[Paper Review] Classical Computation by Quantum Bits

Bobby Antonio, J. Randall+3 more|arXiv (Cornell University)|Sep 11, 2015

Quantum Computing Algorithms and Architecture5 references3 citations

TL;DR

This paper proposes a method to implement classical reversible logic gates—specifically the Toffoli and Fredkin gates—using a single time-independent 3-qubit Hamiltonian with only nearest-neighbor two-body interactions, enabling dissipation-free, atomic-scale classical computation. The approach achieves universal classical logic with minimal overhead by leveraging coherent quantum dynamics without requiring auxiliary systems or long-range couplings, and demonstrates composability into larger circuits like a half-adder.

ABSTRACT

Atomic-scale logic and the minimization of heating (dissipation) are both very high on the agenda for future computation hardware. An approach to achieve these would be to replace networks of transistors directly by classical reversible logic gates built from the coherent dynamics of a few interacting atoms. As superpositions are unnecessary before and after each such gate (inputs and outputs are bits), the dephasing time only needs to exceed a single gate operation time, while fault tolerance should be achieved with low overhead, by classical coding. Such gates could thus be a spin-off of quantum technology much before full-scale quantum computation. Thus motivated, we propose methods to realize the 3-bit Toffoli and Fredkin gates universal for classical reversible logic using a single time-independent 3-qubit Hamiltonian with realistic nearest neighbour two-body interactions. We also exemplify how these gates can be composed to make a larger circuit. We show that trapped ions may soon be scalable simulators for such architectures, and investigate the prospects with dopants in silicon.

Motivation & Objective

• To develop a minimal, low-dissipation classical logic architecture using atomic-scale qubits.
• To realize universal classical reversible gates (Toffoli and Fredkin) using only a single time-independent 3-qubit Hamiltonian with realistic nearest-neighbor interactions.
• To avoid auxiliary systems, levels, or long-range couplings, ensuring experimental feasibility.
• To demonstrate composability of such gates into larger classical circuits, such as a half-adder.
• To show that fault-tolerant classical computation is achievable with low overhead despite inherent error rates.

Proposed method

• Design a time-independent 3-qubit Hamiltonian with nearest-neighbor two-body interactions to implement the Toffoli and Fredkin gates via coherent quantum evolution.
• Use rotating frame transformations to map AC pulses into effective time-independent Hamiltonians, preserving gate unitarity for classical inputs and outputs.
• Implement gate operations using selective addressing on qubit arrays, with frequency-selective pulses to conditionally flip target qubits based on control qubit states.
• Compose larger circuits (e.g., half-adder) by cascading multiple such gates using sequential pulses and appropriate coupling strengths.
• Utilize classical error correction (e.g., parity protection) between gates to maintain reliability despite qubit decoherence and gate errors.
• Validate feasibility in trapped ions and silicon donor systems, showing compatibility with existing quantum hardware platforms.

Experimental results

Research questions

• RQ1 Can universal classical reversible logic be implemented using only a single time-independent 3-qubit Hamiltonian with nearest-neighbor interactions?
• RQ2 Is it possible to achieve Toffoli and Fredkin gates without auxiliary qubits, levels, or long-range couplings?
• RQ3 Can such gates be composed into larger classical circuits like a half-adder using standard quantum control techniques?
• RQ4 What is the accuracy and error threshold of these gates in realistic physical implementations?
• RQ5 Can classical error correction suffice to maintain reliability despite decoherence, given that superpositions are not required between gates?

Key findings

• The Toffoli and Fredkin gates can be implemented using a single time-independent 3-qubit Hamiltonian with only nearest-neighbor two-body interactions, satisfying all design constraints.
• The proposed gates are approximate but accurate enough for classical computation, with error rates below the 1/6 threshold required for reliable classical logic with fault-tolerant coding.
• A half-adder circuit is successfully realized using two Toffoli gates and two frequency-selective pulses, demonstrating circuit composability.
• The use of rotating frames allows AC pulses to implement effective time-independent Hamiltonians, preserving gate functionality without affecting classical outcomes.
• Trapped ions and silicon donor systems are viable platforms for implementing these gates, with error thresholds met in donor-based realizations.
• Decoherence between gates is acceptable since inputs and outputs are classical bits, eliminating the need for error correction during gate intervals.