Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April...

Efficient Circuit Decompositions Using Intermediate QuditsJonathan M. Baker

University of Chicago

Fermilab Quantum Institute, April 24th 2020

Outline1. Basics of Multivalued Quantum Computing

2. Generalized Toffoli

3. Arithmetics Part 1

4. Qubit-Qudit Compression

From Qubits to QuditsClassically:

Bits - Trits -Dits -

From Qubits to QuditsClassically:

Bits - Trits -Dits -

Quantumly:Qubits - Qutrits - Qudits -

Logical Manipulation of Qudit StatesClassically Reversible Operations - Single Qudit Operators

Logical Manipulation of Qudit StatesClassically Reversible Operations - Controlled Qudit Operators

Logical Manipulation of Qudit StatesQutrit CSUM can be written using our set of gates

2-Control Toffoli

Nielsen and Chuang Gokhale et al. (https://arxiv.org/abs/1905.10481)

Generalized Toffoli

Intermediate Qutrits

Generalized Toffoli

Number of Ancilla (30 Controls)

Bridging the gap:

https://arxiv.org/abs/1904.01671

Generalized Toffoli

Gokhale et al. (https://arxiv.org/abs/1905.10481)

Generalized Toffoli Use:

Gokhale et al. (https://arxiv.org/abs/1905.10481)

Ripple Carry Adder

https://arxiv.org/abs/quant-ph/0410184

Ripple Carry Adder - w/ Qutrits

Adder with Temp. Qutrits

Problem: With only two bits, irreversible

Fix: Use Temp. Qutrits

Qubit-Qudit Compression

https://arxiv.org/pdf/2002.10592.pdf

Use Cases: Qubit-Qudit Compression

https://arxiv.org/abs/quant-ph/0406142

A Log Depth Adder (All Binary w/ Ancilla)

A Log Depth Adder (Temp. Qudits, No Ancilla)

Questions?

Efficient Circuit Decompositions Using Intermediate Qudits · Fermilab Quantum Institute, April...

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