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Strawberry Fields: A Software Platform for Photonic Quantum Computing
Nathan Killoran, Josh Izaac, Nicolás Quesada, Ville Bergholm, Matthew Amy, Christian Weedbrook
TL;DR
Strawberry Fields addresses the need for software supporting photonic, continuous-variable quantum computing. It provides Blackbird programming, specialized simulators, and compilation across backends, with examples spanning several quantum algorithms. The platform combines these components into an open-source full-stack architecture for designing, simulating, optimizing, and applying quantum machine learning to continuous-variable circuits.
Problem
Photonic quantum computers require software for programming, simulation, optimization, and quantum machine learning of continuous-variable circuits.
Method
Strawberry Fields combines the Blackbird programming language, three specialized continuous-variable simulators, and an engine that compiles programs across backends.
Results
The platform supports simulations of Gaussian and non-Gaussian circuits, including Gaussian boson sampling, while providing numerical agreement between Fock and Gaussian backends when states fit within the cutoff.
Takeaways & Limitations
Strawberry Fields provides an open-source full-stack architecture for continuous-variable quantum computing and includes examples such as teleportation, gate teleportation, boson sampling, and molecular simulation.
Takeaways & Limitations
The Gaussian backend is not expressive enough for general quantum computations, while the Fock backend restricts each mode to a user-chosen cutoff dimension.
Abstract
from arXiv · showhide
We introduce Strawberry Fields, an open-source quantum programming architecture for light-based quantum computers, and detail its key features. Built in Python, Strawberry Fields is a full-stack library for design, simulation, optimization, and quantum machine learning of continuous-variable circuits. The platform consists of three main components: (i) an API for quantum programming based on an easy-to-use language named Blackbird; (ii) a suite of three virtual quantum computer backends, built in NumPy and TensorFlow, each targeting specialized uses; and (iii) an engine which can compile Blackbird programs on various backends, including the three built-in simulators, and -- in the near future -- photonic quantum information processors. The library also contains examples of several paradigmatic algorithms, including teleportation, (Gaussian) boson sampling, instantaneous quantum polynomial, Hamiltonian simulation, and variational quantum circuit optimization.
2 Vac | q[0]
This section introduces Blackbird syntax for preparing, transforming, and measuring continuous-variable quantum states. It also presents reusable operations and supported composite gates.
- Blackbird state-preparation operations can create coherent, squeezed, and Fock states in qumodes.
- State preparations implicitly reset the existing state of the qumodes.
- The vertical bar separates operations from the registers on which they act.
- Blackbird supports displacement, rotation, squeezing, beamsplitter, cubic phase, and Hermitian-conjugate gate operations.
- Supported composite gates include controlled X, controlled Z, quadratic phase, and two-mode squeezing.
- Blackbird programs can specify measurement operations, including homodyne measurement at angle phi.
3 MeasureHomodyne(phi) | q[0]
This section introduces special homodyne measurements in Blackbird.
- Special homodyne measurements are specified in Blackbird.
7 MeasureP | q[1]
This section introduces heterodyne measurement in Blackbird.
- Blackbird includes a heterodyne measurement operation.
10 MeasureHeterodyne() | q[0]
This section shows shorthand and examples for heterodyne and number-state measurements across qumodes.
- MeasureHD is provided as shorthand for a measurement operation on qumode 1.
- The examples include number-state measurements of various qumodes.
15 MeasureFock() | (q[1], q[2]) # multiple modes
Strawberry Fields provides a Python interface for declaring, running, and inspecting Blackbird continuous-variable computations. Measurements record classical results, condition the remaining quantum state, and reset the measured mode to vacuum.
- Measurements: Measurement results are placed in a classical register while the remaining qumodes become a normalized conditional state.The measured qumode is reset to vacuum, reflecting the energy-absorbing behavior of photonic hardware.
- Running Blackbird Programs in Python: Blackbird programs are declared within an Engine context, which manages the quantum register and executes the circuit.The API imports Strawberry Fields and its operations namespace before creating an Engine and register.
18 S.H | q[1]
Strawberry Fields combines a Blackbird programming interface, an execution engine, and specialized continuous-variable simulators. Its TensorFlow backend additionally supports symbolic computation, batched execution, optimization, and quantum machine learning.
- Optimization and Quantum Machine Learning: TensorFlow enables symbolic circuit execution through computational graphs, with tensors usable in optimization and machine-learning workflows.Symbolic execution requires the TensorFlow backend with eval=False; the resulting state tensor can be combined with TensorFlow operations.
- Optimization and Quantum Machine Learning: Strawberry Fields supports optimization and machine learning on quantum circuits through the TensorFlow backend.The platform includes a complete optimization example in its appendix.
- Strawberry Fields’ Quantum Simulators: Three built-in simulators target distinct uses: Gaussian circuits, non-Gaussian Fock-basis circuits, and TensorFlow-based optimization and machine learning.The Gaussian and Fock backends exploit different state representations, while TensorFlow also uses the Fock representation.
- Architecture: Strawberry Fields is an open-source Python platform for continuous-variable quantum computing centered on the Blackbird language.Its compiler engine converts Blackbird programs for simulator backends and, when available, photonic quantum computers.
- Future Development: The platform is intended to support community exploration, new quantum algorithms, specialized circuits, and machine-learning models.The authors anticipate additional applications and backend modules developed internally and externally.
Appendix A: The CV model
Appendix A introduces the continuous-variable model underlying Strawberry Fields, covering its phase-space formalism, universal gates, decompositions, and Gaussian simulation.
- CV foundations: Continuous-variable quantum computing represents information in infinite-dimensional bosonic modes and uses quadrature or mode operators as its mathematical foundation.
- Universal gates: Gaussian operations are closed under composition, while at least one third-degree-or-higher generator is required to construct higher-order polynomial generators.
- Universal gates: Combining universal single-mode gates with multimode interactions such as beamsplitters yields a universal gate set for N-mode continuous-variable systems.
- Gate decompositions: Multiport interferometers implement passive linear transformations and can be decomposed into N(N −1)/2 beamsplitter gates across 2N −3 layers.An equivalent decomposition uses the same number of beamsplitters in N + 1 layers.
- Gaussian formalism: Gaussian quantum computation can be efficiently simulated classically, whereas non-Gaussian operations are needed for continuous-variable quantum supremacy.Gaussian boson sampling is identified as a restricted setting with Gaussian states and gates but non-Gaussian final measurements.
- Gaussian formalism: The Gaussian backend uses covariance matrices and mean vectors to represent Gaussian states through the symplectic formalism.This formalism maps quantum states into a real symplectic phase space represented by Wigner functions.
Appendix B: Strawberry Fields Operations
Appendix B catalogs Strawberry Fields’ available state preparations, gates, measurements, and multimode Gaussian decompositions, including backend-dependent non-Gaussian operations.
- State preparations: State-preparation operations are listed in Table V, with asterisks marking non-Gaussian preparations.
- Gate operations: Table VI lists single-mode gates, marking non-Gaussian operations that can only run on backends using the Fock representation.
- Gate operations: Strawberry Fields supports two-mode gate operations and multimode Gaussian decompositions, summarized in Tables VII and VIII.
- Measurements: Table IX lists measurement operations and identifies non-Gaussian measurements that require a Fock-representation backend.
- Compound-gate decompositions: The frontend decomposes compound gates, including quadratic phase shifts into squeezing and rotation operations.
- Compound-gate decompositions: Two-mode squeezing and controlled-X gates are decomposed into combinations of beamsplitters and single-mode squeezers.
Appendix C: Quantum Algorithms
The appendix demonstrates Strawberry Fields through quantum teleportation, gate teleportation, boson sampling, Gaussian boson sampling, and related circuit examples. It also illustrates Hamiltonian simulation and variational circuit optimization, while noting practical scalability and optimization limitations.
- Examples: The appendix provides full example code for important algorithms, subroutines, and use cases in Strawberry Fields.The examples are presented in more detail in the online documentation.
- Teleportation: Gate teleportation applies a quadratic phase gate indirectly through projective measurement, rather than directly before teleportation.Additional gates can be incorporated by adding qumodes with suitable projective measurements and conditional phase couplings.
- Boson sampling: Boson sampling uses single-photon inputs and a multimode linear interferometer, with output probabilities determined by permanents of interferometer submatrices.Strawberry Fields represents the interferometer with beamsplitters and phase shifters; the appendix includes a four-mode example.
- Boson sampling: Gaussian boson sampling replaces single-photon Fock inputs with single-mode squeezed states while retaining a computationally hard sampling task.This variation addresses the scalability problem associated with simultaneously emitting single-photon sources.
- Simulation and optimization: The appendix includes a two-node tight-binding Hamiltonian simulation and a variational circuit optimization example targeting the highest probability of a n = 1 Fock output.The Hamiltonian interface also supports arbitrary Bose-Hubbard Hamiltonians generated in OpenFermion through the SFOpenBoson plugin.
- Limitations: Variational optimization fixes the circuit’s discrete structure and optimizes operation parameters, but the objective may be non-convex and need not yield a global optimum.Local optima may nevertheless provide effective solutions for some machine-learning applications.