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A quantum Fredkin gate
Raj B. Patel, Joseph Ho, Franck Ferreyrol, Timothy C. Ralph, Geoff J. Pryde
TL;DR
Scaling quantum computers requires logic gates that can be chained into larger circuits, yet the quantum Fredkin gate had not been demonstrated. This work uses photonic qubit logic and path-mode entanglement to implement the gate, achieving high logical-basis accuracy and record photonic GHZ-state fidelities.
Problem
Scaling quantum circuits is difficult because chaining many gates requires sufficiently precise control of enough quantum systems, exemplified by the Fredkin gate’s requirement for at least five two-qubit gates in the standard circuit model.
Method
The experiment uses linear optics and path-mode entanglement to add control to a SWAP operation, implementing a quantum Fredkin gate without ancilla photons or decomposition into two-qubit gates.
Results
The experiment demonstrates the first quantum Fredkin gate, with 96 ± 4% logical-basis overlap and photonic GHZ-state fidelities up to 0.90 ± 0.01.
Takeaways & Limitations
The gate operates coherently on superposition states, generates genuine tripartite entanglement with the highest reported photonic GHZ-state fidelities, and supports quantum-state characterisation without quantum state tomography.
Takeaways & Limitations
For completely general circuits placing Fredkin gates at arbitrary locations, the C-path methodology may be necessary, at the cost of additional resources and success probability.
Abstract
from arXiv · showhide
Key to realising quantum computers is minimising the resources required to build logic gates into useful processing circuits. While the salient features of a quantum computer have been shown in proof-of-principle experiments, difficulties in scaling quantum systems have made more complex operations intractable. This is exemplified in the classical Fredkin (controlled-SWAP) gate for which, despite theoretical proposals, no quantum analogue has been realised. By adding control to the SWAP unitary, we use photonic qubit logic to demonstrate the first quantum Fredkin gate, which promises many applications in quantum information and measurement. We implement example algorithms and generate the highest-fidelity three-photon GHZ states to-date. The technique we use allows one to add a control operation to a black-box unitary, something impossible in the standard circuit model. Our experiment represents the first use of this technique to control a two-qubit operation and paves the way for larger controlled circuits to be realised efficiently.
Introduction
The quantum Fredkin gate conditionally swaps two target qubits and addresses the resource burden of implementing controlled operations in quantum circuits. This experiment adds control to a SWAP unitary using path-mode entanglement, achieving high logical-basis overlap and demonstrating entanglement and state-characterisation applications.
- Introduction: The quantum Fredkin gate swaps two target-qubit states conditioned on the control qubit, extending the reversible classical controlled-SWAP operation.It is a three-qubit gate whose quantum implementation is difficult because standard circuit decompositions require at least five two-qubit gates.
- Introduction: Prior linear-optical proposals relied on ancilla photons, interference, and multiple probabilistic gates, causing multiplicative reductions in overall success probability.
- Introduction: The experiment adds control to the SWAP unitary using path-mode entanglement, allowing a controlled multi-qubit operation without decomposing it into two-qubit gates.The optical implementation exploits the fact that the unitary leaves the vacuum state unchanged, while polarization encodes the qubits.
- Results: The gate’s measured truth-table overlap was 96 ± 4% in the logical basis.Eight logical inputs were measured with 620 four-fold events per input; the slight fidelity reduction was attributed to imperfect polarization-optics extinction.
- Results: The experiment also estimated nonlinear state functionals without quantum state tomography, including overlaps and purity through interferometric visibility.Measured overlaps were 0.82 ± 0.02, 0.52 ± 0.02, and 0.05 ± 0.01 for target-state pairs with ideal overlaps of 1, 0.5, and 0.
S1. Erasing the which-path information
The experiment tests whether the displaced Sagnac interferometers erase which-path information by measuring Hong–Ou–Mandel interference. The measured visibilities indicate high indistinguishability for both path-mode pairs.
- S1. Erasing the which-path information: Hong–Ou–Mandel measurements test path-mode indistinguishability after each displaced Sagnac interferometer.The dip visibility is defined from the maximum and minimum four-fold event counts.
- S1. Erasing the which-path information: 90±5% visibility was measured for modes 2R and 1G.
- S1. Erasing the which-path information: 91±6% visibility was measured for modes 2B and 1Y, confirming a high degree of indistinguishability.
S2. Generation of three-photon GHZ states
The experiment generates three-photon GHZ states by preparing path-mode entanglement, rejecting selected control-arm terms, and erasing which-path information. Different polarisation and control settings produce the reported GHZ-state variants and a superposition of SWAP and identity operations.
- S2. Generation of three-photon GHZ states: The quantum Fredkin gate generates four of the eight maximally entangled three-photon GHZ states.
- S2. Generation of three-photon GHZ states: Rejecting selected control-arm terms and swapping modes 2B and 1G produces the prepared state used for GHZ-state generation.
- S2. Generation of three-photon GHZ states: Trigger-photon detections in H or V produce two states with a relative phase difference of π.
- S2. Generation of three-photon GHZ states: Classical phase rotation and combination of coincidence data follow erasure of which-path information before the three-photon GHZ state is obtained.
- S2. Generation of three-photon GHZ states: Setting the target polarisations to complementary H/V combinations produces additional GHZ-state variants, while a control superposition prepares a SWAP–identity superposition.