Efficient quantum imaginary time evolution by drifting real time evolution: an approach with low gate and measurement complexity

Huang, Y.; Shao, Yongzhao; Ren, Weiluo; Sun, Jinzhao; Lv, Dingshun

doi:10.48550/arxiv.2203.11112

Cited by 3 publications

(5 citation statements)

References 43 publications

(55 reference statements)

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“…The spin unrestricted UCCSD solver could be useful for cases when it is more convenient to break the spin symmetry to converge to the ground state. We anticipate that the ansatz improvement within this direction, for instance, an unrestricted k-UpCCGSD ansatz [89] or an unrestricted adaptive variational algorithm [90,91] may further reduce the circuit depth with a satisfactory accuracy.…”

Section: Discussionmentioning

confidence: 99%

Ab initio Quantum Simulation of Strongly Correlated Materials with Quantum Embedding

Dingshun

Cao

Sun

et al. 2023

Preprint

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Quantum computing has shown great potential in various quantum chemical applications such as drug discovery, material design, and catalyst optimization. Although significant progress has been made in quantum simulation of simple molecules, ab initio simulation of solid-state materials on quantum computers is still in its early stage, mostly owing to the fact that the system size quickly becomes prohibitively large when approaching the thermodynamic limit. In this work, we introduce an orbital-based multi-fragment approach on top of the periodic density matrix embedding theory, resulting in a significantly smaller problem size for the current near-term quantum computer. We demonstrate the accuracy and efficiency of our method compared with the conventional methodologies and experiments on solid-state systems with complex electronic structures. These include spin polarized states of a hydrogen chain (1D-H), the equation of state of a boron nitride layer (h-BN) as well as the magnetic ordering in nickel oxide (NiO), a prototypical strongly correlated solid. Our results suggest that quantum embedding combined with a chemically intuitive fragmentation can greatly advance quantum simulation of realistic materials, thereby paving the way for solving important yet classically hard industrial problems on near-term quantum devices.

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Section: Discussionmentioning

confidence: 99%

Ab initio Quantum Simulation of Strongly Correlated Materials with Quantum Embedding

Dingshun

Cao

Sun

et al. 2023

Preprint

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“…In this section, we first consider the consequence of the factor of 1 √ c in b µ (but not in M µν ), as derived in the original proposal of Ref. [13] and used in other studies [15,16,18,19,25]. To be explicit, the previous algorithm uses Eq.…”

Section: Convergencementioning

confidence: 99%

“…However, the classical optimization of VQE in a highdimensional, non-linear parameter space poses a chal- * tsuchimochi@gmail.com lenge to determine the ground state without being trapped in a local minimum. Recently, several algorithms based on imaginary time evolution (ITE) have emerged to circumvent the gradient-based parameter optimization [13][14][15][16][17][18][19][20]. ITE is able to transform an arbitrary state to the (nearly) exact ground state, and has been historically applied to fermion systems on the basis of Monte Carlo simulations [21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Ground and excited states from model-space quantum imaginary time evolution for strongly correlated systems

Tsuchimochi¹,

Ryo²,

Ten‐no³

2022

Preprint

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We present various extensions and modifications of quantum imaginary time evolution (QITE), a recently proposed quantum-classical hybrid algorithm that is guaranteed to reach the lowest state of system. We analyze the derivation of the underlying QITE equation order-by-order, and suggest a modification that is theoretically well founded. Our results clearly indicate the soundness of the here-derived equation, enabling a better approximation of the imaginary time propagation by a unitary. With the improved evaluation of the quantum Lanczos introduced in this study, our implementations allow for stable applications of QITE in larger systems. We also discuss how excited states can be obtained using QITE and propose two schemes. The folded-spectrum QITE is a straightforward extension of QITE to excited state simulations, but is found to be impractical owning to its considerably slow convergence. In contrast, the model space QITE can describe multiple states simultaneously because it propagates a model space to the exact one in principle by retaining its orthogonality. Finally, we demonstrate that spin contamination can be effectively removed by shifting the imaginary time propagator, and thus excited states with a particular spin quantum number are efficiently captured without falling into the different spin states that have lower energies. The effectiveness of all these developments is illustrated by noiseless simulations, offering the further insights into quantum algorithms for imaginary time evolution.

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“…Previous studies have explored various strategies to reduce the necessary quantum resources in solving quantum chemical problems, including qubit-reduction methods [27][28][29][30][31][32][33][34], heuristics ansatz construction methods [35][36][37][38], circuit depth reduction methods [39,40] and heuristics parameter training methods [41,42]. Specifically, to address the issue of limited size in current NISQ devices, [28,30,32,33] employed the quantum embedding theory to partition the molecular Hamiltonian into smaller fragments.…”

Section: Introductionmentioning

confidence: 99%

“…This approach reduces the size of operator pool meanwhile decreases the quantum circuit depth. In addition, there are other strategies available to reduce the circuit depth, for instance, the Qdrift-based quantum imaginary time evolution method [39] and the discretely optimized VQE approach [40] offer alternative ways to achieve circuit depth reduction. Finally, training the parameters within quantum circuits may be challenging due to the presence of barren plateaus phenomenon [43][44][45], and heuristics training strategies may help to alleviate this challenge, such as the layerwise training method [41], quasidynamical evolution [42], and suitable parameter initialization strategies [46].…”

Section: Introductionmentioning

confidence: 99%

Orbital expansion variational quantum eigensolver

Wu,

Huang,

Sun

et al. 2023

Quantum Sci. Technol.

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Variational Quantum Eigensolver~(VQE) has emerged as a promising method for investigating ground state properties in quantum chemistry, materials science, and condensed matter physics. However, the conventional VQE method generally lacks systematic improvement and convergence guarantees, particularly when dealing with strongly correlated systems. In light of these challenges, we present a novel framework called Orbital Expansion VQE (OE-VQE) to address these limitations. The key idea is to devise an efficient convergence path by utilizing shallower quantum circuits, starting from a highly compact active space and gradually expanding it until convergence to the ground state is achieved. To validate the effectiveness of the OE-VQE framework, we conducted benchmark simulations on several small yet representative molecules, including the $\rm H_{6}$ chain, $\rm H_{10}$ ring and $\rm N_2$. The simulation results demonstrate that our proposed convergence paths significantly enhance the performance of conventional VQE. Overall, our work sheds valuable insight into the simulation of molecules based on shallow quantum circuits, offering a promising avenue for advancing the efficiency and accuracy of VQE approaches in tackling complex molecular systems.

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Efficient quantum imaginary time evolution by drifting real time evolution: an approach with low gate and measurement complexity

Cited by 3 publications

References 43 publications

Ab initio Quantum Simulation of Strongly Correlated Materials with Quantum Embedding

Ab initio Quantum Simulation of Strongly Correlated Materials with Quantum Embedding

Ground and excited states from model-space quantum imaginary time evolution for strongly correlated systems

Orbital expansion variational quantum eigensolver

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