Modular Computation and the Future of Quantum Computing

In his seminal 1959 lecture “There’s Plenty of Room at the Bottom,” Richard Feynman introduced the idea that quantum effects could someday be harnessed for computation. Since then, researchers have made major strides in realizing quantum computing. Among the most well-known breakthroughs is Shor’s algorithm, which theoretically enables a quantum computer to factor large numbers exponentially faster than classical methods—posing potential challenges to modern cryptographic systems.

Although labs have demonstrated small-scale implementations of Shor’s algorithm (e.g., factoring 143), quantum computing remains in its infancy. Its core principles—superposition, entanglement, and wavefunction collapse—require deep quantum physics to understand. And even for experts, much about quantum behavior remains counterintuitive.

One key point often overlooked is this: quantum computers do not perform arithmetic in the traditional digital sense. Qubits do not compute by manipulating binary numbers; rather, they evolve through quantum states until measurement collapses them into a classical result. These results are typically verified or post-processed by classical digital computers because quantum computation is inherently probabilistic, and results may vary from run to run.

This makes digital arithmetic—a mainstay of classical computing—surprisingly difficult for quantum systems. Quantum gates can simulate some arithmetic operations, but doing so is costly in terms of circuit depth and qubit resources. Some researchers have begun exploring modular arithmetic as a more natural fit for quantum computation, especially given its periodic and state-space properties.

But most quantum researchers have been steadfast in finding quantum states that are binary in nature.  In fact, a “qubit”, while capable of super-position, will finally collapse to a single bit of information.  As all researchers know binary, there is a tendency to pursue binary arithmetic, or at least binary representations.

At MaiTRIX, we believe a better alternative to binary arithmetic for quantum computation is residue number arithmetic. Residue arithmetic operates on digits that are carry-free and independent, making it uniquely suited to the isolated and localized nature of quantum operations. Unlike binary systems that rely on carry propagation and global interaction, residue number systems (RNS) allow for arithmetic on modular digits with minimal inter-qubit dependencies.

There are multiple ways residue arithmetic can be implemented in quantum systems:

• One method encodes residue digits in binary form, then maps them into qubit states.
• A more direct approach encodes the full residue digit (e.g., 0 to 127) directly into quantum states, bypassing binary encoding entirely.

This modular approach brings another key benefit: decoherence mitigation. Decoherence—the loss of quantum state integrity—is a fundamental challenge in quantum computing. It worsens with increased circuit depth, more entanglement, and longer computation times. Modular computation offers a promising strategy by reducing entanglement needs across digits. Since RNS arithmetic avoids carry chains, each digit can be processed in a relatively isolated circuit. This means larger word sizes can be built by scaling up small, low-noise modules rather than constructing monolithic, entangled structures.

An important future direction is the development of a quantum crossbar bus for modular systems. Such a bus could entangle or exchange digit-level states efficiently across a modular architecture—enabling large-scale modular operations without introducing significant decoherence from complex interconnects.

While our current work at MaiTRIX is focused on classical modular arithmetic systems using traditional bits—not qubits—the design principles we’re developing are directly transferable to quantum logic. Our residue-based ALUs, accumulators, and matrix multipliers are built to scale, isolate, and correct errors—features that align remarkably well with the constraints of quantum hardware.

Our long-term vision is that these ideas can inspire a new class of modular quantum circuits that bring quantum computing one step closer to performing robust, general-purpose arithmetic. The foundations are already forming—and we’re excited to contribute a modular blueprint for what’s ahead.