Universal linear optics
Open accessAbstract
Complex quantum optical circuitry: Encoding and manipulating information in the states of single photons provides a potential platform for quantum computing and communication. Carolan et al. developed a reconfigurable integrated waveguide device fabricated in a glass chip (see the Perspective by Rohde and Dowling). The device allowed for universal linear optics transformations on six wave-guides using 15 integrated Mach-Zehnder interferometers, each of which was individually programmable. Functional performance in a number of applications in optics and quantum optics demonstrates the versatility of the device's reprogrammable architecture. Science , this issue p. 711 ; see also p. 696
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Written from the paper’s full text.
TL;DR
The paper experimentally demonstrates a six-mode universal linear optical processor (LPU) that can be reprogrammed to implement any linear optical protocol up to its circuit size. It uses the device to realize heralded quantum logic and entangling gates, boson sampling with verification, and six-dimensional complex Hadamard operations.
Key findings
- A single photonic chip with 15 Mach-Zehnder interferometers and 30 thermo-optic phase shifters was programmed to implement 100 Haar random unitaries with average fidelity 0.999 ± 0.001, and could switch protocols in seconds.
- Heralded gates were demonstrated: a Bell state generator with statistical fidelity F_s = 0.966 ± 0.004 and entanglement witness E = 0.673 ± 0.031, and a heralded CNOT with mean statistical fidelity F_s = 0.927 ± 0.004.
- Boson sampling was implemented for 100 three-photon routines with mean statistical fidelity F_s = 0.950 ± 0.020; zero-transmission-law verification gave minimum violation ν_min = 0.319 ± 0.009 at the six-dimensional Fourier transform, and six-photon Bayesian model comparison reached confidence p = 0.998 after 15 events.
- Complex Hadamard operations were distinguished: mean statistical fidelity F_s = 0.979 ± 0.007 for F^(2)_6 matrices, and F_s = 0.986 ± 0.001 and 0.998 ± 0.001 for G^(4)_6 and S^(0)_6 examples, respectively.
Methods
- The device is a silica-on-silicon planar lightwave circuit with six modes, 15 MZIs, 30 directional couplers, and 30 thermo-optic phase shifters, controlled by custom electronics and cooled by a Peltier unit; photons are generated by SPDC in BiBO and detected with up to 12 single-photon avalanche diodes and time-correlated single-photon counting.
- The LPU was programmed to implement heralded Bell state generation, heralded and unheralded CNOT gates, single-qubit gates, 100 Haar-random boson sampling circuits, zero-transmission-law tests, six-photon verification, and complex Hadamard matrices.
- Analysis used statistical fidelity, quantum process tomography with maximum-likelihood estimation and semidefinite programming, unitary fidelity, Poissonian error propagation, and bootstrap resampling; effective phase accuracy was estimated as δφ = 0.035 rad.
Limitations
- Stated: the LPU is not optimized for highly structured unitaries used in qubit operations, and multi-photon fidelity is primarily limited by photon-source imperfections such as reduced quantum interference and higher-order SPDC terms.
- Stated: near-term improvements require higher-efficiency sources and detectors, while mid-term progress depends on integrating components with larger low-loss circuits.
- Evident: the gates are probabilistic and rely on heralding or post-selection (Bell state p = 2/27, heralded CNOT p = 1/16, unheralded CNOT p = 1/9), and the six-mode size restricts protocols to at most six optical modes; boson-sampling verification remains circumstantial rather than a full classical check.
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- Findingown data§ Universal Linear Optics · p. 2
The device was programmed to implement a new compact four-photon scheme suitable for measurement-based quantum computing, which generates the entangled state of two photonic qubits upon the detection of another two ancilla photons.
“We programmed our device to implement a new compact four-photon scheme, suitable for measurementbased quantum computing, which generates the entangled state of two photonic qubits upon the detection of another two ancilla photons, schematically displayed in Fig. 2(a,b).”
Quote in the paperSubstantial claim - Findingown data§ Universal Linear Optics · p. 4
The unheralded two-photon CNOT gate had process fidelity F_p = 0.909 ± 0.001.
“The process fidelity was found to be F p = 0 . 909 ± 0 . 001, and the average gate fidelity F g = 0 . 927 ± 0 . 001 (see Appendix for details), greater than those previously reported [21, 33, 39].”
Quote in the paperSubstantial claim - Findingown data§ Universal Linear Optics · p. 1
The paper experimentally demonstrates a single reprogrammable optical circuit that is sufficient to implement all possible linear optical protocols up to the size of that circuit.
“Here we experimentally demonstrate the longstanding goal of a single reprogrammable optical circuit that is sufficient to implement all possible linear optical protocols up to the size of that circuit.”
Quote in the paperSubstantial claim - Findingown data§ Universal Linear Optics · p. 2
The mean statistical fidelity between all four experimental and theoretical probability distributions for the Bell state measurements was F_s = 0.966 ± 0.004.
“We implemented both types of measurement, data shown in Fig. 2(c), finding the mean statistical fidelity F s = ∑ i √ p exp i .p th i between all four experimental p exp and theoretical p th probability distributions to be F s = 0 . 966 ± 0 . 004 (see Methods for an explanation of all error analyses).”
Quote in the paperSubstantial claim- Rests on an assumption: For Bell states, measurements in common bases are correlated while measurements in different bases are uncorrelated.
- Findingown data§ Universal Linear Optics · p. 4
These are the first heralded two-qubit processes in integrated optics.
“While these are the first heralded two-qubit processes in integrated optics, several examples of photonic chips specifically fabricated to implement unheralded (and hence not scalable) two-qubit gates have been reported [21, 33, 34].”
Quote in the paperSubstantial claim0 of 3 sources checked
- Findingown data§ Universal Linear Optics · p. 4
The unheralded two-photon CNOT gate had average gate fidelity F_g = 0.927 ± 0.001.
“The process fidelity was found to be F p = 0 . 909 ± 0 . 001, and the average gate fidelity F g = 0 . 927 ± 0 . 001 (see Appendix for details), greater than those previously reported [21, 33, 39].”
Quote in the paperSubstantial claim - Findingnone given§ Universal Linear Optics · p. 1
The system is capable of switching between these and any other linear optical protocol in seconds.
“Our system is capable of switching between these and any other linear optical protocol in seconds.”
Quote in the paperSubstantial claim - Findingown data§ Universal Linear Optics · p. 3
The heralded CNOT gate was successfully implemented on two photonic qubits upon detection of two ancilla photons.
“The heralded CNOT gate is successfully implemented on the two photonic qubits, upon detection of the two ancilla photons.”
Quote in the paperSubstantial claim - Findingown data§ Universal Linear Optics · p. 1
The system was programmed to implement boson sampling with verification tests.
“We programmed this system to implement heralded quantum logic and entangling gates, boson sampling with verification tests, and six-dimensional complex Hadamards.”
Quote in the paperSubstantial claim - Findingown data§ Universal Linear Optics · p. 4
The mean statistical fidelity of the heralded CNOT logical truth table averaged over all computational inputs was F_s = 0.927 ± 0.004 with the ideal.
“We measured the logical truth table for this operation, shown in Fig. 2(f), and found its mean statistical fidelity averaged over all computational inputs to be F s = 0 . 927 ± 0 . 004 with the ideal.”
Quote in the paperSubstantial claim - Findingown data§ Universal Linear Optics · p. 1
The six-mode universal system consists of a cascade of 15 Mach-Zehnder interferometers with 30 thermo-optic phase shifters integrated into a single photonic chip.
“Our six-mode universal system consists of a cascade of 15 MachZehnder interferometers with 30 thermo-optic phase shifters integrated into a single photonic chip that is electrically and optically interfaced for arbitrary setting of all phase shifters, input of up to six photons and their measurement with a 12 single-photon detector system.”
- Also stated in: § Universal Linear Optics · p. 2 · plain
“The device, made with planar lightwave circuit (PLC) technology [27, 28], comprises an array of 30 silica-on-silicon waveguide directional couplers with 30 electronically controlled thermo-optic phase shifters, to form a cascade of 15 MZIs across six modes (see Appendix for further details).”
Quote in the paperSubstantial claim0 of 2 sources checked - Also stated in: § Universal Linear Optics · p. 2 · plain
- Findingown data§ Universal Linear Optics · p. 1
The system implemented 100 Haar random unitaries with average fidelity 0.999 ± 0.001.
“We implemented 100 Haar random unitaries with average fidelity 0.999 ± 0.001.”
Quote in the paperSubstantial claim - Findingown data§ Universal Linear Optics · p. 1
The system was programmed to implement six-dimensional complex Hadamards.
“We programmed this system to implement heralded quantum logic and entangling gates, boson sampling with verification tests, and six-dimensional complex Hadamards.”
Quote in the paperNot a substantial claim - Findingreasoning§ 5. Cross Talk · p. 11
Once corrected for, no evidence of cross talk, thermal or otherwise, is observed.
“Once corrected for no evidence of cross talk, thermal or otherwise, is observed.”
Quote in the paperSubstantial claim - Findingown data§ 6. Phase accuracy · p. 11
The effective phase accuracy is δφ = 0.035 rad.
“finding δ φ = 0 . 035 rad.”
Quote in the paperNot a substantial claim - Findingown data§ Methods: Circuit implementation & analysis · p. 7
The injected two-photon state |1_1,1_2〉 yielded a fidelity of 0.990 ± 0007.
“we injected the one and two photon states | 1 1 〉 and | 1 1 , 1 2 〉 yielding fidelities of 0 . 999 ± 0 . 001 and 0 . 990 ± 0007 respectively.”
Quote in the paperNot a substantial claim - Findingown data§ Methods: Circuit implementation & analysis · p. 7
The statistical fidelity for the common basis measurement σ ̃x⊗σx is Fs = 0.979 ± 0.003.
“We found the statistical fidelity for the common basis measurements σ z ⊗ σ z and σ ˜ x ⊗ σ x to be F s = 0 . 891 ± 0 . 015 and 0 . 979 ± 0 . 003 respectively”
Quote in the paperSubstantial claim - Findingown data§ Universal Linear Optics · p. 4
The mean statistical fidelity over the 100 three-photon boson sampling experiments was ̄F_s = 0.950 ± 0.020.
“For each implementation [Fig. 3(b)], we counted detection events for each of the 20 collision free ways in which three photons can exit the six output ports of the device, and in Fig. 3(c) plot a histogram of fidelities with statistics based on calculations of matrix permanents, finding a mean statistical fidelity of ¯ F s = 0 . 950 ± 0 . 020.”
Quote in the paperSubstantial claim - Findingown data§ Methods: Circuit implementation & analysis · p. 7
The mean statistical fidelity between all experimentally reconstructed truth tables and ideal values is ̄Fs = 0.986 ± 0.001.
“finding a mean statistical fidelity between all experimentally reconstructed truth tables and ideal values to be ¯ F s = 0 . 986 ± 0 . 001.”
Quote in the paperSubstantial claim - Findingown data§ Universal Linear Optics · p. 6
The mean statistical fidelity for the reconstructed correlation manifolds of two-photon detection events scanning over F6^(2) matrices was ̄F_s = 0.979 ± 0.007.
“Here, we reconstruct correlation manifolds of two-photon detection events by scanning over the F (2) 6 matrices, displaying four (out of the 15 sets collected) in Fig. 3(j). We find a mean statistical fidelity of ¯ F s = 0 . 979 ± 0 . 007.”
Quote in the paperSubstantial claim - Findingown data§ Methods: Circuit implementation & analysis · p. 7
The process fidelity for the σz gate is 0.994 ± 0.001.
“We performed single qubit process tomography on the Hadamard ( H ), π/ 8 ( T ) and σ x , σ y , σ z gates, finding process fidelities of 0 . 995 ± 0 . 001, 0 . 978 ± 0 . 001, 0 . 997 ± 0 . 001, 0 . 993 ± 0 . 001, 0 . 994 ± 0 . 001 respectively”
Quote in the paperNot a substantial claim - Findingown data§ Universal Linear Optics · p. 6
For S6^(0), the statistical fidelity was F_s = 0.998 ± 0.001.
“We then implemented an instance of G (4) 6 (that is not contained in F (2) 6 ) and S (0) 6 , and observed their predicted characteristic two-photon quantum interference patterns displayed in Figs. 3(h,i) respectively, finding statistical fidelities to be F s = 0 . 986 ± 0 . 001 and F s = 0 . 998 ± 0 . 001.”
Quote in the paperNot a substantial claim - Findingown data§ Universal Linear Optics · p. 6
The experimental violation of the ZTL, ν = N_s/N, had a minimal value ν_min = 0.319 ± 0.009 occurring when F6 is implemented.
“The experimental points follow the shape of the manifold with the minimal violation of the ZTL ν min = 0 . 319 ± 0 . 009 occurring when F 6 is implemented.”
Quote in the paperNot a substantial claim - Findingown data§ Methods: Circuit implementation & analysis · p. 7
The statistical fidelity for the uncommon basis measurement σz⊗σy is 1.000 ± 0.002.
“and the uncommon bases σ z ⊗ σ x and σ z ⊗ σ y to be 0 . 999 ± 0 . 002 and 1 . 000 ± 0 . 002.”
Quote in the paperNot a substantial claim - Findingown data§ Methods: Circuit implementation & analysis · p. 7
The process fidelity for the Hadamard (H) gate is 0.995 ± 0.001.
“We performed single qubit process tomography on the Hadamard ( H ), π/ 8 ( T ) and σ x , σ y , σ z gates, finding process fidelities of 0 . 995 ± 0 . 001, 0 . 978 ± 0 . 001, 0 . 997 ± 0 . 001, 0 . 993 ± 0 . 001, 0 . 994 ± 0 . 001 respectively”
Quote in the paperNot a substantial claim - Findingown data§ Methods: Circuit implementation & analysis · p. 7
The statistical fidelity for the common basis measurement σz⊗σz is Fs = 0.891 ± 0.015.
“We found the statistical fidelity for the common basis measurements σ z ⊗ σ z and σ ˜ x ⊗ σ x to be F s = 0 . 891 ± 0 . 015 and 0 . 979 ± 0 . 003 respectively”
Quote in the paperNot a substantial claim - Findingown data§ Methods: Circuit implementation & analysis · p. 7
The statistical fidelity for the uncommon basis measurement σz⊗σx is 0.999 ± 0.002.
“and the uncommon bases σ z ⊗ σ x and σ z ⊗ σ y to be 0 . 999 ± 0 . 002 and 1 . 000 ± 0 . 002.”
Quote in the paperNot a substantial claim - Findingown data§ Universal Linear Optics · p. 6
For an instance of G6^(4) not contained in F6^(2), the statistical fidelity was F_s = 0.986 ± 0.001.
“We then implemented an instance of G (4) 6 (that is not contained in F (2) 6 ) and S (0) 6 , and observed their predicted characteristic two-photon quantum interference patterns displayed in Figs. 3(h,i) respectively, finding statistical fidelities to be F s = 0 . 986 ± 0 . 001 and F s = 0 . 998 ± 0 . 001.”
Quote in the paperSubstantial claim - Findingown data§ Methods: Circuit implementation & analysis · p. 7
The injected one-photon state |1_1〉 yielded a fidelity of 0.999 ± 0.001.
“we injected the one and two photon states | 1 1 〉 and | 1 1 , 1 2 〉 yielding fidelities of 0 . 999 ± 0 . 001 and 0 . 990 ± 0007 respectively.”
Quote in the paperNot a substantial claim - Findingown data§ 5. Cross Talk · p. 11
Electrical cross talk was observed due to certain heaters sharing a common ground.
“Electrical cross talk was observed due to certain heaters sharing a common ground.”
Quote in the paperNot a substantial claim - Findingown data§ Universal Linear Optics · p. 4
The device was programmed to implement 100 different boson sampling routines acting on three-photon ensembles.
“Acting on three-photon ensembles we programmed our device to implement 100 different boson sampling routines.”
Quote in the paperSubstantial claim - Findingown data§ Universal Linear Optics · p. 6
After collecting 15 six-fold coincidence events, the confidence that the six-photon detections were sampled from a quantum (indistinguishable) rather than classical (distinguishable) distribution was p = 0.998.
“After collecting 15 six-fold coincidence events, we determine a confidence of p = 0 . 998 that we are sampling from a quantum (not classical) distribution.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [49] J. Carolan, J. D. A. Meinecke, P. J. Shadbolt, N. J. Russell, N. Ismail, K. W¨ orhoff, T. Rudolph, M. G. Thompson, J. L. O'Brien, J. C. F. Matthews, and A. Laing, Nat. Photon. 8 , 621 (2014).
Not checked in the free run.
- Rests on an assumption: An essential requirement of boson sampling is indistinguishability among photons.
- Findingown data§ 2. Fabrication · p. 10
The mean insertion loss (fibre to fibre) averaged over all modes is 2.4dB (42%).
“The mean insertion loss (fibre to fibre) when averaged over all modes is 2.4dB (42%).”
Quote in the paperNot a substantial claim - Findingown data§ 1. Zero-Transmission Law · p. 12
In our implementation, 12 out of the total 20 outputs are suppressed in the collision-free subspace.
“In this subspace, 12 out of the total of 20 outputs are suppressed and ν is calculated as the ratio of events in these 12 outputs to the total events recorded.”
Quote in the paperSubstantial claim - Findingown data§ Universal Linear Optics · p. 6
The device was programmed to implement 16 examples of the F6^(2)(θ1,θ2) two-parameter set of six-dimensional matrices, including F6 (the 6-dimensional FT), which occurs at θ1,θ2 = π,0.
“We programmed our device to implement 16 examples of the F (2) 6 ( θ 1 , θ 2 ) two-parameter set of six dimensional matrices, including F 6 (the 6 dimensional FT), which occurs at θ 1 , θ 2 = π, 0.”
Quote in the paperSubstantial claim - Findingown data§ Universal Linear Optics · p. 4
The average process fidelity for the Hadamard, π/8, and three Pauli gates was F_p = 0.992 ± 0.008.
“We implemented and performed full quantum process tomography for these two gates and for the three Pauli gates, as shown in Fig. 2(k), finding an average process fidelity of F p = 0 . 992 ± 0 . 008.”
Quote in the paperSubstantial claim - Findingown data§ Methods: Circuit implementation & analysis · p. 7
The process fidelity for the π/8 (T) gate is 0.978 ± 0.001.
“We performed single qubit process tomography on the Hadamard ( H ), π/ 8 ( T ) and σ x , σ y , σ z gates, finding process fidelities of 0 . 995 ± 0 . 001, 0 . 978 ± 0 . 001, 0 . 997 ± 0 . 001, 0 . 993 ± 0 . 001, 0 . 994 ± 0 . 001 respectively”
Quote in the paperNot a substantial claim - Findingown data§ Methods: Circuit implementation & analysis · p. 7
The process fidelity for the σx gate is 0.997 ± 0.001.
“We performed single qubit process tomography on the Hadamard ( H ), π/ 8 ( T ) and σ x , σ y , σ z gates, finding process fidelities of 0 . 995 ± 0 . 001, 0 . 978 ± 0 . 001, 0 . 997 ± 0 . 001, 0 . 993 ± 0 . 001, 0 . 994 ± 0 . 001 respectively”
Quote in the paperNot a substantial claim - Findingown data§ Universal Linear Optics · p. 6
The average ZTL violation of the nine points predicted to maximally violate was ̄ν_max = 0.638 ± 0.029.
“The average ZTL violation of the nine points that are predicted to maximally violate is ¯ ν max = 0 . 638 ± 0 . 029.”
Quote in the paperSubstantial claim - Findingown data§ Methods: Circuit implementation & analysis · p. 7
The process fidelity for the σy gate is 0.993 ± 0.001.
“We performed single qubit process tomography on the Hadamard ( H ), π/ 8 ( T ) and σ x , σ y , σ z gates, finding process fidelities of 0 . 995 ± 0 . 001, 0 . 978 ± 0 . 001, 0 . 997 ± 0 . 001, 0 . 993 ± 0 . 001, 0 . 994 ± 0 . 001 respectively”
Quote in the paperNot a substantial claim - Premisecitation§ Universal Linear Optics · p. 1
A specific array of basic two-mode operations is mathematically sufficient to implement any unitary operator on optical modes.
“In fact, since any linear optical (LO) circuit is described by a unitary operator, and a specific array of basic two-mode operations is mathematically sufficient to implement any unitary operator on optical modes [7], it is theoretically possible to construct a single device with sufficient versatility to implement any possible LO operation up to the specified number of modes.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [7] source
Not checked in the free run.
- Interpretationcitation§ Universal Linear Optics · p. 1
It is theoretically possible to construct a single device with sufficient versatility to implement any possible LO operation up to the specified number of modes.
“In fact, since any linear optical (LO) circuit is described by a unitary operator, and a specific array of basic two-mode operations is mathematically sufficient to implement any unitary operator on optical modes [7], it is theoretically possible to construct a single device with sufficient versatility to implement any possible LO operation up to the specified number of modes.”
Quote in the paperSubstantial claim - Premisecitation§ Universal Linear Optics · p. 1
Any linear optical circuit is described by a unitary operator.
“In fact, since any linear optical (LO) circuit is described by a unitary operator, and a specific array of basic two-mode operations is mathematically sufficient to implement any unitary operator on optical modes [7], it is theoretically possible to construct a single device with sufficient versatility to implement any possible LO operation up to the specified number of modes.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [7] source
Not checked in the free run.
- Interpretationreasoning§ Universal Linear Optics · p. 2
Such an LPU can implement any LO protocol.
“Such an LPU can implement any LO protocol, and here we focus on several protocols at the forefront of quantum information science and technology.”
Quote in the paperSubstantial claim - Interpretationown data§ Universal Linear Optics · p. 4
The unheralded two-photon CNOT gate fidelities were greater than those previously reported.
“The process fidelity was found to be F p = 0 . 909 ± 0 . 001, and the average gate fidelity F g = 0 . 927 ± 0 . 001 (see Appendix for details), greater than those previously reported [21, 33, 39].”
Quote in the paperSubstantial claim0 of 3 sources checked - Premisecitation§ Universal Linear Optics · p. 1
The full space of m-dimensional unitary matrices can be parametrised as a product of approximately m^2/2 two-dimensional unitary primitives, each with two free parameters.
“The full space of m -dimensional unitary matrices (or unitaries) can be parametrised as a product of ≈ m 2 / 2 two-dimensional unitary primitives, each with two free parameters.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [16]
Not checked in the free run.
- Premisecitation§ Universal Linear Optics · p. 4
Several examples of photonic chips specifically fabricated to implement unheralded two-qubit gates have been reported.
“While these are the first heralded two-qubit processes in integrated optics, several examples of photonic chips specifically fabricated to implement unheralded (and hence not scalable) two-qubit gates have been reported [21, 33, 34].”
Quote in the paperSubstantial claim0 of 3 sources checked - Interpretationreasoning§ Universal Linear Optics · p. 1
An arbitrarily reconfigurable LO network would be realised by implementing these unitary primitives as two-mode Mach-Zehnder interferometers with two beamsplitters and two phase shifters, such that any given LO network corresponds to a set of phase shift values.
“An arbitrarily reconfigurable LO network would be realised by implementing these unitary primitives as two-mode Mach-Zehnder interferometers (MZIs) with two beamsplitters (or integrated directional couplers) and two phase shifters, such that any given LO network corresponds to a set of phase shift values.”
Quote in the paperSubstantial claim- Rests on an assumption: Any given unitary corresponds to a unique set of parameter values.
- Interpretationown data§ Universal Linear Optics · p. 4
These results show a test of the performance of the LPU over many circuit configurations randomly and unbiasedly chosen from the full space of all possible configurations.
“These results show a test of the performance of our LPU over many circuit configurations randomly and unbiasedly chosen from the full space of all possible configurations.”
Quote in the paperSubstantial claim - Premisecitation§ Universal Linear Optics · p. 6
The zero transmission law predicts that correlated photon detection for most of the exponentially growing number of configurations is strictly suppressed if the circuit is set to implement the Fourier transform on optical modes.
“The zero transmission law (ZTL) [53] predicts that correlated photon detection for most of the exponentially growing number of configurations is strictly suppressed if the circuit is set to implement the Fourier transform (FT) on optical modes.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [53] M. C. Tichy, M. Tiersch, F. de Melo, F. Mintert, and A. Buchleitner, Phys. Rev. Lett. 104 , 220405 (2010). source
Not checked in the free run.
- Interpretationown data§ Methods: Circuit implementation & analysis · p. 6
This system demonstrates fidelities greater than those reported for optical chips custom made for LO quantum processing tasks.
“Nevertheless, this system demonstrates fidelities greater than those reported for optical chips that have been custom made for LO quantum processing tasks.”
Quote in the paperSubstantial claim - Premisecitation§ Methods: Circuit implementation & analysis · p. 7
The unheralded (post-selected) CNOT gate is a two-photon scheme that requires detection of the two photonic qubits in a computational state to signal success with probability p = 1/9 [35-37].
“The unheralded (or post-selected) CNOT gate shown in Fig. 2(h) is a two-photon scheme that requires the detection of the two photonic qubits in a computational state to signal the success of the gate with probability p = 1 / 9 [35-37].”
Quote in the paperNot a substantial claim0 of 3 sources checked - Premisecitation§ 1. Zero-Transmission Law · p. 12
For an n photon, m-periodic initial state input into the Fourier transform, final states are suppressed when the sum of the mode assignment list multiplied by m is not divisible by n.
“For an n photon, m -periodic initial state ⃗ r input into the FT, final states ⃗ s are suppressed when the sum of the mode assignment list d ⃗ ( ⃗ s ) (i.e. the list of positions of the photons in the output state) multiplied by m is not divisible by n”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [68] M. C. Tichy, Entanglement and interference of identical particles , Ph.D. thesis, Universit´ at Freiburg (2011). source
Not checked in the free run.
- Study design and conductown data§ 5. Cross Talk · p. 11
A final correction is applied due to an observed reduction in quantum interference at certain points within the chip caused by polarisation rotation.
“A final correction is applied due to an observed reduction in quantum interference at certain points within the chip caused by polarisation rotation.”
Quote in the paperNot a substantial claim - Interpretationown data§ Methods: Circuit implementation & analysis · p. 7
Operations requiring only one-photon interference demonstrate very high fidelities.
“demonstrating very high fidelities for operations requiring only one-photon interference.”
Quote in the paperNot a substantial claim - Premisecitation§ Universal Linear Optics · p. 4
A small set of single qubit gates including the Hadamard and π/8 gates, combined with two-qubit operations, is sufficient to realise a universal gate set for quantum computing.
“Combined with two-qubit operations, a small set of single qubit gates [Fig. 2(j)], including the Hadamard ( ˆ H ) and π/ 8 ( ˆ T ) gates are sufficient to realise a universal gate set for quantum computing [40].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [40] source
Not checked in the free run.
- Study design and conductcitation§ Universal Linear Optics · p. 4
Each boson sampling circuit configuration was chosen randomly from the Haar measure via a direct parameterisation of the circuit parameters.
“Each circuit configuration was chosen randomly from the Haar measure, which we implemented via a direct parameterisation of our circuit parameters [45], the probability density functions of which are displayed in Fig. 3(a).”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [45] source
Not checked in the free run.
- Premisecitation§ 1. Zero-Transmission Law · p. 12
The most general form of the zero-transmission law applies to any periodic input state to the Fourier transform matrix [68].
“The most general form of the ZTL applies to any periodic input state to the FT matrix [68].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [68] M. C. Tichy, Entanglement and interference of identical particles , Ph.D. thesis, Universit´ at Freiburg (2011). source
Not checked in the free run.
- Premisecitation§ Universal Linear Optics · p. 4
Quantum interference among the photons contributes to the pattern of the probability distribution in boson sampling.
“Quantum interference among the photons [43] contributes to the pattern of the probability distribution.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [43] source
Not checked in the free run.
- Interpretationcitation§ Universal Linear Optics · p. 4
In multi-photon experiments, deviations from unit fidelity are primarily caused by imperfections in the photon source such as reduced quantum interference between different pair creation events and higher order terms in the SPDC process.
“Note, in multi-photon experiments deviations from unit fidelity are primarily caused by imperfections in the photon source such as reduced quantum interference between different pair creation events [41], and higher order terms in the SPDC process.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [41] source
Not checked in the free run.
- Premisecitation§ Universal Linear Optics · p. 4
The classical intractability of boson sampling arises because the probability amplitude for each correlated photon detection event is given by a classically hard function, known as the permanent, of the submatrix that describes a particular route of photons through the circuit.
“The classical intractability arises because the probability amplitude for each correlated photon detection event is given by a classically hard function, known as the permanent [44], of the submatrix that describes a particular route of photons through the circuit.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [44]
Not checked in the free run.
- Interpretationreasoning§ 3. Bell state generator · p. 12
With knowledge of the data from the σz measurement, we are able to calculate the expectation of σx.
“such that, with knowledge of the data from the σ z measurement, we are able to calculate the expectation of σ x .”
Quote in the paperNot a substantial claim - Premisecitation§ Methods: Circuit implementation & analysis · p. 7
The heralded CNOT gate is a four-photon scheme [32] adapted for implementation with the six-mode LPU plus a seventh auxiliary coupling mode on chip.
“The heralded CNOT gate shown in Fig. 2(e), is a four-photon scheme [32] that has been adapted for implementation with the six-mode LPU, plus a seventh auxiliary coupling mode (mode 0) also contained on our chip.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [32] source
Not checked in the free run.
- Study design and conductnone given§ 3. Bell state generator · p. 12
It was possible to remove events caused by the non-ideal input from the measurement statistics in the Bell state generator.
“As in the case of the heralded CNOT gate, it was possible to remove events caused by the non-ideal input from the measurement statistics.”
Quote in the paperNot a substantial claim- Rests on an assumption: The unwanted photon terms from the non-ideal SPDC source can be removed by post-selection/detection without affecting the logical operation.
- Premisecitation§ Universal Linear Optics · p. 6
In LO experimental implementations, discrimination among CHMs can be accomplished via the observation of characteristic patterns of photonic quantum interference.
“In LO experimental implementations, discrimination among CHMs can be accomplished via the observation of characteristic patterns of photonic quantum interference [59-62].”
Quote in the paperSubstantial claim0 of 4 sources checked- cites [59] K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, and M. Zukowski, Appl. Phys. B 60 , S111 (2004). source
Not checked in the free run.
- cites [60] A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O'Brien, Nat. Comms. 2 , 224 (2011). source
Not checked in the free run.
- cites [61] A. Laing, T. Lawson, E. Mart´ ın L´ opez, and J. L. O'Brien, Phys. Rev. Lett. 108 , 260505 (2012).
Not checked in the free run.
- cites [62] N. Spagnolo, C. Vitelli, L. Aparo, P. Mataloni, F. Sciarrino, A. Crespi, R. Ramponi, and R. Osellame, Nat. Comms. 4 , 1606 (2013). source
Not checked in the free run.
- Interpretationown data§ Methods: Circuit implementation & analysis · p. 7
Dialling errors are non-uniform across the space of unitaries.
“implying dialling errors are non-uniform across the space of unitaries.”
Quote in the paperNot a substantial claim - Interpretationreasoning§ 3. Bell state generator · p. 12
The circuit used for Bell state generation implements a single qubit POVM with three elements {E+, E-, E1} corresponding to detection in modes {1,2,3}.
“This circuit implements a single qubit POVM with three elements, { E + , E -, E 1 } where”
Quote in the paperSubstantial claim
- May combine two claims. 12
- Classified as probably not a substantial claim. 9
May combine two claims.
Findingown data§ Universal Linear Optics · p. 1The system was programmed to implement heralded quantum logic and entangling gates.
“We programmed this system to implement heralded quantum logic and entangling gates, boson sampling with verification tests, and six-dimensional complex Hadamards.”
Quote in the paperSubstantial claimMay combine two claims.
Findingcitation§ Universal Linear Optics · p. 2The entanglement witness E calculated from these measurements was 0.673 ± 0.031, where E > 1/2 witnesses entanglement.
“We used these measurements to verify the entanglement of our state by calculating E = 1 / 2( 〈 σ x ⊗ σ x 〉 + 〈 σ z ⊗ σ z 〉 ), finding a value of E = 0 . 673 ± 0 . 031 where E > 1 / 2 witnesses entanglement [30].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [30] source
Not checked in the free run.
May combine two claims.
Findingown data§ Universal Linear Optics · p. 1The system is electrically and optically interfaced for arbitrary setting of all phase shifters, input of up to six photons, and measurement with a 12 single-photon detector system.
“Our six-mode universal system consists of a cascade of 15 MachZehnder interferometers with 30 thermo-optic phase shifters integrated into a single photonic chip that is electrically and optically interfaced for arbitrary setting of all phase shifters, input of up to six photons and their measurement with a 12 single-photon detector system.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ Universal Linear Optics · p. 4For the Bell state generator, the heralded CNOT, and the unheralded CNOT, the unitary fidelities were F_U = 0.998 ± 0.002, 0.994 ± 0.008, and 0.988 ± 0.005 respectively.
“For the Bell state generator, the heraldedand unheralded-CNOT respectively we found F U = 0 . 998 ± 0 . 002 , 0 . 994 ± 0 . 008 and 0 . 988 ± 0 . 005.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Findingnone given§ 2. Fabrication · p. 10The electric power required for a 2π phase shift is ∼0.8 W.
“The electric power required for a 2 π phase shift is ∼ 0 . 8 W .”
Quote in the paperNot a substantial claimMay combine two claims.
Findingreasoning§ 2. Heralded CNOT · p. 12Our photon source is based upon two independent SPDC events which produce the state ∑ η_i |i,i〉, such that in the four photon subspace |ψ4〉 ≈ |1111〉 + |2200〉 + |0022〉.
“Our photon source is based upon two independent SPDC events which produce the state ∑ i η i | i, i 〉 , such that in the four photon subspace we have | ψ 4 〉 ≈ | 1111 〉 + | 2200 〉 + | 0022 〉 .”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ Methods: Circuit implementation & analysis · p. 7Recalculating statistical fidelities based on the recovered unitary U′ for three three-photon boson sampling unitaries increased the mean statistical fidelity and reduced the range Fmax_s - Fmin_s from 0.102 to 0.023.
“This increased the mean statistical fidelity and reduced range F max s - F min s from 0 . 102 to 0 . 023”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Premisecitation§ Universal Linear Optics · p. 6The FT and F6^(2) are examples in the more general class of complex Hadamard matrices, which are related to mutually unbiased bases and are of fundamental interest in quantum information theory.
“The FT and F (2) 6 are examples in the more general class of complex Hadamard matrices (CHMs), which are related to mutually unbiased bases [54] and are of fundamental interest in quantum information theory [55].”
Quote in the paperNot a substantial claim0 of 2 sources checkedProbably not a substantial claim: may not pass S3 (load-bearing).
Premisecitation§ Universal Linear Optics · p. 6The ZTL has been proposed as a certificate for the capability of a device to implement boson sampling.
“Because large scale many-photon quantum interference is at the core of the ZTL, it has been proposed as a certificate for the capability of a device to implement boson sampling [52].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [52] M. C. Tichy, K. Mayer, A. Buchleitner, and K. Mølmer, Phys. Rev. Lett. 113 , 020502 (2014).
Not checked in the free run.
Probably not a substantial claim: may not pass S4 (based).
Study design and conductnone given§ 4. Circuit Characterisation · p. 10The triangular arrangement of our device allows each phase shifter to be isolated and characterised independently of any other.
“The triangular arrangement of our device allows each phase shifter to be isolated and characterised independently of any other.”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim. May combine two claims.
Interpretationreasoning§ 6. Phase accuracy · p. 11The δφ value lumps together error caused by the circuit, the control electronics and the calibration procedure, so is a good metric for our effective phase accuracy.
“This value lumps together error caused by the circuit, the control electronics and the calibration procedure, so is a good metric for our effective phase accuracy.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationnone given§ Methods: Circuit implementation & analysis · p. 7Detection in ancilla modes {3,4} of the compact Bell state generator occurs with probability p = 2/27 and heralds the state |Φ+〉 over the remaining modes with unit probability in the ideal case.
“Detection in ancilla modes { 3 , 4 } occurs with probability p = 2 / 27 and heralds the state | Φ + 〉 = ( | 1 1 , 0 2 , 1 5 , 0 6 〉 + | 0 1 , 1 2 , 0 5 , 1 6 〉 ) / √ 2 (where | n i 〉 represents n photons in the i th mode) over the remaining modes with unit probability in the ideal case.”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
Study design and conductown data§ Universal Linear Optics · p. 6The ZTL verification protocol was implemented in the same device and with the same procedure as the boson sampling experiments.
“Crucially, this verification protocol is implemented in the same device and with the same procedure as that for the boson sampling experiments above.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Premisecitation§ Universal Linear Optics · p. 6In the N = {2,3,5} case, all CHMs are equivalent to the respective FT matrix, while for N = 4 there exists a one parameter equivalence class.
“In the N = { 2 , 3 , 5 } case, all CHMs are equivalent to the respective FT matrix, while for N = 4 there exists a one parameter equivalence class.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [56] W. Tadej and K. ˙ Zyczkowski, Open Syst. Inf. Dyn. 13 , 133 (2006). source
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing).
Interpretationreasoning§ Methods: Circuit implementation & analysis · p. 7Compiling F(2)_6 onto our LPU requires unique phase shift values across the entire device for each implementation θ1, θ2 ∈ [0,2π).
“compiling F (2) 6 onto our LPU requires unique phase shift values across the entire device for each implementation θ 1 , θ 2 ∈ [0 , 2 π ).”
Quote in the paperNot a substantial claimMay combine two claims.
Premisecitation§ Methods: Circuit implementation & analysis · p. 7In the ideal case, detection of the two ancilla photons in the heralded CNOT occurs with probability p = 1/16 and guarantees the CNOT logic has been performed on the two photonic qubits.
“In the ideal case, the detection of the two ancilla photons, which occurs with probability p = 1 / 16, guarantees the CNOT logic has been performed on the two photonic qubits.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [32] source
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Premisecitation§ Universal Linear Optics · p. 6While a full classification of N = 6 CHMs is unknown, it is currently conjectured that the set consists of an isolated matrix S6^(0) which does not belong to any family, and a newly discovered four-parameter generic family G6^(4).
“Whilst a full classification of N = 6 CHMs is unknown, it is currently conjectured that the set consists of an isolated matrix S (0) 6 which does not belong to any family [57], and a newly discovered four-parameter generic family G (4) 6 [58].”
Quote in the paperNot a substantial claim0 of 2 sources checked
The paper relies on this without support.
For Bell states, measurements in common bases are correlated while measurements in different bases are uncorrelated.
“For Bell states, measurements in common bases should be correlated while measurements in different bases should be uncorrelated.”
The paper relies on this without support.
An essential requirement of boson sampling is indistinguishability among photons.
“An essential requirement of boson sampling is the indistinguishability among photons.”
The paper relies on this without support.
Any given unitary corresponds to a unique set of parameter values.
“Any given unitary then corresponds to a unique set of parameter values.”
The paper relies on this without support.
Up until now, observations of characteristic photonic quantum interference patterns have been too experimentally challenging for the six-dimensional case.
“Up until now, these observations have been too experimentally challenging for the six-dimensional case.”
The paper relies on this without support.
The unwanted photon terms from the non-ideal SPDC source can be removed by post-selection/detection without affecting the logical operation.
“Operating the BSG with the non-ideal state from our SPDC source requires the Bell state to be detected to remove the unwanted photon terms”
“Once again, the non-ideal input state requires a computational detection to remove unwanted terms.”
The paper relies on this without support.
The 8th lossy balancing mode can be equivalently implemented as a reduction in detection efficiency on the lower ancilla mode.
“The function of an 8th lossy balancing mode is implemented in post-processing as an equivalent reduction in detection efficiency on the lower ancilla mode”
The paper relies on this without support.
The |2200〉 and |0022〉 terms do not produce output states in the computational subspace.
“the other terms should not produce output states in the computational subspace”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the latter experiment, the circuit was too small to fully implement a heralded CNOT gate and only the classical XOR logic operations were demonstrated.
“In the latter experiment, the circuit was too small to fully implement a heralded CNOT gate and only the classical XOR logic operations were demonstrated.”
From Integrated-optics heralded controlled-NOT gate for polarization-encoded qubits (2018) · cites this paper as [26]
The paper says the heralded CNOT was implemented, not that the circuit was too small to implement it (Universal Linear Optics, p. 3; Methods, p. 7). It reports a computational truth-table test of that gate, but also reports quantum process tomography of a separate, unheralded CNOT (p. 3), contrary to the claim that only classical XOR logic was demonstrated. (LLM, conf=0.84)
Checked by a reasoning model — may be wrong.
Experimental — accuracy not yet measuredOur work expands on the first demonstrations of unheralded integrated CNOT gates using polarization-encoding or path-encoding, combining the desirable features of heralding, integration, and polarization encoding.
“Our work expands on the first demonstrations of unheralded integrated CNOT gates using polarization-encoding or pathencoding, [25][26][27] combining the desirable features of heralding, integration, and polarization encoding.”
From Integrated-optics heralded controlled-NOT gate for polarization-encoded qubits (2018) · cites this paper as [26]
The Unheralded CNOT section (p. 11) describes an integrated, unheralded CNOT using dual-rail (path-encoded) qubits. But Universal Linear Optics (p. 3) says earlier photonic chips had implemented unheralded two-qubit gates; it identifies this paper’s first integrated two-qubit processes as heralded ones. The source therefore supports the example of a path-encoded unheralded gate, but not its characterization as a first demonstration of that kind. (LLM, conf=0.88)
Experimental — accuracy not yet measuredMultiphoton quantum walks have the potential to demonstrate an undisputed quantum advantage through the boson-sampling algorithm.
“Further attention has been devoted to the computational complexity of multiphoton quantum walks, which has the potential to demonstrate an undisputed quantum advantage through the boson-sampling algorithm (13–19).”
From Two-photon quantum walk in a multimode fiber (2016) · cites this paper as [18]
In “Implementing boson sampling” (p. 4), the paper describes boson sampling with many photons as a potential route to computational capabilities beyond classical machines. It does not identify this as a result about multiphoton quantum walks. The “Verifying boson sampling” passage (p. 4) also says that checking large-scale results remains an open question, so the paper does not support calling the advantage “undisputed.” (LLM, conf=0.84)
Experimental — accuracy not yet measuredThe technological progress of integrated quantum photonics has enabled demonstrations of unheralded integrated CNOT gates, and recently also of a heralded CNOT gate.
“The technological progress of integrated quantum photonics has enabled demonstrations of unheralded integrated CNOT gates, [25][26][27] and recently also of a heralded CNOT gate.26”
From Integrated-optics heralded controlled-NOT gate for polarization-encoded qubits (2018) · cites this paper as [26]
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Self-citationHighly indistinguishable heralded single-photon sources using parametric down conversion
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Boson-Sampling in the light of sample complexityPreprint
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Complex Hadamard matrices of order 6: a four-parameter family
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Self-citationCalibration and high fidelity measurement of a quantum photonic chip
Li, H. W., Wabnig, J., Bitauld, D., Shadbolt, P., Politi, A., Laing, A., O'Brien, J. L., & Niskanen, A. O. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/6/063017 · Cited by 11 · see citing works
Self-citation
Flagged first, then by citations
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Cited by
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Quantum computational advantage using photons
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Integrated photonic quantum technologies
Wang, J., Sciarrino, F., Laing, A., & Thompson, M. G. (2020) · Nature Photonics · doi:10.1038/s41566-019-0532-1 · Cited by 1,576 · see citing works
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Optimal design for universal multiport interferometers
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Multidimensional quantum entanglement with large-scale integrated optics
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Self-citationPhotonic quantum information processing: a concise review
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Quantum transport simulations in a programmable nanophotonic processor
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Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light
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Hybrid integration methods for on-chip quantum photonics
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“For example, fast modulation is critical for wave-packet engineering [82] and demultiplexing many single photons from a single quantum emitter [83], while quasi-static phase tuning [84] can be used to “trim” waveguides for high-fidelity linear optical operations [85].”
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Chi, Y., Huang, J., Zhang, Z., Mao, J., Zhou, Z., Chen, X., Zhai, C., Bao, J., Dai, T., Yuan, H., et al. (2022) · Nature Communications · doi:10.1038/s41467-022-28767-x · Cited by 273 · see citing works
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Simulating the vibrational quantum dynamics of molecules using photonics
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Photonic implementation of boson sampling: a review
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- Authors
- Carolan, J., Harrold, C., Sparrow, C., Martín-López, E., Russell, N. J., Silverstone, J. W., Shadbolt, P. J., Matsuda, N., Oguma, M., Itoh, M., Marshall, G. D., Thompson, M. G., Matthews, J. C. F., Hashimoto, T., O’Brien, J. L., & Laing, A.
- Affiliations
- University of Bristol (GB)
- Nokia (United Kingdom) (GB)
- Imperial College London (GB)
- NTT (Japan) (JP)
- Corresponding author
- Laing, Anthony
- ORCID
- Venue
- Science
- Published
- 2015-08-14
- Volume
- 349
- Issue
- 6249
- Pages
- 711-716
- ISSN
- 0036-8075 (ISSN-L)
- 1095-9203
- OpenAlex
- W2097100165
- Semantic Scholar
- 009e98d679ea67ae8b7a71f0ccd62b9b0eaae3ef
- Cited by
- 1,093
- References
- 71
- Citations by year
- 2026: 67 · 2025: 91 · 2024: 104 · 2023: 102 · 2022: 110 · 2021: 118 · 2020: 116 · 2019: 127 · 2018: 92 · 2017: 86 · 2016: 71 · 2015: 8 · 2014: 1
- FWCI
- 83.99
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Science (publishedVersion)
- PubMed (publishedVersion)
- Bristol Research (University of Bristol) (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- UWA Profiles and Research Repository (UWA) (submittedVersion)
- arXiv (Cornell University)
- Funders
- U.S. Air Force Office of Scientific Research (AFOSR)
- U.S. Army Research Office (ARO) (W911NF-14-1-0133)
- European Research Council (ERC)
- Engineering and Physical Sciences Research Council (EPSRC)
- PIQUE (FP7-PEOPLE-2013-ITN)
- Centre for Nanoscience and Quantum Information (NSQI)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Photonic and Optical Devices
- Keywords
- Mach-Zehnder interferometer, thermo-optic phase shifters, photonic integrated circuits, entangling gates, boson sampling, Haar random unitaries, single-photon detection, quantum computing
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