CO$Φ$ - COmpiling PHotonics into dIgital quantum circuits

AI summary

Overview

Research area: Quantum computing, specifically the intersection of photonic (continuous-variable) quantum computing and qubit-based digital quantum circuits.

Technical level: Advanced. The paper assumes familiarity with quantum optics, Fock states, and gate-based quantum circuits.

Scope: The paper develops a Fock-space truncation method for mapping quantum-optical operations onto qubit circuits, provides explicit constructions for small truncations, and releases a compiler that translates photonic programs into OpenQASM.

What This Paper Is About

Photonic quantum computing and qubit-based digital quantum computing are usually treated as separate hardware paradigms with incompatible descriptions. This paper builds a bridge between them by approximating the infinite-dimensional state space of a single optical mode with a finite-dimensional Fock space, then expressing standard photonic operations as qubit-based quantum circuits. The goal is to let photonic circuits be simulated on ordinary digital quantum computers, with particular attention to low-photon-number Gaussian Boson Sampling.

Key Contributions

1. A truncation framework for mapping photonics to qubits. The authors introduce a finite Fock-space truncation of single-mode optical states as the key mechanism for encoding photonic information into qubit registers.
2. Qubit-circuit representations of core photonic operations. They derive circuit representations for the phase-rotation operator, the displacement operator, the squeezing operator, and the beam splitter.
3. Explicit circuit constructions for small truncations. Concrete quantum circuits are given for Fock-space truncation dimensions N = 2 and N = 4.
4. A practical compiler, COΦ. The authors release a Python-based tool that compiles Blackbird quantum-optics programs into qubit-based OpenQASM circuits using the truncated Fock-space encoding, available on GitHub.

Main Findings

• Bridging two paradigms is feasible: The abstract claims that quantum-optical systems can be mapped onto qubit-based circuits through Fock-space truncation, providing a common representation for photonic and digital approaches.
• Basic photonic operations have circuit representations: Representations were developed for phase rotation, displacement, squeezing, and beam splitting, forming a reusable toolkit for building photonic circuits out of qubit gates.
• Small truncations are worked out explicitly: Complete circuit constructions are presented for N = 2 and N = 4, giving concrete, checkable examples rather than only a general formalism.
• Benchmarking defines a usable regime: The authors report benchmarking the implemented operations and identify where the method applies and where it breaks down. The abstract does not state specific benchmark values, error rates, or resource counts.
• Low-photon Gaussian Boson Sampling is the highlighted use case: The method is described as especially relevant to simulating Gaussian Boson Sampling when photon numbers are small.
• A working tool accompanies the theory: COΦ demonstrates that the approach can be automated end-to-end, from a photonic program description to an OpenQASM circuit.

Methodology in Plain English

An optical mode can in principle hold any number of photons, which makes its state space infinite-dimensional and awkward to represent on a qubit machine. The researchers cap the photon number at a finite cutoff, turning the problem into a finite-dimensional one that a fixed number of qubits can encode. Within that capped space, they work out how each standard optical operation—rotating a phase, displacing a state, squeezing it, or combining two modes at a beam splitter—can be rebuilt from qubit gates. They write out these circuits explicitly for the smallest nontrivial cutoffs, test how well the rebuilt operations match their photonic counterparts, and use that testing to mark the boundaries of the method. Finally, they package the translation into a compiler that reads a photonic program and emits a qubit circuit description.

Why This Matters

The work gives researchers a route to run photonic algorithms on the qubit-based quantum computers that are most widely available, rather than requiring dedicated optical hardware. It also provides a common language for comparing the two paradigms.

Real-world and research applications:

• Simulating optical circuits on digital hardware: Testing photonic algorithms without building an interferometer.
• Low-photon Gaussian Boson Sampling: Exploring a problem of interest in photonic quantum advantage experiments at small photon numbers.
• Prototyping and education: Letting students and developers experiment with quantum optics through qubit simulators and familiar circuit tooling.
• Cross-platform compilation: Translating programs written for one hardware model into circuits for another, which supports portable quantum software.

Industry relevance: Most cloud-accessible quantum processors are qubit-based, while photonic systems remain specialized. A compiler that converts photonic programs into OpenQASM makes photonic algorithm development accessible on existing digital backends and fits into standard quantum software stacks.

Future Directions

• Scaling beyond small truncations: Extending the constructions from N = 2 and N = 4 to larger cutoffs and quantifying the resulting resource costs.
• Multi-mode and broader operation sets: Generalizing the encoding and compiler coverage to larger optical circuits and operations beyond the four treated here.
• Hardware validation: Running the compiled circuits on actual qubit devices to measure how truncation error and hardware noise combine.
• Refining the applicability boundary: Turning the reported benchmarking into practical guidance on which problems and photon regimes the method can handle.

Target Audience

Quantum computing researchers working on simulation, compilation, or hybrid hardware strategies; photonic and continuous-variable quantum specialists interested in porting their circuits to qubit machines; quantum software developers who use or extend Blackbird and OpenQASM toolchains; and graduate students studying the relationship between continuous-variable and discrete-variable quantum computing.

Authors’ abstract

Photonic and qubit-based (digital) approaches to quantum computing are largely regarded as separate paradigms. This article aims to bridge these paradigms by developing a method for mapping quantum-optical systems onto qubit-based quantum circuits. The key ingredient enabling this mapping is the introduction of a truncation of the Fock space describing single-mode optical states. Within this framework, representations of basic photonic operations are developed, including the phase-rotation operator, the displacement operator, the squeezing operator, and the beam splitter. Explicit quantum circuit constructions are provided for Fock-space truncations of dimension $N=2$ and $N=4$. We discuss benchmarking of the implemented operations and identify the regime of applicability and the limitations of the proposed method. The presented results can be used to simulate quantum optical circuits on qubit-based quantum computers, with special relevance to Gaussian Boson Sampling in the low-photon-number regime. To demonstrate the practical applicability of this approach, we complement the theoretical framework with a Python-based quantum programming tool CO$Φ$ that compiles Blackbird quantum-optics programs into qubit-based OpenQASM circuits using a truncated Fock-space encoding. The compiler is available on GitHub at https://github.com/Quantum-Cosmos-Lab/cophi.