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Deterministic multi-mode gates on a scalable photonic quantum computing platform
Mikkel V. Larsen, Xueshi Guo, Casper R. Breum, Jonas S. Neergaard-Nielsen, Ulrik L. Andersen
TL;DR
The paper addresses the lack of a fully universal, scalable gate set demonstrated on photonic cluster states. It implements deterministic programmable Gaussian gates through phase-controlled quadrature measurements and demonstrates a three-mode circuit, while fault-tolerant scaling still requires lower noise and GKP-qubit error correction.
Problem
Photonic cluster-state quantum computing had not yet demonstrated a full gate set for universal scalable computation, despite its scalability potential.
Method
The platform teleports programmable Gaussian gates through a 2D optical cluster state using phase-controlled continuous-variable quadrature measurements.
Results
The experiment implements a universal multi-mode Gaussian gate set and combines 10 single-mode and 2 two-mode gates in a three-mode circuit.
Takeaways & Limitations
The deterministic telecom-compatible architecture provides a route toward scalable photonic measurement-based computation, provided its noise and qubit-encoding requirements are met.
Takeaways & Limitations
Fault-tolerant computation requires significantly lower gate noise, increased squeezing, and GKP qubits for error correction.
Abstract
from arXiv · showhide
Quantum computing can be realized with numerous different hardware platforms and computational protocols. A highly promising approach to foster scalability is to apply a photonic platform combined with a measurement-induced quantum information processing protocol where gate operations are realized through optical measurements on a multipartite entangled quantum state -- a so-called cluster state. Heretofore, a few quantum gates on non-universal or non-scalable cluster states have been, but a full set of gates for universal scalable quantum computing has not been realized. We propose and demonstrate the deterministic implementation of a multi-mode set of measurement-induced quantum gates in a large two-dimensional (2D) optical cluster state using phase-controlled continuous variable quadrature measurements. Each gate is simply programmed into the phases of the high-efficiency quadrature measurements which execute the transformations by teleportation through the cluster state. Using these programmable gates, we demonstrate a small quantum circuit consisting of 10 single-mode gates and 2 two-mode gates on a three-mode input state. On this platform, fault-tolerant universal quantum computing is possible if the cluster state entanglement is improved and a supply of Gottesman-Kitaev-Preskill qubits is available. Moreover, it operates at the telecom wavelength and is therefore network connectable without quantum transducers.
Computation scheme
The platform performs programmable Gaussian measurement-based quantum computation by teleporting gates through a 2D cluster state, with measurement phases selecting the transformations. It implements universal single- and two-mode gates and combines them into a three-mode circuit, while finite squeezing introduces noise that must be corrected for fault tolerance.
- Computation scheme: The cluster-state processor programs quantum algorithms as measurement phases that teleport single- and two-mode Gaussian gates through the cylindrical cluster state.Quadrature measurements use basis settings to determine the implemented gate sequence, while measurement outcomes produce correctable displacement by-products.
- Computation scheme: Finite squeezing adds Gaussian gate noise, so fault-tolerant operation requires substantially lower noise and GKP-qubit error correction to prevent accumulation.The paper identifies increased cluster-state squeezing and GKP ancilla states as requirements for fault-tolerant universal computation.
- Quantum gates: The implemented rotation, modified shear, squeezing, and controlled-Z operations form a universal multi-mode Gaussian gate set.The modified controlled-Z can be converted to a pure controlled-Z by reversing the accompanying Fourier transformations.
- Quantum gates: Gate tomography shows measured symplectic matrices agree with theoretical transformations, while cluster-state entanglement lowers single-mode gate noise below the 6 dB vacuum limit.At zero pump power the cluster state is vacuum and the measured noise is 6 dB; increasing pump power reduces noise through stronger entanglement.
- Quantum circuit: The room-temperature telecom-compatible platform is currently restricted to six modes but can be scaled by increasing squeezing bandwidth and detector bandwidth.The authors estimate that several-gigahertz bandwidths could increase the number of input modes to several thousands.
Supplementary Information for
Deterministic multi-mode gates on a scalable photonic quantum computing platform are demonstrated by Mikkel V. Larsen and colleagues. The work is identified as arXiv:2010.14422v2, dated 28 August 2021.
- Supplementary Information for: The paper is titled “Deterministic multi-mode gates on a scalable photonic quantum computing platform.”The listed authors are Mikkel V. Larsen, Xueshi Guo, Casper R. Breum, Jonas S. Neergaard-Nielsen, and Ulrik L. Andersen.
- Supplementary Information for: The manuscript is identified as arXiv:2010.14422v2 and dated 28 Aug 2021.
1 Experimental setup
The experiment uses phase-controlled homodyne measurements and temporal-mode processing to implement gates, with telecom-wavelength fiber components supporting extended acquisition.
- Measurement control: The EOM-controlled homodyne basis settings implement the desired gate during measurement, while quadrature traces are recorded by a DSO.The AWG drives the EOMs, and a function generator triggers the AWG, scope, and locking scheme.
- Temporal-mode processing: Each temporal-mode outcome is extracted from the recorded quadrature trace using a corresponding temporal-mode function.The function uses a normalization factor N and an optimized κ = 2π × 2.0 MHz to minimize gate noise.
- Acquisition: 228 consecutive temporal modes are acquired, corresponding to 19 turnarounds of the cylindrical cluster state with N = 12.This acquisition enables multiple gates to be implemented and characterized in parallel.
- Optical hardware: The setup operates at 1550 nm, using 50 m and 600 m fibers that produce τ ≈250 ns and N = 12, respectively.Fiber stretchers provide phase locking with negligible optical loss.
2 Computation scheme
The platform coils a dual-rail 1D cluster state into a local 2D structure, projects it into computational wires, and implements gates by phase-controlled quadrature measurements. Finite squeezing introduces noise, while the demonstrated architecture supports six computational wires and two-mode gate teleportation.
- Wire projection: Control-mode measurements project the coiled-up cluster state into wires whose edge weights alternate between −1 and 1.The control modes are measured in ±π/4 bases, and the resulting graph is used for computation.
- Single-mode computation: Each gate is implemented by teleporting input states along the cluster state, with the measurement bases determining the applied operation.The computation proceeds through projective quadrature measurements, and displacement outcomes can be tracked or feed-forward compensated.
- Wire projection: Six computational wires are obtained from N = 12 temporal modes, and increasing N scales the number of available modes.The projected wires are numbered w ∈ {0, 1, 2, 3, 4, 5}.
- Two-mode gate: Two-mode gates teleport two input modes through a 10-mode projected cluster state into two output modes with a basis-dependent Gaussian operation.The input modes are B,k and B,k+2, while the outputs are B,k+2N and B,k+2N+2.
- Noise and limitations: Finite squeezing adds correlated quadrature noise that vanishes in the infinite-squeezing limit, while projection can increase the effective momentum-squeezed variance to 2e−2rV0.Gate noise accumulates across the circuit unless removed by GKP error correction, which was not implemented here.
3 Gate tomography
Gate tomography characterizes implemented multi-mode Gaussian operations by estimating their symplectic transformations and added noise from correlations between entangled input and reference modes. The measurements certify agreement with target transformations and quantify noise across single-mode gates, two-mode gates, and circuits.
- Tomography method: Gate tomography probes each operation with entangled input-reference states, using output-reference quadrature correlations to estimate the implemented symplectic matrix and gate noise.Displacement by-products are compensated in the measurement results; the noise variance is inferred from output variance relative to the input-based expectation.
- Two-mode gate: Two-mode gate tomography estimates the operation from correlations within 228 temporal modes, with ε_j assumed identical across modes within each even or odd wire.The compensated gate noise agrees with the initial momentum squeezed variance of 4.4 dB below vacuum variance across the tested controlled-Z settings.
- Single-mode gates: Single-mode tomography implements and characterizes eight gates in parallel within 228 temporal modes, using four correlation measurements per 2×2 symplectic matrix.The remaining wires estimate input-reference correlations needed for the tomography procedure.
- Single-mode gates: The measured single-mode gate transformations agree well with theoretical symplectic matrices, while compensated gate noise agrees with the initial momentum squeezing of 4.4 dB below vacuum variance.Gate noise is also measured as a function of pump power and averaged over quadratures and seven rotation angles.
- Circuit: Circuit tomography estimates the symplectic matrix from input-reference correlations and finds compensated gate noise consistent with 4.4 dB-below-vacuum initial momentum squeezing.The even- and odd-wire correlation factors are estimated as ε_j = −2.14 ± 0.03 and 2.12 ± 0.06, respectively.
4 Gate noise
Gate noise arises from finite squeezing in the cluster state and is reduced by stronger squeezing, higher efficiency, and broader squeezing bandwidth, although losses and phase fluctuations can limit improvement.
- 4.4 dB squeezing is expected to yield 1.6 dB, or 1.4V0, of single-mode gate noise, consistent with the measured value.The single-mode gate-noise factor adds 6 dB to the initial squeezing variance.
- 6 dB gate noise occurs without squeezing, while increasing pump power lowers gate noise until optical losses and phase fluctuations cause saturation.The saturation is described as a technical rather than fundamental limit.
- Fault-tolerant computation requires optical losses and phase control to be optimized, and the relevant target is a fault-tolerant squeezing threshold rather than merely noise below vacuum variance.The threshold depends on the concatenated qubit error-correction code.
- Gate noise decreases with higher efficiency, pump power, and squeezing bandwidth, with predictions evaluated for experimental and more optimal OPO bandwidths.The current-efficiency prediction agrees well with the experimentally measured gate noise.
- With sufficiently high efficiency and phase control, persistent noise reduction at increasing pump power could eventually enable fault-tolerant computation, subject to the error-correction threshold.Scaling the encoded modes also requires a squeezing-source bandwidth broad enough to cover shortened temporal modes.