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S. Lloyd

Publications and source records attributed to S. Lloyd.

At least 19 recordsLinked to original sources
arXiv2021

Error mitigation via stabilizer measurement emulation

Dynamical decoupling (DD) is a widely-used quantum control technique that takes advantage of temporal symmetries in order to partially suppress quantum errors without the need resource-intensive error detection and correction protocols. This and other open-loop error mitigation techniques are critical for quantum information processing in the era of Noisy Intermediate-Scale Quantum technology. However, despite its utility, dynamical decoupling does not address errors which occur at unstructured times during a circuit, including certain commonly-encountered noise mechanisms such as cross-talk and imperfectly calibrated control pulses. Here, we introduce and demonstrate an alternative technique - `quantum measurement emulation' (QME) - that effectively emulates the measurement of stabilizer operators via stochastic gate application, leading to a first-order insensitivity to coherent errors. The QME protocol enables error suppression based on the stabilizer code formalism without the need for costly measurements and feedback, and it is particularly well-suited to discrete coherent errors that are challenging for DD to address.

quant-ph↗
arXiv2016

An efficient quantum algorithm for spectral estimation

We develop an efficient quantum implementation of an important signal processing algorithm for line spectral estimation: the matrix pencil method, which determines the frequencies and damping factors of signals consisting of finite sums of exponentially damped sinusoids. Our algorithm provides a quantum speedup in a natural regime where the sampling rate is much higher than the number of sinusoid components. Along the way, we develop techniques that are expected to be useful for other quantum algorithms as well - consecutive phase estimations to efficiently make products of asymmetric low rank matrices classically accessible and an alternative method to efficiently exponentiate non-Hermitian matrices. Our algorithm features an efficient quantum-classical division of labor: The time-critical steps are implemented in quantum superposition, while an interjacent step, requiring only exponentially few parameters, can operate classically. We show that frequencies and damping factors can be obtained in time logarithmic in the number of sampling points, exponentially faster than known classical algorithms.

quant-ph↗
arXiv2014

Numerical Evidence for Robustness of Environment-Assisted Quantum Transport

Recent theoretical studies show that decoherence process can enhance transport efficiency in quantum systems. This effect is known as environment-assisted quantum transport (ENAQT). The role of ENAQT in optimal quantum transport is well investigated, however, it is less known how robust ENAQT is with respect to variations in the system or its environment characteristic. Toward answering this question, we simulated excitonic energy transfer in Fenna-Matthews-Olson (FMO) photosynthetic complex. We found that ENAQT is robust with respect to many relevant parameters of environmental interactions and Frenkel-exciton Hamiltonian including reorganization energy, bath frequency cutoff, temperature, and initial excitations, dissipation rate, trapping rate, disorders, and dipole moments orientations. Our study suggests that the ENAQT phenomenon can be exploited in robust design of highly efficient quantum transport systems.

quant-ph↗
arXiv2014

On the complexity of controlling quantum many-body dynamics

We demonstrate that arbitrary time evolutions of many-body quantum systems can be reversed even in cases when only part of the Hamiltonian can be controlled. The reversed dynamics obtained via optimal control --contrary to standard time-reversal procedures-- is extremely robust to external sources of noise. We provide a lower bound on the control complexity of a many-body quantum dynamics in terms of the dimension of the manifold supporting it, elucidating the role played by integrability in this context.

quant-ph↗
arXiv2014

An information theoretical analysis of quantum optimal control

We show that if an efficient classical representation of the dynamics exists, optimal control problems on many-body quantum systems can be solved efficiently with finite precision. We show that the size of the space of parameters necessary to solve quantum optimal control problems defined on pure, mixed states and unitaries is polynomially bounded from the size of the of the set of reachable states in polynomial time. We provide a bound for the minimal time necessary to perform the optimal process given the bandwidth of the control pulse, that is the continuous version of the Solovay-Kitaev theorem. We explore the connection between entanglement present in the system and complexity of the control problem, showing that one-dimensional slightly entangled dynamics can be efficiently controlled. Finally, we quantify how noise affects the presented results.

quant-ph↗
arXiv2012

Geometrical effects on energy transfer in disordered open quantum systems

We explore various design principles for efficient excitation energy transport in complex quantum systems. We investigate energy transfer efficiency in randomly disordered geometries consisting of up to 20 chromophores to explore spatial and spectral properties of small natural/artificial Light-Harvesting Complexes (LHC). We find significant statistical correlations among highly efficient random structures with respect to ground state properties, excitonic energy gaps, multichromophoric spatial connectivity, and path strengths. These correlations can even exist beyond the optimal regime of environment-assisted quantum transport. For random configurations embedded in spatial dimensions of 30 A and 50 A, we observe that the transport efficiency saturates to its maximum value if the systems contain 7 and 14 chromophores respectively. Remarkably, these optimum values coincide with the number of chlorophylls in (Fenna-Matthews-Olson) FMO protein complex and LHC II monomers, respectively, suggesting a potential natural optimization with respect to chromophoric density.

quant-ph↗
arXiv2010

Generalized minimal output entropy conjecture for one-mode Gaussian channels: definitions and some exact results

A formulation of the generalized minimal output entropy conjecture for Gaussian channels is presented. It asserts that, for states with fixed input entropy, the minimal value of the output entropy of the channel (i.e. the minimal output entropy increment for fixed input entropy) is achieved by Gaussian states. In the case of centered channels (i.e. channels which do not add squeezing to the input state) this implies that the minimum is obtained by thermal (Gibbs) inputs. The conjecture is proved to be valid in some special cases.

quant-ph↗
arXiv2010

The bosonic minimum output entropy conjecture and Lagrangian minimization

We introduce a new form for the bosonic channel minimal output entropy conjecture, namely that among states with equal input entropy, the thermal states are the ones that have slightest increase in entropy when sent through a infinitesimal thermalizing channel. We then detail a strategy to prove the conjecture through variational techniques. This would lead to the calculation of the classical capacity of a communication channel subject to thermal noise. Our strategy detects input thermal ensembles as possible solutions for the optimal encoding of the channel, lending support to the conjecture. However, it does not seem to be able to exclude the possibility that other input ensembles can attain the channel capacity.

quant-ph↗
arXiv2010

Efficient estimation of nearly sparse many-body quantum Hamiltonians

We develop an efficient and robust approach to Hamiltonian identification for multipartite quantum systems based on the method of compressed sensing. This work demonstrates that with only O(s log(d)) experimental configurations, consisting of random local preparations and measurements, one can estimate the Hamiltonian of a d-dimensional system, provided that the Hamiltonian is nearly s-sparse in a known basis. We numerically simulate the performance of this algorithm for three- and four-body interactions in spin-coupled quantum dots and atoms in optical lattices. Furthermore, we apply the algorithm to characterize Hamiltonian fine structure and unknown system-bath interactions.

quant-ph↗
arXiv2010

Minimum output entropy of Gaussian channels

We show that the minimum output entropy for all single-mode Gaussian channels is additive and is attained for Gaussian inputs. This allows the derivation of the channel capacity for a number of Gaussian channels, including that of the channel with linear loss, thermal noise, and linear amplification.

quant-ph↗
arXiv2009

Experimental Quantum Private Queries with linear optics

The Quantum Private Query is a quantum cryptographic protocol to recover information from a database, preserving both user and data privacy: the user can test whether someone has retained information on which query was asked, and the database provider can test the quantity of information released. Here we introduce a new variant Quantum Private Query algorithm which admits a simple linear optical implementation: it employs the photon's momentum (or time slot) as address qubits and its polarization as bus qubit. A proof-of-principle experimental realization is implemented.

quant-ph↗
arXiv2004

Bang-Bang refocusing of a qubit exposed to telegraph noise

We investigate the decoherence effect of telegraph noise on a single qubit, usually provoked by bistable fluctuators. To diminish the dephasing and relaxation impact an effective refocusing scheme (so-called Bang-Bang pulses) is proposed. Detailed numerical as well as analytical random walk analysis allows in particular to evaluate the applicability of non-perfect Bang-Bang pulses.

cond-mat.mes-hall↗
arXiv2003

DC measurements of macroscopic quantum levels in a superconducting qubit structure with a time-ordered meter

DC measurements are made in a superconducting, persistent current qubit structure with a time-ordered meter. The persistent-current qubit has a double-well potential, with the two minima corresponding to magnetization states of opposite sign. Macroscopic resonant tunneling between the two wells is observed at values of energy bias that correspond to the positions of the calculated quantum levels. The magnetometer, a Superconducting Quantum Interference Device (SQUID), detects the state of the qubit in a time-ordered fashion, measuring one state before the other. This results in a different meter output depending on the initial state, providing different signatures of the energy levels for each tunneling direction. From these measurements, the intrawell relaxation time is found to be about 50 microseconds.

cond-mat.supr-con↗
arXiv2003

Projective Measurement Scheme for Solid-State Qubits

We present an effective measurement scheme for the solid-state qubits that does {\bf not} introduce extra decoherence to the qubits until the measurement is switched on by a resonant pulse. The resonant pulse then maximally entangles the qubit with the detector. The scheme has the feature of being projective, noiseless, and switchable. This method is illustrated on the superconducting persistent-current qubit, but can be applied to the measurement of a wide variety of solid-state qubits, the {\bf direct} detection of the electromagnetic signals of which gives poor resolution of the qubit states.

quant-ph↗
arXiv2003

Compensation of decoherence from telegraph noise by means of bang-bang control

With the growing efforts in isolating solid-state qubits from external decoherence sources, the origins of noise inherent to the material start to play a relevant role. One representative example are charged impurities in the device material or substrate, which typically produce telegraph noise and can hence be modelled as bistable fluctuators. In order to demonstrate the possibility of the active suppression of the disturbance from a {\em single} fluctuator, we theoretically implement an elementary bang-bang control protocol. We numerically simulate the random walk of the qubit state on the Bloch sphere with and without bang-bang compensation by means of the stochastic Schrödinger equation and compare it with an analytical saddle point solution of the corresponding Langevin equation in the long-time limit. We find that the deviation with respect to the noiseless case is significantly reduced when bang-bang pulses are applied, being scaled down approximately by the ratio of the bang-bang period and the typical flipping time of the bistable fluctuation. Our analysis gives not only the effect of bang-bang control on the variance of these deviations, but also their entire distribution. As a result, we expect that bang-bang control works as a high-pass filter on the spectrum of noise sources. This indicates how the influence of $1/f$-noise ubiquitous to the solid state world can be reduced.

cond-mat.mes-hall↗
arXiv2003

Universal control of quantum subspaces and subsystems

We describe a broad dynamical-algebraic framework for analyzing the quantum control properties of a set of naturally available interactions. General conditions under which universal control is achieved over a set of subspaces/subsystems are found. All known physical examples of universal control on subspaces/systems are related to the framework developed here.

quant-ph↗