Two-parameter counter-diabatic driving in quantum annealing

Prielinger, Luise; Hartmann, Andreas; Yamashiro, Yu; Nishimura, Kohji; Lechner, Wolfgang; Nishimori, Hidetoshi

doi:10.1103/physrevresearch.3.013227

Cited by 35 publications

(22 citation statements)

References 44 publications

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“…(5) [30], which establishes a close connection between the TBQCP and the variational version of the optimal control theory. Equations (16)(17)(18) are solved in a self-consistent way, starting with trial controls ε (0) k (t) (k = 0, 1) and monotonically increasing the value of the desired physical observable O(T ) = ψ(T )|O(T )|ψ(T ) , see more details in Ref. [30].…”

Section: Tbqcp Optimization Methodsmentioning

confidence: 99%

“…However, the time required to keep the adiabatic condition valid can be too long to be useful in practical situations. Several alternatives have been proposed to circumvent this problem, such as the local adiabatic evolution or the use of counter-diabatic drivings [17,18]. Related to AQA, the method of quantum annealing (QA) emerged as a quantum version of the classical optimization technique of simulated annealing [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

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Optimal solutions to quantum annealing using two independent control functions

Fernandes,

de Lima,

Castelano

2021

Preprint

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We investigate the quantum computing paradigm consisted of obtaining a target state that encodes the solution of a certain computational task by evolving the system with a combination of the problem-Hamiltonian and the driving-Hamiltonian.We analyze this paradigm in the light of Optimal Control Theory considering each Hamiltonian modulated by an independent control function. In the case of short evolution times and bounded controls, we analytically demonstrate that an optimal solution consists of both controls tuned at their upper bound for the whole evolution time. This optimal solution is appealing because of its simplicity and experimental feasibility. To numerically solve the control problem, we propose the use of a quantum optimal control technique adapted to limit the amplitude of the controls.As an application, we consider a teleportation protocol and compare the fidelity of the teleported state obtained for the two-control functions with the usual singlecontrol function scheme and with the quantum approximate optimization algorithm (QAOA). We also investigate the energetic cost and the robustness against systematic errors in the teleportation protocol, considering different time evolution schemes.We show that the scheme with two-control functions yields a higher fidelity than the other schemes for the same evolution time.

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Section: Tbqcp Optimization Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal solutions to quantum annealing using two independent control functions

Fernandes,

de Lima,

Castelano

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…More recently, it has been shown that signatures of universality are present in the full kink-number distribution and that all cumulants scale as a universal power-law of the quench time [16,[27][28][29][30][31]. The universal dynamics of defect formation is not always desirable, and a variety of works have been devoted to circumvent it using diverse control protocols [32][33][34][35][36][37][38][39][40][41][42], beyond the use of nonlinear quenches and inhomogeneous driving. In addition, quasi-free fermion models have been discussed in the context of quantum thermodynamics, as a test-bed to explore work statistics and fluctuation theorems [43][44][45][46] and as a working substance in a quantum thermodynamic cycle [47].…”

Section: Introductionmentioning

confidence: 99%

Exact thermal properties of free-fermionic spin chains

2021

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An exact description of integrable spin chains at finite temperature is provided using an elementary algebraic approach in the complete Hilbert space of the system. We focus on spin chain models that admit a description in terms of free fermions, including paradigmatic examples such as the one-dimensional transverse-field quantum Ising and XY models. The exact partition function is derived and compared with the ubiquitous approximation in which only the positive parity sector of the energy spectrum is considered. Errors stemming from this approximation are identified in the neighborhood of the critical point at low temperatures. We further provide the full counting statistics of a wide class of observables at thermal equilibrium and characterize in detail the thermal distribution of the kink number and transverse magnetization in the transverse-field quantum Ising chain.

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“…[5] found that in many cases an approximate local variational AGP exists, which allows one to significantly suppress dissipative effects even in chaotic systems. This method has been extensively applied to quantum spin systems with many promising results [6][7][8][9][10][11][12][13]. Moreover, Ref.…”

Section: Introductionmentioning

confidence: 99%

Counter-diabatic driving in the classical $β$-Fermi-Pasta-Ulam-Tsingou chain

Gjonbalaj,

Campbell,

Polkovnikov

2021

Preprint

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Shortcuts to adiabaticity (STAs) have been used to make rapid changes to a system while eliminating or minimizing excitations in the system's state. In quantum systems, these shortcuts allow us to minimize inefficiencies and heating in experiments and quantum computing protocols, but the theory of STAs can also be generalized to classical systems. We focus on one such STA, approximate counter-diabatic (ACD) driving, and numerically compare its performance in two classical systems: a quartic anharmonic oscillator and the β Fermi-Pasta-Ulam-Tsingou (FPUT) lattice. In particular, we modify an existing variational technique to optimize the approximate driving and then develop classical figures of merit to quantify the performance of the driving. We find that relatively simple forms for the ACD driving can dramatically suppress excitations regardless of system size. ACD driving in classical nonlinear oscillators could have many applications, from minimizing heating in bosonic gases to finding optimal local dressing protocols in interacting field theories.

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Two-parameter counter-diabatic driving in quantum annealing

Cited by 35 publications

References 44 publications

Optimal solutions to quantum annealing using two independent control functions

Optimal solutions to quantum annealing using two independent control functions

Exact thermal properties of free-fermionic spin chains

Counter-diabatic driving in the classical $β$-Fermi-Pasta-Ulam-Tsingou chain

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