Quantum Computing From Feynman’s Point of View

Quantum computing, in modern terms, represents a new era of technology. In this post, we explore the concept of quantum computing as envisioned by Richard Feynman, which aims at simulating physical world by harnessing quantum physics. By leveraging superposition, entanglement, and discreteness, it models complex systems beyond the reach of classical computers.

Feynman’s Quantum Principles

Feynman’s lecture in 1981, later published as the seminal paper “Simulating Physics with Computers” laid out the core principles and conceptual foundations of quantum computing paradigm. Feynman posed a fundamental challenge:

    “What kind of computer are we going to use to simulate physics?”
    “Can physics be simulated by a universal computer (locally interconnected)?” — [p. 467]

He then asked a deeper, even more visionary question:

      “What, in other words, is the universal quantum simulator? (assuming this discretization of space and time). If you had discrete quantum systems, what other discrete quantum systems are exact imitators of it, and is there a class against which everything can be matched?” — [p. 475]

These foundational questions gave rise to the essential framework of quantum computing centered around the following four key principles: 

Superposition: The Basis of Quantum Information

Feynman emphasized that quantum systems—even simple, discrete ones—can exist in superposed states. He illustrated this through systems with just two possible states: occupied or unoccupied.

    “Every finite quantum mechanical system can be described exactly such that at each point in space-time this system has only two possible base states. Either that point is occupied, or unoccupied.” — [p. 475]

He gave two canonical examples of such two-state systems:

• Spin-½ particles, such as electrons, where the two states represent spin-up and spin-down, analogous to occupied/unoccupied.
• Photon polarization, where a photon’s polarization can be classified into two states, such as horizontal and vertical polarization (linear polarization).

“Polarizations of photons, which is an example of a two-state system… When a photon comes, you can say it’s either x polarized or y polarized.” — [p. 481]

A notable feature of two-state systems is coherence—the property where the phase of one state determines the phase of the other, highlighting their quantum mechanical interconnection.

Entanglement: Nonlocal Correlation

To explain entanglement, Feynman described a two-photon correlation experiment, inspired by the Einstein-Podolsky-Rosen paradox. When two entangled photons are measured, one reveals information about the other—even when separated.

“When they’re [photons] separated, they must have the same pattern because you can determine what I’m going to get by measuring yours.” — [p. 484]

When two photons are entangled, their properties (like polarization) become linked, even when the photons are far apart in space. Once this entanglement is created, measuring one photon immediately reveals information about the other. This highlights how quantum information is nonlocal—a key feature in quantum computing and quantum communication.

Information Encoding

Feynman emphasized that, as in classical physics, each quantum particle carries two essential pieces of information—typically associated with position (x) and momentum (p). However, unlike in classical systems, these quantities cannot be simultaneously and precisely measured for the same particle due to Heisenberg’s Uncertainty Principle. In quantum mechanics, a state requires both position and momentum information, but these are probabilistic and non-commutative—measuring one inherently disturbs the other.

“States are described by a second-order device, with two informations (“position” and “velocity”). So we have to have two pieces of information associated with a particle, analogous to the classical situation, in order to describe configurations.” — [p. 477]

The “two pieces of information” reflects Wave-Particle Duality, where a quantum particle exhibits both wave-like and particle-like behaviors, requiring two complementary descriptions: (i) the wavefunction ψ(x), which captures the position-dependent amplitude and phase, and (ii) its Fourier transform ψ̃(p), which encodes the same information in momentum space—together forming a complementary quantum representation.

This dual encoding forms the basis for how quantum computers store and process information. Unlike classical systems that use single values, quantum systems represent their state using a complex-valued wavefunction, which encodes information of both amplitudes and phases across multiple possible outcomes of measurements.

Discretization: Digital Nature of Quantum Systems

Feynman also suggested that we might need to abandon the classical assumption of continuity, where variables vary continuously across space and time, in order to build quantum simulators:

“We might change the idea that space is continuous to the idea that space perhaps is a simple lattice… and that time jumps discontinuously.” — [paraphrased from p. 475]

This idea aligns well with digital computation and quantum logic, where the goal is to simulate nature using a limited and discrete set of computational elements such as finite number of bits and memory.

Conclusion

Ultimately, Feynman’s message is clear: nature is inherently quantum, not classical —  as he famously put it:

“… nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical, and by golly it’s a wonderful problem, because it doesn’t look so easy.” — [p. 486]