Matrix product state pre-training for quantum machine learning

Dborin, James; Barratt, Fergus; Wimalaweera, Vinul; Wright, Lewis; Green, Andrew G.

doi:10.1088/2058-9565/ac7073

Cited by 40 publications

(35 citation statements)

References 39 publications

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“…A prominent family of classical simulation techniques allowing for large-scale simulations of quantum systems is represented by Tensor Networks. A number of major contributions in this framework include winning strategies for the main physical problems in one-dimensional quantum many-body systems [20] and, more recently, significant contributions in Machine Learning [21][22][23]. The goal of Tensor Networks is to provide an efficient representation of the quantum many-body wave functions in the form of a generic network of tensors, connected by means of auxiliary indices [24,25].…”

Section: A Dmrg Results 25 1 Introductionmentioning

confidence: 99%

“…The mapping onto a quantum circuit can be achieved by exploiting the MPS nature of the final state. It is indeed well-known that, in a N qubits system, any MPS having maximum bond dimension χ = 2 n can be obtained from the trivial state 2 |0 0 0〉 = |0...0〉 by applying sequentially N unitary gates, each acting (at most) on log 2 χ + 1 = n + 1 qubits [21,[41][42][43] (see Appendix B for additional information). These unitaries can be further decomposed into two-qubits gates.…”

Section: Mps Compilation To Quantum Circuitsmentioning

confidence: 99%

“…In the simplest case of an MPS with bond dimension χ = 2, equal to the physical dimension of the local Hilbert space, the MPS can be exactly mapped to a "staircase" of two-qubits unitary gates, acting sequentially on |0 0 0〉. This mapping is well-established [21,[41][42][43] and relies on the following fact: MPS local tensors can always be chosen as left or right isometries, which can be completed to unitary matrices, in turn decomposed into quantum gates. These tricks can be easily extended to the general case of an MPS with maximum bond dimension χ = 2 n , consequently obtaining a quantum circuit defined by a sequence of unitaries acting (at most) on log 2 χ+1 = n+1 qubits [41-Figure 13: Exact mapping of a right-normalized MPS -with maximum bond dimension χ = 2 n (n = 3 in the figure) -to a staircase quantum circuit involving N unitaries, each acting non-trivially on up to log 2 χ + 1 = n + 1 qubits.…”

Section: B Mps Compilation To Quantum Circuitsmentioning

confidence: 99%

See 2 more Smart Citations

Quantum Annealing for Neural Network optimization problems: a new approach via Tensor Network simulations

Lami¹,

Torta²,

Santoro³

et al. 2022

Preprint

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Quantum Annealing (QA) is one of the most promising frameworks for quantum optimization. Here, we focus on the problem of minimizing complex classical cost functions associated with prototypical discrete neural networks, specifically the paradigmatic Hopfield model and binary perceptron. We show that the adiabatic time evolution of QA can be efficiently represented as a suitable Tensor Network. This representation allows for simple classical simulations, well-beyond small sizes amenable to exact diagonalization techniques. We show that the optimized state, expressed as a Matrix Product State (MPS), can be recast into a Quantum Circuit, whose depth scales only linearly with the system size and quadratically with the MPS bond dimension. This may represent a valuable starting point allowing for further circuit optimization on near-term quantum devices.

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Section: A Dmrg Results 25 1 Introductionmentioning

confidence: 99%

Section: Mps Compilation To Quantum Circuitsmentioning

confidence: 99%

Section: B Mps Compilation To Quantum Circuitsmentioning

confidence: 99%

See 1 more Smart Citation

Quantum Annealing for Neural Network optimization problems: a new approach via Tensor Network simulations

Lami¹,

Torta²,

Santoro³

et al. 2022

Preprint

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show abstract

“…However, calculating an accurate classical representation depends on the structure of entanglement of the systems and will not be trivial in all phases or the entire spectrum of states [20]. Furthermore, once a classical representation of the state of interest is calculated constructing a faithful quantum circuit to represent it in a quantum computer may also be difficult and is an active field of research [21,22].…”

Section: Introductionmentioning

confidence: 99%

Algebraic Bethe Circuits

Sopena

Gordon

Sierra

et al. 2022

Quantum

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The Algebraic Bethe Ansatz (ABA) is a highly successful analytical method used to exactly solve several physical models in both statistical mechanics and condensed-matter physics. Here we bring the ABA into unitary form, for its direct implementation on a quantum computer. This is achieved by distilling the non-unitary R matrices that make up the ABA into unitaries using the QR decomposition. Our algorithm is deterministic and works for both real and complex roots of the Bethe equations. We illustrate our method on the spin-12 XX and XXZ models. We show that using this approach one can efficiently prepare eigenstates of the XX model on a quantum computer with quantum resources that match previous state-of-the-art approaches. We run small-scale error-mitigated implementations on the IBM quantum computers, including the preparation of the ground state for the XX and XXZ models on 4 sites. Finally, we derive a new form of the Yang-Baxter equation using unitary matrices, and also verify it on a quantum computer.

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“…Additionally, unlike the method proposed in Ref. [34], the protocol is not hindered by cumulative approximation error build-up when only a limited number of circuit layers are employed.…”

mentioning

confidence: 99%

Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage

Rudolph¹,

Miller

Chen

et al. 2022

Preprint

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While recent breakthroughs have proven the ability of noisy intermediate-scale quantum (NISQ) devices to achieve quantum advantage in classically-intractable sampling tasks, the use of these devices for solving more practically relevant computational problems remains a challenge. Proposals for attaining practical quantum advantage typically involve parametrized quantum circuits (PQCs), whose parameters can be optimized to find solutions to diverse problems throughout quantum simulation and machine learning. However, training PQCs for real-world problems remains a significant practical challenge, largely due to the phenomenon of barren plateaus in the optimization landscapes of randomly-initialized quantum circuits. In this work, we introduce a scalable procedure for harnessing classical computing resources to determine task-specific initializations of PQCs, which we show significantly improves the trainability and performance of PQCs on a variety of problems. Given a specific optimization task, this method first utilizes tensor network (TN) simulations to identify a promising quantum state, which is then converted into gate parameters of a PQC by means of a high-performance decomposition procedure. We show that this task-specific initialization avoids barren plateaus, and effectively translates increases in classical resources to enhanced performance and speed in training quantum circuits. By demonstrating a means of boosting limited quantum resources using classical computers, our approach illustrates the promise of this synergy between quantum and quantum-inspired models in quantum computing, and opens up new avenues to harness the power of modern quantum hardware for realizing practical quantum advantage.

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Matrix product state pre-training for quantum machine learning

Cited by 40 publications

References 39 publications

Quantum Annealing for Neural Network optimization problems: a new approach via Tensor Network simulations

Quantum Annealing for Neural Network optimization problems: a new approach via Tensor Network simulations

Algebraic Bethe Circuits

Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage

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