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Experimental realization of universal quantum gates and a six-qubit entangled state using a photonic quantum walk
Open accessAbstract
For quantum computation using photons, performing deterministic quantum gate operations is a challenge due to the probabilistic nature of the photon-photon interaction. Encoding qubits in multiple degrees-of-freedom of photons and controlling operations between them is one of the promising ways to navigate the probabilistic behavior. Using single-photon discrete-time quantum walk in combination with polarization and path degrees-of-freedom, we experimentally demonstrate the realization of a universal set of quantum gates with high fidelity at room temperature. The deterministic realization of quantum gates through photonic quantum walk are characterized via quantum state tomography. For a three-qubit system using a single photon, the first qubit is encoded using polarization information, and the other two qubits are encoded using path information, closely resembling a Galton-board setup. To generate a six-qubit Greenberger-Horne-Zeilinger state, entangled photon pairs are used to entangle the two three-qubit modules on which gate operations are performed. We also provide insights into the mapping of photonic quantum walk operations to quantum circuits and propose methods to resourcefully scale. This demonstration marks a significant progress towards using quantum walks for quantum computing and provides a framework for using fewer photons in combination with different degrees-of-freedom of photon to scale the number of qubits.
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TL;DR
The paper experimentally demonstrates a universal set of quantum gates and a six-qubit GHZ state using single-photon discrete-time quantum walks with polarization and path degrees of freedom. Gates are realized deterministically at room temperature and characterized by quantum state tomography and entanglement visibility.
Key findings
- Universal gates—Hadamard, phase, and controlled-NOT—were implemented using a single photon’s polarization and path degrees of freedom, with the paper reporting “100% success probability” and high fidelity at room temperature.
- Two- and three-qubit modules were built by encoding the first qubit in polarization and additional qubits in path; C-NOT between path qubits was especially high fidelity because it is implemented by swapping or relabeling paths.
- A six-qubit GHZ state was generated by entangling two three-qubit modules with an SPDC photon pair; entanglement-witness visibilities in the H and D bases were 98.3% and 95.1%, respectively.
- Supporting characterization included single-photon Mach-Zehnder visibility \(V \approx 93.4\%\), Bell-state fidelity 98.12%, H/V and A/D visibilities of 98.6% and 98.1%, and a Bell-CHSH violation \(S = 2.77(\pm 0.001)\).
Methods
- Heralded single photons and entangled photon pairs were generated via type-II spontaneous parametric down-conversion in a 10-mm PPKTP crystal pumped by a 405 nm CW diode laser, with the crystal at 32.3°C for degenerate 810 nm emission.
- Qubits were encoded in polarization using quarter-half-quarter wave plates and in path using beam splitters, Mach-Zehnder interferometry, and phase control; gate operations were mapped from discrete-time quantum walk coin and shift operators.
- Output states were characterized by quantum state tomography for two- and three-qubit gates, and the six-qubit GHZ state was assessed by entanglement-witness visibility measurements; the paper reports average ten gate operations for two-qubit QST and up to twenty-eight for three-qubit QST.
Limitations
- Stated: the beam splitter used for two-qubit tomography was not exactly 50:50 (BS005), which significantly impacts fidelity; path-encoded qubits are sensitive to phase instability, and no active stabilization was used, only passive stabilization.
- Stated: Hadamard on the path qubit relies on path interference and slightly lowers fidelity during QST; the polarization-controlled C-NOT used a PBS with 1000:1 extinction ratio, and better extinction would improve results.
- Stated and evident: scaling by using a single photon in multiple two-qubit path networks causes fidelity loss, while involving more photons makes connections between modules probabilistic; the six-qubit state is characterized by visibility/witness rather than full six-qubit tomography in the provided text.
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“We report high fidelity for all universal quantum gate operations by performing quantum state tomography (QST).”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > I. INTRODUCTION
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“A single photon's polarization and its interference along different paths achieve all multi-qubit gate operations in a three-qubit system.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > I. INTRODUCTION
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“We have demonstrated that some of the two-qubit gates, C-NOT between path qubits, are easily realizable in the scheme compared to other approaches.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > III. CONCLUSION
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In the paper
“Using single-photon discrete-time quantum walk in combination with polarization and path degrees-of-freedom, we experimentally demonstrate the realization of a universal set of quantum gates with high fidelity at room temperature.”
- Also stated in: § III. CONCLUSION · boosted
“In this work we have report the experimental demonstration of realizing universal set of quantum gates using photonic quantum walk.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Rests on an assumption: Photons are naturally resistant to interactions with background electromagnetic fields and can function efficiently at room temperature while maintaining stability and coherence during quantum operations.
- Also stated in: § III. CONCLUSION · boosted
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In the paper
“all universal gates are implemented”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > IV. METHODS
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“To generate a six-qubit Greenberger-Horne-Zeilinger state, entangled photon pairs are used to entangle the two three-qubit modules on which gate operations are performed.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > Abstract
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“By placing a PBS in the two separate three qubit units we can generate the six-qubit GHZ state |Ψ⟩ GHZ = 1 √ 2 (|0⟩ ⊗6 + |1⟩ ⊗6 ).”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > Gate
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“We can note that the fidelity of C-NOT gate between two path qubits is very high when compared to C-NOT between the polarization and path qubits.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > TABLE I: Q-H-Q angles for Pauli gates.
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“the beam splitter used for interference is not exactly 50:50(BS005) for both S-and P-polarizations.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > IV. METHODS
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“In the scheme only one photon is involved to realize two-qubit and three-qubit system.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > III. CONCLUSION
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“Since, BS as a Hadamard operation for our purpose, we always consider an extra phase of π to the |1⟩ arm, so that the final unitary transformation matrix exactly resembles Hadamard transformation[57,58].”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > V. APPENDIX
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“Building on the polarization-path encoded state, the two paths are further split to realize polarization-path-path encoded state, enabling a threequbit system.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > IV. METHODS
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“In Table II fidelity of all the one-and two-qubit quantum gate operation on two-qubit state composing of polarization and path degree-of-freedom obtained after performing QST is reported.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > TABLE I: Q-H-Q angles for Pauli gates.
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“The measured visibilities in the H/V and A/D bases were 98.6% and 98.1%, respectively, with a Bell-CHSH inequality violation of S = 2.77(±0.001).”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > IV. METHODS
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“the Hadamard gate on the path qubit inherently relies on path interference, which slightly lowers its fidelity during QST.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > IV. METHODS
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“manipulating δϕ enables the preparation of all fundamental states: |+⟩, |-⟩, |L⟩, and |R⟩.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > V. APPENDIX
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“The visibility in the H and D bases for these paths was measured to be 98.3% and 95.1%, respectively.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > Gate
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“In Fig. 1(d) the measured visibility for the single-photon MZI is V ≈ 93.4%, is shown.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > TABLE I: Q-H-Q angles for Pauli gates.
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“In the scheme, multiple qubits were encoded using polarization and paths degree of freedom of single photon and universal quantum gates were implemented with 100% success probability, and high fidelity.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > III. CONCLUSION
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“For the six-qubit system an entangled photon pairs from SPDC process was used to source two threequbit modules and realize full six-qubit GHZ state.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > III. CONCLUSION
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“At a pump power of 15 mW, the photon generation rate is 6.93 × 10 5 counts/s, with a heralding efficiency of 22.3% after coupling to a single-mode fiber.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > V. APPENDIX
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“The obtained coincidence visibility for H & D basis is 98.3% and 95.1%.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > V. APPENDIX
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“solid red and black plot represent the numerical fit that is in agreement with the experimental data.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > V. APPENDIX
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“This polarization-path dual encoding facilitates the implementation of polarization-controlled operations and path-controlled operations, enabling quantum computations to be performed by emulating gates through unitary evolution.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > I. INTRODUCTION
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“The interferometer was fully enclosed using a custom-built isolation cover and mounted within cage assemblies to suppress air currents and enhance environmental isolation.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > IV. METHODS
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- Rests on an assumption: Path-encoded qubits are sensitive to phase instability.
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In the paper
“To assess the quality of the prepared GHZ state, we used an entanglement witness measurement in the path states associated with specific polarizations.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > Gate
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“In particular, discrete-time one-dimensional quantum walks have been employed to engineer various high-dimensional quantum states, highlighting their versatility and potential, [40,41].”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > I. INTRODUCTION
What the sources say
- Not matchedcites [40]
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“Optical fibers used in the setup were jacketed and thermally insulated to further suppress phase noise arising from temperature fluctuations.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > IV. METHODS
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- Rests on an assumption: Path-encoded qubits are sensitive to phase instability.
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“motorized wave-plates were incorporated to avoid repeatedly opening and closing the enclosure, thereby maintaining consistent environmental conditions.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > IV. METHODS
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- Rests on an assumption: Path-encoded qubits are sensitive to phase instability.
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In the paper
“By choosing the proper angles of Q-H-Q we can get all the Pauli matrices, enabling all the singlequbit operations on polarization qubits.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > TABLE I: Q-H-Q angles for Pauli gates.
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In the paper
“This is because to use of only swapping of path between path qubits to implement C-NOT gate.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > TABLE I: Q-H-Q angles for Pauli gates.
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In the paper
“Additionally, theoretical proposals report that quantum walks are also primitive for implementing quantum gates, thereby enabling universal quantum computation using both, continuous-time [49][50][51] and discrete-time [52,53] quantum walk variants.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > I. INTRODUCTION
What the sources say
- Not matchedcites [49]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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In the paper
“These quantum walks have also been experimentally implemented using linear optical systems that control the polarization, path, and other degrees of freedom of single-photon states [42][43][44][45][46][47][48].”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > I. INTRODUCTION
What the sources say
- Not matchedcites [42]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [43]
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- Not matchedcites [45]
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- Not matchedcites [46]
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- Not matchedcites [48]
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“Fidelities directly accounts for experimental inaccuracies involved in the process.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > III. CONCLUSION
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In the paper
“despite the inherent probabilistic nature of the photon-photon interaction that has to be invoked to probabilistically implement quantum gate operations reducing the success probability of computational task [16][17][18].”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > I. INTRODUCTION
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In the paper
“In addition, one can access various degrees-of-freedom of single photons to simultaneously encode multiple-qubits and experimentally control them to generate complex quantum states, demonstration of eighteen-qubit GHZ state generation using six-entangled photons is one such example [24].”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > I. INTRODUCTION
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- Not matchedcites [24]
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In the paper
“The discrete-time quantum walk framework reported here can be readily implemented on a photonic integrated circuits (PICs), provided polarization control within the circuit is achievable and promising results are being reported in that direction [11].”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > Gate
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- Not matchedcites [11]
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In the paper
“These are definite and not probabilistic in nature, making this a robust scheme.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > I. INTRODUCTION
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In the paper
“Moreover, the CNOT gate between the path-encoded qubits can be realized more easily by appropriately rerouting or relabeling the paths, making the implementation two-qubit gate straight forward and efficient.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > TABLE I: Q-H-Q angles for Pauli gates.
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In the paper
“precision mirror mounts with low thermal expansion coefficients were em-ployed, effectively reducing phase fluctuations.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > IV. METHODS
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- Rests on an assumption: Path-encoded qubits are sensitive to phase instability.
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In the paper
“Though all the six-qubits in the system are not directly connected to one another, through entangled photon pairs they can be connected and engineered to control a six-qubit system as shown in Fig. 5(d).”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > Gate
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In the paper
“This quantum walk based quantum computing scheme can be extended to other photonic degrees of freedom-such as frequency, time-bin, and orbital angular momentum-using hybrid encoding strategies.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > III. CONCLUSION
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None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“The collection of operators { Ŝ0 ± , Ŝ1 ± , Ĉ(τ, η, ζ, θ), I} constitute a versatile set of operators representing the quantum walk.Moreover, this set of operators can be effectively employed to realize the universal set of quantum-gates within the discrete-time quantum walk framework.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > II. RESULTS
What the sources say
- Not matchedcites [52]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [53]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This flexibility enables scalable and high-dimensional quantum photonic architectures.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > III. CONCLUSION
Tests✓ Asserted: passes✗ Checkable: fails✓ Load-bearing: passes✗ Based: failsProbably not a substantial claim. It may be too vague to check against evidence. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However, single photon in multiple network of two-qubit position basis will results in loss of fidelity.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > Gate
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The reported fidelities for various quantum gates using our scheme in bulk optics can be improved in PICs which offer advantages over bulk optics, including better scalability by mitigating issues like alignment and sustained stability.”
§ Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk > Gate
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.
The paper relies on this without support.
Photons are naturally resistant to interactions with background electromagnetic fields and can function efficiently at room temperature while maintaining stability and coherence during quantum operations.
“Since photons are naturally resistant to interactions with background electromagnetic fields, they can function efficiently at room temperature while maintaining stability and coherence during quantum operations.”
The paper relies on this without support.
Path-encoded qubits are sensitive to phase instability.
“Path-encoded qubits are sensitive to phase instability.”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
GHZ visibility checks name different path pairs
MinorThe results text says the visibility checks compare |00⟩ with |10⟩ and |01⟩ with |11⟩. The figure caption instead identifies the measured coincidences as |00⟩-|00⟩ and |11⟩-|11⟩, while reporting the same H- and D-basis visibilities.
“Due to the C-NOT gate operations, we performed visibility checks between the |00⟩ and |10⟩ paths of the two three-qubit units.Similarly, visibility checks were conducted between the |01⟩ and |11⟩ paths of the two three-qubit units.The visibility in the H and D bases for these paths was measured to be 98.3% and 95.1%, respectively.”
“The plots (a) and (b) shows the coincidence between arms |00⟩, |00⟩ and |11⟩, |11⟩ for H and D basis respectively, shown in Fig5.The red and blue dots are the data points measured experimentally and solid blue, red lines are the numerical fits.The obtained coincidence visibility for H & D basis is 98.3% and 95.1%.”
Citations
Cites
Quantum supremacy using a programmable superconducting processor
Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J. C., Barends, R., Biswas, R., Boixo, S., Brandao, F. G. S. L., Buell, D. A., et al. (2019) · Nature · doi:10.1038/s41586-019-1666-5 · Cited by 7,720
A scheme for efficient quantum computation with linear optics
Knill, E., Laflamme, R., & Milburn, G. J. (2001) · Nature · doi:10.1038/35051009 · Cited by 5,880
Raussendorf, R., & Briegel, H. J. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.5188 · Cited by 4,477
Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems
Engel, G. S., Calhoun, T. R., Read, E. L., Ahn, T.-K., Mančal, T., Cheng, Y.-C., Blankenship, R. E., & Fleming, G. R. (2007) · Nature · doi:10.1038/nature05678 · Cited by 3,315
Linear optical quantum computing with photonic qubits
Kok, P., Munro, W. J., Nemoto, K., Ralph, T. C., Dowling, J. P., & Milburn, G. J. (2007) · Reviews of Modern Physics · doi:10.1103/revmodphys.79.135 · Cited by 2,904
Clarke, J. L., & Wilhelm, F. K. (2008) · Nature · doi:10.1038/nature07128 · Cited by 2,129
Quantum simulations with ultracold atoms in optical lattices
Gross, C., & Bloch, I. (2017) · Science · doi:10.1126/science.aal3837 · Cited by 1,527
Experimental one-way quantum computing
Walther, P., Resch, K. J., Rudolph, T., Schenck, E., Weinfurter, H., Vedral, V., Aspelmeyer, M., & Zeilinger, A. (2005) · Nature · doi:10.1038/nature03347 · Cited by 1,273
Environment-assisted quantum walks in photosynthetic energy transfer
Mohseni, M., Rebentrost, P., Lloyd, S., & Aspuru-Guzik, A. (2008) · The Journal of Chemical Physics · doi:10.1063/1.3002335 · Cited by 1,189
Quantum random-walk search algorithm
Shenvi, N., Kempe, J., & Whaley, K. B. (2003) · Physical Review A · doi:10.1103/physreva.67.052307 · Cited by 1,150
Flagged first, then by citations
Research works printed but not linked: 3
- 10.1103/physrevlett.104.050502 · DOI · Paper page
- G. Weihs, Coherence and Statistics of Photons and Atoms
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/r7yp-1vz4 for generic state preparation and state tomography.
Cited by
Sorted by citations
Deterministic quantum teleportation of a path-encoded state using entangled photons
Krishnan, A. T., Sengupta, K., Dinesh, S. P., & Chandrashekar, C. M. (2025) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-025-00434-2 · Cited by 5
Self-citationClassical‐to‐Quantum Transfer of Geometric Phase for Controlled Manipulation of Quantum State
Kumar, V., Kaushik, C., Ebrahimzadeh, M., Chandrashekar, C. M., & Samanta, G. K. (2026) · Advanced Quantum Technologies · doi:10.1002/qute.70461 · Cited by 3
Self-citationShu, H. (2026) · Optics Express · doi:10.1364/oe.590422 · Cited by 2
Deutsch-Jozsa and Bernstein-Vazirani algorithm using single-particle discrete-time quantum walk
Sangwan, R., Ramaswamy, V., Sukumar, H., & Raghava, G. N. (2025) · IEEE International Conference on Electronics, Computing and Communication Technologies (CONECCT) · doi:10.1109/conecct65861.2025.11306771 · Cited by 2
Quantum walk with coherent multiple translations induces fast quantum gate operations
Zhang, Y., Qiao, X., Wang, L., He, Y., Dong, Z., Chen, X., & Yuan, L. (2026) · Light Science & Applications · doi:10.1038/s41377-025-02106-3 · Cited by 1
Metadata
- Authors
- Sengupta, K., Dinesh, S. P., Shafi, K. M., Asokan, S., & Chandrashekar, C. M.
- Affiliations
- Indian Institute of Science Bangalore (IN)
- Homi Bhabha National Institute (IN)
- Venue
- Physical Review Applied
- Publisher
- American Physical Society (APS)
- Published
- 2025-08-06
- Volume
- 24
- Issue
- 2
- ISSN
- 2331-7019 (ISSN-L)
- OpenAlex
- W4412403190
- Cited by
- 7
- References
- 58
- Citations by year
- 2026: 5 · 2025: 2
- FWCI
- 1.80
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Applied (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Office of Principal Scientific Advisor (Prn.SA/QSim/2020)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- photonic quantum walks, universal quantum gates, GHZ states, polarization encoding, path encoding, deterministic quantum gates, quantum circuit mapping
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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