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REVIEW 4 major objections 5 minor 45 references

Quantum State Preparation by Improved MPS Method

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Improved MPS preparation loads bounded-rank amplitude states in $O(\log n)$ depth and needs only two CNOTs per two-qubit gate.

desk verdict Useful topology-aware MPS preparation recipe, but the log-depth claim is known and the fidelity argument is weaker than advertised. read the letter →

arxiv 2508.12821 v1 pith:O5GCZGDL submitted 2025-08-18 quant-ph

Chao Wang , Pengrui Zhou , Xi-Ning Zhuang , Ziwei Cui , Menghan Dou , Zhao-Yun Chen , Guo-Ping Guo This is my paper · ORCID
classification quant-ph
keywords quantumstatepreparationamplitudeencodingmatrixproductlogarithmiccircuitdepthtwo-qubitgatedecompositionCNOTcounttensornetworkboundedMPSrank
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper aims to show that amplitude-encoded quantum states with bounded matrix-product-state rank can be prepared by a unitary circuit of logarithmic depth, instead of the linear depth of standard MPS methods. The key move is to apply SVD-based two-qubit disentanglers in parallel layers, approximately zeroing one qubit per gate so the number of entangled qubits halves each round. A second claim is that every two-qubit unitary arising from the SVD can be implemented with two CNOT gates plus single-qubit gates, cutting the two-qubit gate count by roughly one third for complex amplitudes. If correct, this makes loading smooth functions and financial distributions practical on near-term hardware, including grid-connected chips where the depth scales as the square root of the qubit count.

What carries the argument

The carrying object is the SVD of the $4\times 2^{n-2}$ amplitude matrix $A_{a,b}$: applying $U^{-1}$ from $A=USV^\dagger$ converts the amplitudes into diagonal singular-value rows, so one qubit is disentangled up to truncation. This makes two-qubit gates position-independent, enabling parallel layers of $\lfloor n/2\rfloor$ gates that halve the number of active qubits per round (the tree/hypercube tensor-network ordering) and yield $O(\log n)$ depth. The second mechanism is the unitary equivalence class $\{\mathrm{diag}(U_1,U_2)U^{-1}\}$, combined with the cosine-sine/KAK decomposition, which produces the two-CNOT implementation of each two-qubit gate. A third supporting piece is the ring subadditivity/submultiplicativity of MPS ranks, which certifies that sums and products of basic function states remain preparable at bounded cost.

What would settle it

Take an $n$-qubit state whose Schmidt decomposition across some middle cut has three equal nonzero coefficients (bond dimension 3). IMPS with $\chi=2$ truncates one of the three Schmidt modes at that cut, so the overlap of the prepared state with the exact target is at most $2/3$ there; computing this overlap for increasing $n$ will show the logarithmic-depth circuit does not prepare the exact state and that fidelity saturates below one, isolating the bound on the claim.

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Extended reading notes

Core claim

Starting from an MPS with bond dimension $\chi=2$, the protocol builds a $4\times 2^{n-2}$ amplitude matrix $A_{a,b}$ for any pair of qubits $(a,b)$, performs the SVD $A=USV^\dagger$, and applies $U^{-1}$; the state of qubit $a$ becomes the two dominant singular-value rows, so after truncation that qubit is approximately $|0\rangle$. Because the pair is arbitrary, the paper pairs disjoint qubits into a single parallel layer, disentangling roughly half the remaining qubits per layer, which gives the claimed $O(\log n)$ depth via a tree- or hypercube-tensor-network ordering. For two-qubit unitaries, the paper uses the freedom to left-multiply by an arbitrary block-diagonal unitary and a cosine-sine (KAK) decomposition to obtain a representative implemented by two CNOT gates and single-qubit rotations, stated as Theorem 1. The paper further proves subadditivity and submultiplicativity of MPS rank for element-wise sums and products of function states, identifying a ring of bounded-rank functions that includes cosine, linear, exponential-derived, and common distribution states, and gives numerical evidence that the hypercube ordering beats conventional MPS and TTN in fidelity at matched depth.

Load-bearing premise

The whole depth and fidelity guarantee rests on truncating every SVD to its two largest singular values (bond dimension $\chi=2$); if the target state has substantial weight in the discarded singular vectors, the logarithmic-depth circuit only produces an approximation whose fidelity can be far from one.

Editorial extensions

If this is right

  • Bounded-rank states such as cosine, linear, GHZ, and W states—and any element-wise sum or product built from exponentials, cosines, and linear functions—are preparable exactly in $O(\log n)$ depth.
  • Complex-valued amplitude loading uses roughly one third fewer CNOT gates per two-qubit unitary, directly cutting the dominant error source on noisy hardware.
  • On an $n\times m$ grid chip, the same construction prepares a state in depth about $(m+n)/2$, i.e. $O(\sqrt{N})$ for a square grid, and rank-2 function states in $O(\max(m,n))$.
  • The protocol remains unitary and does not require mid-circuit measurement or ancillas, so the prepared states can be reused inside amplitude estimation or quantum Monte Carlo subroutines.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An implicit consequence is that the equivalence-class trick behind the two-CNOT decomposition is not tied to MPS: any SVD-based two-qubit synthesis with the same block-unitary and cosine-sine structure could inherit the one-third CNOT saving, so it is worth testing on generic unitary compilation pipelines.
  • The paper's edge-contraction view turns chip mapping into a graph problem; a testable extension is to search contraction orders that minimize truncation error, not just depth, which could improve fidelity on irregular topologies beyond the grid example.
  • The rank-ring result suggests a generative recipe: if a financial payoff or probability density can be written as a short sum or product of exponentials, cosines, and polynomials, its MPS rank is bounded by a simple formula, making efficient loading a syntactic check rather than a numerical search.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The manuscript proposes an improved Matrix Product State (IMPS) amplitude-encoding protocol. The method applies SVD-based two-qubit disentangling gates in parallel at each stage, which the authors claim yields O(log n) circuit depth for states with bounded MPS rank. A second ingredient uses a Cartan/KAK decomposition to replace each generic two-qubit unitary by an element of an equivalence class implementable with two CNOT gates instead of three. The paper defines a ring of bounded-MPS-rank functions and reports numerical comparisons on three functions and three distributions using MPS, TTN, HEN, and HTN connectivity schemes, claiming higher fidelity and lower depth, together with a discussion of grid-topology adaptation.

Significance. If established, the claimed log-depth preparation of bounded-MPS-rank amplitude states with roughly one-third fewer two-qubit gates would be practically useful for NISQ-era amplitude encoding and for quantum Monte Carlo integration. The SVD-based parallel disentangling idea is transparent, the equivalence-class construction around Eq. (6) is a useful observation, and the numerical experiments cover relevant financial and distribution-type benchmarks. However, the central proposition and theorem are not supported by the submitted text: Proposition 1 has no error analysis, and Theorem 1's proof is in a missing appendix. In addition, the numerical comparison changes the truncation/reset protocol between method families, and the benchmarks are generated from the same bounded-rank ring that the method assumes. These gaps currently limit the significance of the results.

major comments (4)
  1. [Sec. 2.1, Proposition 1] Proposition 1 is asserted with a gate-counting argument rather than a proof. The observation that floor(n/2) two-qubit gates can be applied in parallel per layer only establishes a circuit-depth upper bound if the truncations are exact or have controlled errors. No cumulative error bound for O(log n) layers of chi=2 truncation is provided, and no theorem connects the global MPS rank of the target state to the error of the intermediate SVDs. The proposition should be replaced by a precise statement with proof for the exact rank-2 case and a separate approximate statement with an error bound in terms of the discarded singular values.
  2. [Sec. 2.2, Theorem 1] The proof of Theorem 1 is said to be provided in Appendix A, but no Appendix A appears in the manuscript. The two-CNOT decomposition is one of the paper's main contributions, so this proof must be included. Moreover, the theorem as worded ('Any fourth-order unitary matrix arising from the SVD in MPS amplitude preparation') is too broad: for a 4 by 2^{n-2} amplitude matrix the left singular matrix can be an arbitrary 4x4 unitary, and a generic two-qubit unitary requires three CNOT gates. The theorem should be restricted to the equivalence-class matrices constructed in Eq. (6), with a proof that those matrices admit a two-CNOT decomposition.
  3. [Sec. 3, numerical comparisons] The fidelity comparison is not controlled. Section 3 states that for MPS and TTN 'truncation involves resetting the amplitude to its original length after each layer,' whereas for HTN and HEN 'the amplitude length is reset after each U-depth.' Because the reported fidelity advantage of HTN/HEN is the paper's main empirical claim, the comparison must use identical reset/truncation rules for all four methods, or both rules must be reported for each method. In addition, Fig. 8 compares the chip-adapted IMPS at U-depths 5 and 10 with the traditional MPS at U-depth 11, so the claim of 'comprehensively surpasses its fidelity' should be stated with the depth difference made explicit.
  4. [Sec. 2.3, exact rank-2 claim] The statement that 'we can precisely prepare states with an MPS rank of 2' in O(log n) depth is not proved for the schedules actually used. For a non-contiguous pair (a,b), the matrix A_{a,b} in Eq. (1) has rank bounded by the product of the two boundary bond dimensions, which is up to chi^2 = 4 even for a rank-2 MPS, so truncating to the two largest singular values is not exact. The exactness claim appears plausible for the TTN schedule, where each pair is adjacent in the residual order at each stage, but it must be stated for that schedule and proved, and the HTN/HEN schedules need a separate error analysis.
minor comments (5)
  1. [Sec. 1] The terms U-depth and layer are defined at the end of the introduction, but in Section 3 'layer' is used for both the core preparation block and for a sequential two-qubit gate layer; please use one consistent terminology.
  2. [Sec. 2.1] The reference list contains a duplicated entry: references [46, 47, 47] are cited in the sentence on reinforcement learning; please correct.
  3. [Sec. 2.3, Theorem 2] The 'well-known theorem for tensor networks' on the ring structure is stated without a citation or proof; please add a reference or a proof sketch.
  4. [Fig. 2] The caption lists the disentangled qubits but not the gate pairs for each layer; for reproducibility, list the pairs acted on in each layer (e.g., second layer pairs (1,3) and (5,7)).
  5. [Sec. 3] The numerical benchmarks are all generated from the bounded-rank ring structure introduced in Sec. 2.3; while this is consistent with the stated scope, a test on states with known MPS rank outside this construction would strengthen the claimed broad applicability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central depth and gate-count claims follow from SVD/CSD derivations and circuit scheduling, not from fitted inputs or load-bearing self-citation.

full rationale

No circular derivation chain is present. The O(log n) depth claim in Proposition 1 is a resource count of the parallel SVD-disentangling schedule, not a prediction imported from fitted data. The two-CNOT gate reduction in Theorem 1 follows from a cosine-sine/KAK decomposition and an explicit gauge choice (Eqs. 5-6), with the decomposition proof deferred to an appendix; it does not define the target theorem into existence. The bounded-rank function class in Sec. 2.3 rests on the standard subadditivity/submultiplicativity of MPS ranks (Theorem 2) and is not used as an input to any fitted prediction. The only self-citation visible in the text, Ref. [23], appears in the introduction when discussing training-based approaches and is not load-bearing for the paper's claims. The numerical validation uses functions drawn from the ring-generated class the paper itself defines, and Sec. 3 notes that MPS/TTN and HTN/HEN use different truncation protocols; these are limitations on the strength and fairness of the empirical comparisons, and Proposition 1 lacks an explicit fidelity bound for the chi=2 truncation on non-contiguous pairings. These are correctness and validation-design concerns, not circular reductions. Under the stated rules, the absence of a constructed equivalence between inputs and claimed outputs means the appropriate finding is no significant circularity.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The method's resource guarantees rest on the low-rank MPS assumption and on unproven (appendix-missing) decomposability of the two-qubit gates; no physical entities or fitted constants are introduced beyond the design choice chi=2.

free parameters (1)
  • MPS bond dimension (singular value truncation) chi = 2
    The method fixes chi=2 for all SVD truncations; no analytic fidelity guarantee is given for the benchmark functions, so the success of the method rests on this hand-chosen constant.
assumptions (5)
  • domain assumption The target quantum state is well approximated by an MPS with bond dimension 2 at every step of the disentangling process.
    Sec 2.1 sets d=2, chi=2 and discards all but the two largest singular values after each SVD; the claimed O(log n) depth and fidelity are conditional on this assumption.
  • ad hoc to paper The amplitude matrix A_{a,b} admits an SVD whose top-two retained subspace is sufficient for the application.
    Eqs. (2)-(3) truncate to the top two singular values; this algorithmic approximation is validated only numerically, not derived.
  • standard math MPS rank subadditivity and submultiplicativity (Theorem 2) hold for the ring of element-wise addition and multiplication of discretized functions.
    Used in Sec 2.3 to bound the rank of test functions; stated as well-known without proof.
  • domain assumption Any two-qubit gate of the form in Eq. (6) can be implemented with two CNOT gates and single-qubit gates.
    Relied on for the 33% gate-count reduction; presented as Theorem 1 but the proof is deferred to a missing Appendix A.
  • domain assumption The hardware topologies (chain, grid, hypercube) allow the assumed parallel execution of non-adjacent gates without additional crosstalk constraints.
    The depth analysis in Sec 3 assumes all gates in a layer can run in parallel with no further restrictions.

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Pith. "Pith review of Quantum State Preparation by Improved MPS Method." pith.science (2026). https://pith.science/paper/O5GCZGDL

@misc{pith2026250812821,
  author       = {Pith},
  title        = {Pith review of: Quantum State Preparation by Improved MPS Method},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O5GCZGDL}},
  note         = {Machine review of arXiv:2508.12821}
}
read the original abstract

Efficient encoding of classical information plays a fundamental role in numerous practical quantum algorithms. However, the preparation of an arbitrary amplitude-encoded state has been proven to be time-consuming, and its deployment on current noisy devices can be challenging. In this work, we propose an improved Matrix Product State(MPS) method preparation protocol with an exponential reduction on the circuit depth, as well as topological adaptability. By refined utilization of the disentangling principle, we also reduce approximately 33% two-qubit gate count. To validate our method, we study various families of functions and distributions with provably bounded MPS rank. Numerical experiments show that our method significantly reduces circuit depth while achieving higher fidelity for states arising in financial and other applications.

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Works this paper leans on

45 extracted references · 33 canonical work pages

  1. [37]

    Preparation of matrix product states with log-depth quantum circuits.Physical Review Letters, 132(4):040404, 2024

    Daniel Malz, Georgios Styliaris, Zhi-Yuan Wei, and J Ignacio Cirac. Preparation of matrix product states with log-depth quantum circuits.Physical Review Letters, 132(4):040404, 2024

    work page 2024

  2. [1]

    Quantum algorithm for linear systems of equations.Physical review letters, 103(15):150502, 2009

    Aram W Harrow, Avinatan Hassidim, and Seth Lloyd. Quantum algorithm for linear systems of equations.Physical review letters, 103(15):150502, 2009

    2009

  3. [2]

    Quantum algorithm for systems of linear equations with exponentially improved dependence on precision

    Andrew M Childs, Robin Kothari, and Rolando D Somma. Quantum algorithm for systems of linear equations with exponentially improved dependence on precision. SIAM Journal on Computing, 46(6):1920–1950, 2017

    1920

  4. [3]

    Toward pric- ing financial derivatives with an ibm quantum computer.Physical Review Research, 3(1):013167, 2021

    Ana Martin, Bruno Candelas, Ángel Rodríguez-Rozas, José D Martín-Guerrero, Xi Chen, Lucas Lamata, Román Orús, Enrique Solano, and Mikel Sanz. Toward pric- ing financial derivatives with an ibm quantum computer.Physical Review Research, 3(1):013167, 2021

    work page 2021

  5. [4]

    Quantum spectral methods for differential equa- tions.Communications in Mathematical Physics, 375(2):1427–1457, 2020

    Andrew M Childs and Jin-Peng Liu. Quantum spectral methods for differential equa- tions.Communications in Mathematical Physics, 375(2):1427–1457, 2020

    work page 2020

  6. [5]

    Linear combination of hamiltonian simulation for nonunitary dynamics with optimal state preparation cost.Physical Review Letters, 131(15):150603, 2023

    Dong An, Jin-Peng Liu, and Lin Lin. Linear combination of hamiltonian simulation for nonunitary dynamics with optimal state preparation cost.Physical Review Letters, 131(15):150603, 2023

    2023

  7. [6]

    Quantum algorithm for time-dependent dif- ferential equations using dyson series.Quantum, 8:1369, 2024

    Dominic W Berry and Pedro CS Costa. Quantum algorithm for time-dependent dif- ferential equations using dyson series.Quantum, 8:1369, 2024

    work page 2024

  8. [7]

    Time-marching based quantum solvers for time- dependent linear differential equations.Quantum, 7:955, 2023

    Di Fang, Lin Lin, and Yu Tong. Time-marching based quantum solvers for time- dependent linear differential equations.Quantum, 7:955, 2023

    work page 2023

Show all 45 references
  1. [8]

    Heralded state preparation in a superconducting qubit.Physical review letters, 109(5):050506, 2012

    JE Johnson, Christopher Macklin, DH Slichter, R Vijay, EB Weingarten, John Clarke, and Irfan Siddiqi. Heralded state preparation in a superconducting qubit.Physical review letters, 109(5):050506, 2012

    2012

  2. [9]

    Experimental demonstration of fault-tolerant state preparation with su- perconducting qubits.Physical review letters, 119(18):180501, 2017

    Maika Takita, Andrew W Cross, Antonio D Córcoles, Jerry M Chow, and Jay M Gambetta. Experimental demonstration of fault-tolerant state preparation with su- perconducting qubits.Physical review letters, 119(18):180501, 2017

    2017

  3. [10]

    Superconducting qubits: Current state of play.Annual Review of Condensed Matter Physics, 11(1):369–395, 2020

    Morten Kjaergaard, Mollie E Schwartz, Jochen Braumüller, Philip Krantz, Joel I-J Wang, Simon Gustavsson, and William D Oliver. Superconducting qubits: Current state of play.Annual Review of Condensed Matter Physics, 11(1):369–395, 2020

    2020

  4. [11]

    Quantum computation with universal error mitigation on a superconducting quantum processor.Science advances, 5(9):eaaw5686, 2019

    Chao Song, Jing Cui, H Wang, J Hao, H Feng, and Ying Li. Quantum computation with universal error mitigation on a superconducting quantum processor.Science advances, 5(9):eaaw5686, 2019

    2019

  5. [12]

    Quantum circuit design for objective function maximization in gate-model quantum computers.Quantum Information Processing, 18(7):225, 2019

    Laszlo Gyongyosi and Sandor Imre. Quantum circuit design for objective function maximization in gate-model quantum computers.Quantum Information Processing, 18(7):225, 2019. 13

    2019

  6. [13]

    Parallel quantum simulation of large systems on small nisq computers

    Fergus Barratt, James Dborin, Matthias Bal, Vid Stojevic, Frank Pollmann, and An- drew G Green. Parallel quantum simulation of large systems on small nisq computers. npj Quantum Information, 7(1):79, 2021

    2021

  7. [14]

    Quantum circuit synthesis and compilation optimization: Overview and prospects.arXiv preprint arXiv:2407.00736, 2024

    Yan Ge, Wu Wenjie, Chen Yuheng, Pan Kaisen, Lu Xudong, Zhou Zixiang, Wang Yuhan, Wang Ruocheng, and Yan Junchi. Quantum circuit synthesis and compilation optimization: Overview and prospects.arXiv preprint arXiv:2407.00736, 2024

    2024

  8. [15]

    An algebraic quantum circuit compression algorithm for hamiltonian simulation.SIAM Journal on Matrix Analysis and Appli- cations, 43(3):1084–1108, 2022

    Daan Camps, Efekan Koökcuü, Lindsay Bassman Oftelie, Wibe A De Jong, Alexan- der F Kemper, and Roel Van Beeumen. An algebraic quantum circuit compression algorithm for hamiltonian simulation.SIAM Journal on Matrix Analysis and Appli- cations, 43(3):1084–1108, 2022

    2022

  9. [16]

    Quantum singu- lar value transformation and beyond: exponential improvements for quantum matrix arithmetics

    András Gilyén, Yuan Su, Guang Hao Low, and Nathan Wiebe. Quantum singu- lar value transformation and beyond: exponential improvements for quantum matrix arithmetics. InProceedings of the 51st annual ACM SIGACT symposium on theory of computing, pages 193–204, 2019

    2019

  10. [17]

    Quantum state preparation without coherent arithmetic.arXiv preprint arXiv:2210.14892, 2022

    Sam McArdle, András Gilyén, and Mario Berta. Quantum state preparation without coherent arithmetic.arXiv preprint arXiv:2210.14892, 2022

    2022 arXiv

  11. [18]

    Nonlinear transformation of complex amplitudes via quantum singular value transformation.Physical Review Research, 6(4):043227, 2024

    Naixu Guo, Kosuke Mitarai, and Keisuke Fujii. Nonlinear transformation of complex amplitudes via quantum singular value transformation.Physical Review Research, 6(4):043227, 2024

    2024

  12. [19]

    Quantum-state preparation with universal gate decompositions.Physical Review A—Atomic, Molecular, and Optical Physics, 83(3):032302, 2011

    Martin Plesch and Časlav Brukner. Quantum-state preparation with universal gate decompositions.Physical Review A—Atomic, Molecular, and Optical Physics, 83(3):032302, 2011

    2011

  13. [20]

    Quantum algorithms for approximate function loading.Physical Review Research, 5(3):033114, 2023

    Gabriel Marin-Sanchez, Javier Gonzalez-Conde, and Mikel Sanz. Quantum algorithms for approximate function loading.Physical Review Research, 5(3):033114, 2023

    2023

  14. [21]

    Efficient quantum amplitude encoding of polynomial functions.Quantum, 8:1297, 2024

    Javier Gonzalez-Conde, Thomas W Watts, Pablo Rodriguez-Grasa, and Mikel Sanz. Efficient quantum amplitude encoding of polynomial functions.Quantum, 8:1297, 2024

    2024

  15. [22]

    Ibm quantum computers: Evolution, performance, and future directions.The Journal of Supercomputing, 81(5):687, 2025

    Muhammad AbuGhanem. Ibm quantum computers: Evolution, performance, and future directions.The Journal of Supercomputing, 81(5):687, 2025

    2025

  16. [23]

    Statistics- informed parameterized quantum circuit via maximum entropy principle for data science and finance.arXiv preprint arXiv:2406.01335, 2024

    Xi-Ning Zhuang, Zhao-Yun Chen, Cheng Xue, Xiao-Fan Xu, Chao Wang, Huan-Yu Liu, Tai-Ping Sun, Yun-Jie Wang, Yu-Chun Wu, and Guo-Ping Guo. Statistics- informed parameterized quantum circuit via maximum entropy principle for data science and finance.arXiv preprint arXiv:2406.01335, 2024

    2024 arXiv

  17. [24]

    A generative modeling approach for benchmarking and training shallow quantum circuits.npj Quantum information, 5(1):45, 2019

    Marcello Benedetti, Delfina Garcia-Pintos, Oscar Perdomo, Vicente Leyton-Ortega, Yunseong Nam, and Alejandro Perdomo-Ortiz. A generative modeling approach for benchmarking and training shallow quantum circuits.npj Quantum information, 5(1):45, 2019

    2019

  18. [25]

    Quantum generative adversarial networks for learning and loading random distributions.npj Quantum Information, 5(1):103, 2019

    Christa Zoufal, Aurélien Lucchi, and Stefan Woerner. Quantum generative adversarial networks for learning and loading random distributions.npj Quantum Information, 5(1):103, 2019

    2019

  19. [26]

    Generative quantumlearningofjointprobabilitydistributionfunctions.Physical Review Research, 4(4):043092, 2022

    Elton Yechao Zhu, Sonika Johri, Dave Bacon, Mert Esencan, Jungsang Kim, Mark Muir, Nikhil Murgai, Jason Nguyen, Neal Pisenti, Adam Schouela, et al. Generative quantumlearningofjointprobabilitydistributionfunctions.Physical Review Research, 4(4):043092, 2022

    2022

  20. [27]

    Simulations of shor’s algorithm using matrix product states.Quantum Information Processing, 16:1–13, 2017

    David S Wang, Charles D Hill, and Lloyd CL Hollenberg. Simulations of shor’s algorithm using matrix product states.Quantum Information Processing, 16:1–13, 2017

    2017

  21. [28]

    Towards quantum machine learning with tensor networks.Quantum Science and technology, 4(2):024001, 2019

    William Huggins, Piyush Patil, Bradley Mitchell, K Birgitta Whaley, and E Miles 14 Stoudenmire. Towards quantum machine learning with tensor networks.Quantum Science and technology, 4(2):024001, 2019

    2019

  22. [29]

    Encoding of matrix product states into quantum circuits of one-and two-qubit gates.Physical Review A, 101(3):032310, 2020

    Shi-Ju Ran. Encoding of matrix product states into quantum circuits of one-and two-qubit gates.Physical Review A, 101(3):032310, 2020

    2020

  23. [30]

    Efficient quantum circuits for accurate state preparation of smooth, differentiable functions

    Adam Holmes and Anne Y Matsuura. Efficient quantum circuits for accurate state preparation of smooth, differentiable functions. In2020 IEEE International Confer- ence on Quantum Computing and Engineering (QCE), pages 169–179. IEEE, 2020

    2020

  24. [31]

    Quantum state preparation using tensor networks.Quantum Science and Technology, 8(3):035027, 2023

    Ar A Melnikov, Alena A Termanova, Sergey V Dolgov, Florian Neukart, and MR Perelshtein. Quantum state preparation using tensor networks.Quantum Science and Technology, 8(3):035027, 2023

    2023

  25. [32]

    Matrix product states and projected entangled pair states: Concepts, symmetries, theorems

    J Ignacio Cirac, David Perez-Garcia, Norbert Schuch, and Frank Verstraete. Matrix product states and projected entangled pair states: Concepts, symmetries, theorems. Reviews of Modern Physics, 93(4):045003, 2021

    2021

  26. [33]

    The density-matrix renormalization group in the age of matrix product states.Annals of physics, 326(1):96–192, 2011

    Ulrich Schollwöck. The density-matrix renormalization group in the age of matrix product states.Annals of physics, 326(1):96–192, 2011

    2011

  27. [34]

    Qubit-efficient simulation of thermal states with quantum tensor networks

    Yuxuan Zhang, Shahin Jahanbani, Daoheng Niu, Reza Haghshenas, and Andrew C Potter. Qubit-efficient simulation of thermal states with quantum tensor networks. Physical Review B, 106(16):165126, 2022

    2022

  28. [35]

    Quantum state preparation of normal distributions using matrix product states.npj Quantum Information, 10(1):15, 2024

    Jason Iaconis, Sonika Johri, and Elton Yechao Zhu. Quantum state preparation of normal distributions using matrix product states.npj Quantum Information, 10(1):15, 2024

    2024

  29. [36]

    Matrix product state pre-training for quantum machine learning.Quantum Science and Technology, 7(3):035014, 2022

    James Dborin, Fergus Barratt, Vinul Wimalaweera, Lewis Wright, and Andrew G Green. Matrix product state pre-training for quantum machine learning.Quantum Science and Technology, 7(3):035014, 2022

    2022

  30. [38]

    Constant-depth preparation of matrix product states with adaptive quantum circuits

    Kevin C Smith, Abid Khan, Bryan K Clark, Steven M Girvin, and Tzu-Chieh Wei. Constant-depth preparation of matrix product states with adaptive quantum circuits. PRX Quantum, 5(3):030344, 2024

    2024

  31. [39]

    Quantum computational finance: Monte carlo pricing of financial derivatives.Physical Review A, 98(2):022321, 2018

    Patrick Rebentrost, Brajesh Gupt, and Thomas R Bromley. Quantum computational finance: Monte carlo pricing of financial derivatives.Physical Review A, 98(2):022321, 2018

    2018

  32. [40]

    Option pricing using quantum computers.Quantum, 4:291, 2020

    Nikitas Stamatopoulos, Daniel J Egger, Yue Sun, Christa Zoufal, Raban Iten, Ning Shen, and Stefan Woerner. Option pricing using quantum computers.Quantum, 4:291, 2020

    2020

  33. [41]

    Efficient hamiltonian simulation for solving option price dynamics.Physical Review Research, 5(4):043220, 2023

    Javier Gonzalez-Conde, Ángel Rodríguez-Rozas, Enrique Solano, and Mikel Sanz. Efficient hamiltonian simulation for solving option price dynamics.Physical Review Research, 5(4):043220, 2023

    2023

  34. [42]

    Quadratic quantum speedup in eval- uating bilinear risk functions.arXiv preprint arXiv:2304.10385, 2023

    Gabriele Agliardi, Corey O’Meara, Kavitha Yogaraj, Kumar Ghosh, Piergiacomo Sabino, Marina Fernández-Campoamor, Giorgio Cortiana, Juan Bernabé-Moreno, Francesco Tacchino, Antonio Mezzacapo, et al. Quadratic quantum speedup in eval- uating bilinear risk functions.arXiv preprint...

    2023

  35. [43]

    A universal quantum circuit for two-qubit transformations with three cnots gates.arXiv preprint quant-ph/0307177, 2003

    G Vidal and CM Dawson. A universal quantum circuit for two-qubit transformations with three cnots gates.arXiv preprint quant-ph/0307177, 2003

    2003 arXiv

  36. [44]

    An introduction to cartan’s kak decomposition for qc programmers

    Robert R Tucci. An introduction to cartan’s kak decomposition for qc programmers. arXiv preprint quant-ph/0507171, 2005

    2005 arXiv

  37. [45]

    Manuel S Rudolph, Jing Chen, Jacob Miller, Atithi Acharya, and Alejandro Perdomo- 15

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.