: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/31.jpg)
Fermilab Quantum Institute, April 24th 2020
Use Cases: Qubit-Qudit Compression
https://arxiv.org/pdf/2002.10592.pdf
![Page 32: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/32.jpg)
Fermilab Quantum Institute, April 24th 2020
Qubit-Qudit Compression
https://arxiv.org/pdf/2002.10592.pdf
![Page 33: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/33.jpg)
Fermilab Quantum Institute, April 24th 2020
Qubit-Qudit Compression
https://arxiv.org/pdf/2002.10592.pdf
![Page 34: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/34.jpg)
Fermilab Quantum Institute, April 24th 2020
Outline1. Basics of Multivalued Quantum Computing
2. Generalized Toffoli
3. Arithmetics Part 1
4. Qubit-Qudit Compression
5. Arithmetics Part 2
![Page 35: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/35.jpg)
Fermilab Quantum Institute, April 24th 2020
https://arxiv.org/abs/quant-ph/0406142
A Log Depth Adder (All Binary w/ Ancilla)
![Page 36: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/36.jpg)
Fermilab Quantum Institute, April 24th 2020
A Log Depth Adder (Temp. Qudits, No Ancilla)
https://arxiv.org/pdf/2002.10592.pdf
![Page 37: Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April 24th 2020 Outline 1. Basics of Multivalued Quantum Computing 2. Generalized Toffoli](https://reader033.vdocument.in/reader033/viewer/2022042621/5f64db28fec35d68bf562c0b/html5/thumbnails/37.jpg)
Fermilab Quantum Institute, April 24th 2020
Questions?