Parity-Based Time-Bin Encoding Enabling SWAP Between Polarization and Time-Bin Qubits

summary

The gist

The gist: This work introduces a parity-based time-bin encoding that enables a deterministic SWAP between polarization and time-bin qubits on a single photon using standard optical components.

In short

The work introduces a parity-based time-bin encoding for single photons to enable deterministic swapping between polarization and time-bin qubits. This encoding maps logical states to even or odd multiples of a time spacing, allowing a physical delay of one spacing ($\Delta t$) to flip the logical time bin. This enables standard quantum gates like CNOTs, which compose into a full SWAP gate for routing degrees of freedom on a single photon.

Key concepts

Parity-Based Time-Bin Encoding: This encoding assigns logical states $|0\rangle_T$ and $|1\rangle_T$ to even and odd multiples of the time spacing $\Delta t$. This means that a physical delay of exactly one $\Delta t$ causes the photon to transition between these two logical states, providing a mechanism for controlled temporal qubit flips.
CNOT Operations Decomposition: The SWAP gate is decomposed into three sequential CNOT operations: $\text{SWAP} = ext{CNOT}_{P\rightarrow T} ext{CNOT}_{T\rightarrow P} ext{CNOT}_{P\rightarrow T}$ (or an equivalent sequence). This decomposition is crucial because it shows how the required polarization-time bin routing can be achieved using standard, physically realizable CNOT gates.
Physical Implementation of Gates: The paper details how the CNOT operations are realized using optical components. $\text{CNOT}_{T\rightarrow P}$ uses an Electro-Optic Modulator (EOM) to induce polarization rotation based on voltage, while $\text{CNOT}_{P\rightarrow T}$ utilizes a Polarization Beam Splitter (PBS) and a time delay ($\Delta t$) to achieve the necessary polarization-controlled temporal shift.

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This episode discusses

Parity-Based Time-Bin Encoding Enabling SWAP Between Polarization and Time-Bin Qubits · Paper Radio

The paper

Parity-Based Time-Bin Encoding Enabling SWAP Between Polarization and Time-Bin Qubits · Read on arXiv

Adam Sultan, Connor Kupchak

Carleton University

Multi-degree-of-freedom photonic quantum processing requires routing between degree-of-freedom (DOF) qubit encodings on a single photon. A SWAP between polarization and time-bin qubits is an advantageous primitive for such architectures, however conventional early/late time-bin encoding does not support bidirectional logical time-bin flips from late to early which limits the ability to implement certain quantum operations. We introduce a parity-based time-bin encoding in which logical T and T correspond to even and odd multiples of a spacing Δt, so that a physical delay of Δt implements T T. This encoding is the enabling ingredient that makes a polarization-controlled delay line implement CNOT P to T and aligns naturally with periodic refractive index modulation for CNOT T to P. Composing three such CNOT operations sequentially results in a deterministic SWAP between polarization and time-bin degrees of freedom. We quantify how EOM voltage errors reduce the polarization-flip probability and estimate timing requirements from modulator switching, detector resolution, and timing jitter, giving an illustrative timing budget.

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Parity-Based Time-Bin Encoding Enabling SWAP Between Polarization and Time-Bin Qubits".

Mira: The gist: This work introduces a parity-based time-bin encoding that enables a deterministic SWAP between polarization and time-bin qubits on a single photon using standard optical components.

Kai: First, who's behind it and why it matters.

Title and authors: Kai: So, this paper is called "Parity-Based Time-Bin Encoding Enabling SWAP Between Polarization and Time-Bin Qubits," and it's written by Adam Sultan and Connor Kupchak from Carleton University in Ottawa, Canada. I find the title pretty descriptive of what they’re doing.

Mira: Yeah, it sounds like they are proposing a way to actually route information between these two different kinds of qubits—polarization and time-bin—on a single photon, which is a really useful thing for building bigger systems.

Lev: Routing between DOFs on one photon is definitely the goal here; if you want to do multi-degree-of-freedom photonic processing, you need some kind of way to move information around between those different encodings.

Kai: Exactly, and conventional early or late time-bin encodings just don't let you flip the logical state back and forth in a bidirectional way.

Mira: That's the problem they are tackling; they introduce this parity-based encoding where even multiples of a spacing Delta t map to one logical time-bin, and odd multiples map to the other.

Lev: So, what does this parity mapping actually enable them to do physically?

The paper's summary: Kai: Basically, the core idea is that a physical delay of Delta t can now implement a logical qubit flip between those two time-bin states.

Mira: That’s the key part; they show that this encoding lets them design specific operations where a physical shift of Delta t corresponds to flipping the logical time-bin state.

Lev: So, what are the actual CNOT gates they're building with? Because that's where I get practical.

Kai: They decompose the SWAP gate into three sequential CNOT operations, which is a standard identity in quantum computing, and they show how those specific CNOTs work with their new encoding.

Mira: Specifically, they have a CNOTP to T operation that uses a polarization-controlled delay line implemented by a PBS-delay-PBS stage.

Lev: A physical delay line? How does that map to the logical operation you need?

Kai: It implements H⟩ even⟩ maps to H⟩ even⟩, but V⟩ even⟩ maps to V odd, which is a polarization controlled delay.

Mira: And then they have the CNOTT to P operation which uses an Electro-Optic Modulator, where a voltage applied to the EOM induces a polarization rotation.

Lev: So, you’ve got one gate using optical delay and another using light modulation? That sounds like they are trying to build these operations with standard components.

The paper's improvements: Kai: One of the big points they make is that this parity-based time-bin encoding makes each CNOT physically realizable using standard optical components.

Mira: Conventional encoding doesn't support bidirectional flips from late to early, but this new setup does allow for those necessary logical time-bin flips.

Lev: But what about the practical constraints? Does this mean we can just build it anywhere, or are there serious engineering headaches?

Kai: They do look at the timing requirements; they state that the Delta t spacing has to be much larger than the switching time and open time, specifically Delta t is greater than tauswitch plus tauopen.

Mira: They give a more practical engineering rule: Delta t should be greater than tauswitch plus tauopen plus det plus sigma jitter, where sigma jitter is the combined RMS timing jitter from the source trigger to the detector chain.

Lev: That gives us a concrete starting point for design, which they suggest is Delta t equal to one nanosecond, leading to an overall gate time of approximately two point five nanoseconds for that three-CNOT sequence.

Conclusion: Kai: So, to wrap up the paper "Parity-Based Time-Bin Encoding Enabling SWAP Between Polarization and Time-Bin Qubits," they've shown how parity mapping enables a deterministic SWAP between polarization and time-bin qubits on a single photon.

Mira: The real implication is that this provides a concrete routing primitive for multi-degree-of-freedom photonic circuits, like building something such as a polarization Toffoli gate.

Lev: It's good to see them tackle the physical realization with standard optics, because building it on real hardware is always the hardest part.

Kai: Exactly; they successfully composed three sequential CNOT operations using this parity encoding to achieve that deterministic SWAP between polarization and time-bin degrees of freedom.

Mira: So, in short, they solved the problem of needing bidirectional logical time-bin flips by using a parity grid instead of simple early or late arrival times.

Lev: For me, the practical aspect is that setting Delta t to one nanosecond gives us a realistic target for gate speeds when we factor in all the timing jitter and detector noise.

Kai: Yeah, it sets a clear benchmark for how fast we can actually expect these operations to run on real hardware.

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