arXiv subjects

D. A. Lidar

Publications and source records attributed to D. A. Lidar.

At least 19 recordsLinked to original sources

arXiv2025

Decoherence of a tunable capacitively shunted flux qubit

Quantum annealing is a method to solve optimization problems that leverages quantum tunneling in a coupled qubit system. We present a detailed study of the coherence of a tunable capacitively-shunted flux qubit, designed for coherent quantum annealing applications. We find that for high qubit frequencies, thermal noise in the bias line makes a significant contribution to the relaxation, arising from the design choice to experimentally explore both fast annealing and high-frequency control. The measured dephasing rate is primarily due to intrinsic low-frequency flux noise in the two qubit loops, with additional contribution from the low-frequency noise of control electronics used for fast annealing. Our results characterize decoherence in a realistic setup for quantum annealing and are relevant for ongoing efforts toward building superconducting quantum annealers with increased coherence.

quant-ph↗

arXiv2025

Beyond unital noise in variational quantum algorithms: noise-induced barren plateaus and limit sets

Variational quantum algorithms (VQAs) hold much promise but face the challenge of exponentially small gradients. Unmitigated, this barren plateau (BP) phenomenon leads to an exponential training overhead for VQAs. Perhaps the most pernicious are noise-induced barren plateaus (NIBPs), a type of unavoidable BP arising from open system effects, which have so far been shown to exist for unital noise maps. Here, we generalize the study of NIBPs to more general completely positive, trace-preserving maps, investigating the existence of NIBPs in the unital case and a class of non-unital maps we call Hilbert-Schmidt (HS)-contractive. The latter includes amplitude damping. We identify the associated phenomenon of noise-induced limit sets (NILS) of the VQA cost function and prove its existence for both unital and HS-contractive non-unital noise maps. Along the way, we extend the parameter shift rule of VQAs to the noisy setting. We provide rigorous bounds in terms of the relevant variables that give rise to NIBPs and NILSs, along with numerical simulations of the depolarizing and amplitude-damping maps that illustrate our analytical results.

quant-ph↗

arXiv2025

Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup Problem

Simon's problem is to find a hidden period (a bitstring) encoded into an unknown 2-to-1 function. It is one of the earliest problems for which an exponential quantum speedup was proven for ideal, noiseless quantum computers, albeit in the oracle model. Here, using two different 127-qubit IBM Quantum superconducting processors, we demonstrate an algorithmic quantum speedup for a variant of Simon's problem where the hidden period has a restricted Hamming weight $w$. For sufficiently small values of $w$ and for circuits involving up to 58 qubits, we demonstrate an exponential speedup, albeit of a lower quality than the speedup predicted for the noiseless algorithm. The speedup exponent and the range of $w$ values for which an exponential speedup exists are significantly enhanced when the computation is protected by dynamical decoupling. Further enhancement is achieved with measurement error mitigation. This constitutes a demonstration of a bona fide quantum advantage for an Abelian hidden subgroup problem.

quant-ph↗

arXiv2025

Dissipative Landau-Zener tunneling in the crossover regime from weak to strong environment coupling

Landau-Zener tunneling, which describes the transition in a two-level system during a sweep through an anti-crossing, is a model applicable to a wide range of physical phenomena. Realistic quantum systems are affected by dissipation due to coupling to their environments. An important aspect of understanding such open quantum systems is the relative energy scales of the system itself and the system-environment coupling, which distinguishes the weak- and strong-coupling regimes. Using a tunable superconducting flux qubit, we observe the crossover from weak to strong coupling to the environment in Landau-Zener tunneling. Our results confirm previous theoretical studies of dissipative Landau-Zener tunneling in the weak and strong coupling limits. We devise a spin bath model that effectively captures the crossover regime. This work is relevant for understanding the role of dissipation in quantum annealing, where the system is expected to go through a cascade of Landau-Zener transitions before reaching the target state.

quant-ph↗

arXiv2024

Optimizing for periodicity: a model-independent approach to flux crosstalk calibration for superconducting circuits

Flux tunability is an important engineering resource for superconducting circuits. Large-scale quantum computers based on flux-tunable superconducting circuits face the problem of flux crosstalk, which needs to be accurately calibrated to realize high-fidelity quantum operations. Typical calibration methods either assume that circuit elements can be effectively decoupled and simple models can be applied, or require a large amount of data. Such methods become ineffective as the system size increases and circuit interactions become stronger. Here we propose a new method for calibrating flux crosstalk, which is independent of the underlying circuit model. Using the fundamental property that superconducting circuits respond periodically to external fluxes, crosstalk calibration of N flux channels can be treated as N independent optimization problems, with the objective functions being the periodicity of a measured signal depending on the compensation parameters. We demonstrate this method on a small-scale quantum annealing circuit based on superconducting flux qubits, achieving comparable accuracy with previous methods. We also show that the objective function usually has a nearly convex landscape, allowing efficient optimization.

quant-ph↗

arXiv2021

Calibration of flux crosstalk in large-scale flux-tunable superconducting quantum circuits

Magnetic flux tunability is an essential feature in most approaches to quantum computing based on superconducting qubits. Independent control of the fluxes in multiple loops is hampered by crosstalk. Calibrating flux crosstalk becomes a challenging task when the circuit elements interact strongly. We present a novel approach to flux crosstalk calibration, which is circuit model independent and relies on an iterative process to gradually improve calibration accuracy. This method allows us to reduce errors due to the inductive coupling between loops. The calibration procedure is automated and implemented on devices consisting of tunable flux qubits and couplers with up to 27 control loops. We devise a method to characterize the calibration error, which is used to show that the errors of the measured crosstalk coefficients are all below 0.17%.

quant-ph↗

arXiv2020

Prospects for Quantum Enhancement with Diabatic Quantum Annealing

We assess the prospects for algorithms within the general framework of quantum annealing (QA) to achieve a quantum speedup relative to classical state of the art methods in combinatorial optimization and related sampling tasks. We argue for continued exploration and interest in the QA framework on the basis that improved coherence times and control capabilities will enable the near-term exploration of several heuristic quantum optimization algorithms that have been introduced in the literature. These continuous-time Hamiltonian computation algorithms rely on control protocols that are more advanced than those in traditional ground-state QA, while still being considerably simpler than those used in gate-model implementations. The inclusion of coherent diabatic transitions to excited states results in a generalization called diabatic quantum annealing (DQA), which we argue for as the most promising route to quantum enhancement within this framework. Other promising variants of traditional QA include reverse annealing and continuous-time quantum walks, as well as analog analogues of parameterized quantum circuit ansatzes for machine learning. Most of these algorithms have no known (or likely to be discovered) efficient classical simulations, and in many cases have promising (but limited) early signs for the possibility of quantum speedups, making them worthy of further investigation with quantum hardware in the intermediate-scale regime. We argue that all of these protocols can be explored in a state-of-the-art manner by embracing the full range of novel out-of-equilibrium quantum dynamics generated by time-dependent effective transverse-field Ising Hamiltonians that can be natively implemented by, e.g., inductively-coupled flux qubits, both existing and projected at application scale.

quant-ph↗

arXiv2013

Analysis of the quantum Zeno effect for quantum control and computation

Within quantum information, many methods have been proposed to avoid or correct the deleterious effects of the environment on a system of interest. In this work, expanding on our earlier paper [G. A. Paz-Silva et al., Phys. Rev. Lett. 108, 080501 (2012), arXiv:1104.5507], we evaluate the applicability of the quantum Zeno effect as one such method. Using the algebraic structure of stabilizer quantum error correction codes as a unifying framework, two open-loop protocols are described which involve frequent non-projective (i.e., weak) measurement of either the full stabilizer group or a minimal generating set thereof. The effectiveness of the protocols is measured by the distance between the final state under the protocol and the final state of an idealized evolution in which system and environment do not interact. Rigorous bounds on this metric are derived which demonstrate that, under certain assumptions, a Zeno effect may be realized with arbitrarily weak measurements, and that this effect can protect an arbitrary, unknown encoded state against the environment arbitrarily well.

quant-ph↗

arXiv2012

Universality proof and analysis of generalized nested Uhrig dynamical decoupling

Nested Uhrig dynamical decoupling (NUDD) is a highly efficient quantum error suppression scheme that builds on optimized single axis UDD sequences. We prove the universality of NUDD and analyze its suppression of different error types in the setting of generalized control pulses. We present an explicit lower bound for the decoupling order of each error type, which we relate to the sequence orders of the nested UDD layers. We find that the error suppression capabilities of NUDD are strongly dependent on the parities and relative magnitudes of all nested UDD sequence orders. This allows us to predict the optimal arrangement of sequence orders. We test and confirm our analysis using numerical simulations.

quant-ph↗

arXiv2012

Optimally combining dynamical decoupling and quantum error correction

We show how dynamical decoupling (DD) and quantum error correction (QEC) can be optimally combined in the setting of fault tolerant quantum computing. To this end we identify the optimal generator set of DD sequences designed to protect quantum information encoded into stabilizer subspace or subsystem codes. This generator set, comprising the stabilizers and logical operators of the code, minimizes a natural cost function associated with the length of DD sequences. We prove that with the optimal generator set the restrictive local-bath assumption used in earlier work on hybrid DD-QEC schemes, can be significantly relaxed, thus bringing hybrid DD-QEC schemes, and their potentially considerable advantages, closer to realization.

quant-ph↗

arXiv2012

Decoherence-protected quantum gates for a hybrid solid-state spin register

Protecting the dynamics of coupled quantum systems from decoherence by the environment is a key challenge for solid-state quantum information processing. An idle qubit can be efficiently insulated from the outside world via dynamical decoupling, as has recently been demonstrated for individual solid-state qubits. However, protection of qubit coherence during a multi-qubit gate poses a non-trivial problem: in general the decoupling disrupts the inter-qubit dynamics, and hence conflicts with gate operation. This problem is particularly salient for hybrid systems, wherein different types of qubits evolve and decohere at vastly different rates. Here we present the integration of dynamical decoupling into quantum gates for a paradigmatic hybrid system, the electron-nuclear spin register. Our design harnesses the internal resonance in the coupled-spin system to resolve the conflict between gate operation and decoupling. We experimentally demonstrate these gates on a two-qubit register in diamond operating at room temperature. Quantum tomography reveals that the qubits involved in the gate operation are protected as accurately as idle qubits. We further illustrate the power of our design by executing Grover's quantum search algorithm, achieving fidelities above 90% even though the execution time exceeds the electron spin dephasing time by two orders of magnitude. Our results directly enable decoherence-protected interface gates between different types of promising solid-state qubits. Ultimately, quantum gates with integrated decoupling may enable reaching the accuracy threshold for fault-tolerant quantum information processing with solid-state devices.

cond-mat.mes-hall↗

arXiv2012

Zeno effect for quantum computation and control

It is well known that the quantum Zeno effect can protect specific quantum states from decoherence by using projective measurements. Here we combine the theory of weak measurements with stabilizer quantum error correction and detection codes. We derive rigorous performance bounds which demonstrate that the Zeno effect can be used to protect appropriately encoded arbitrary states to arbitrary accuracy, while at the same time allowing for universal quantum computation or quantum control.

quant-ph↗

arXiv2011

Quadratic Dynamical Decoupling with Non-Uniform Error Suppression

We analyze numerically the performance of the near-optimal quadratic dynamical decoupling (QDD) single-qubit decoherence errors suppression method [J. West et al., Phys. Rev. Lett. 104, 130501 (2010)]. The QDD sequence is formed by nesting two optimal Uhrig dynamical decoupling sequences for two orthogonal axes, comprising N1 and N2 pulses, respectively. Varying these numbers, we study the decoherence suppression properties of QDD directly by isolating the errors associated with each system basis operator present in the system-bath interaction Hamiltonian. Each individual error scales with the lowest order of the Dyson series, therefore immediately yielding the order of decoherence suppression. We show that the error suppression properties of QDD are dependent upon the parities of N1 and N2, and near-optimal performance is achieved for general single-qubit interactions when N1=N2.

quant-ph↗

arXiv2010

Accuracy vs run time in adiabatic quantum search

Adiabatic quantum algorithms are characterized by their run time and accuracy. The relation between the two is essential for quantifying adiabatic algorithmic performance, yet is often poorly understood. We study the dynamics of a continuous time, adiabatic quantum search algorithm, and find rigorous results relating the accuracy and the run time. Proceeding with estimates, we show that under fairly general circumstances the adiabatic algorithmic error exhibits a behavior with two discernible regimes: the error decreases exponentially for short times, then decreases polynomially for longer times. We show that the well known quadratic speedup over classical search is associated only with the exponential error regime. We illustrate the results through examples of evolution paths derived by minimization of the adiabatic error. We also discuss specific strategies for controlling the adiabatic error and run time.

quant-ph↗

arXiv2010

Channel Capacities of an Exactly Solvable Spin-Star System

We calculate the entanglement-assisted and unassisted channel capacities of an exactly solvable spin star system, which models the quantum dephasing channel. The capacities for this non-Markovian model exhibit a strong dependence on the coupling strengths of the bath spins with the system, the bath temperature, and the number of bath spins. For equal couplings and bath frequencies, the channel becomes periodically noiseless.

quant-ph↗

arXiv2009

Linear Quantum Error Correction

We develop a generalized theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This theory describes entanglement-assisted QEC for invertible noise maps, which we use to provides an example of the physical implementation of non-CP recovery maps. We argue that a consistent map-based theory of fault-tolerant QEC (whether Markovian or not) requires linear, non-CP maps, and that this impacts the value of the fault-tolerance threshold.

quant-ph↗

arXiv2009

Quantum Error Correction Beyond Completely Positive Maps

By introducing an operator sum representation for arbitrary linear maps, we develop a generalized theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This theory of "linear quantum error correction" is applicable in cases where the standard and restrictive assumption of a factorized initial system-bath state does not apply.

quant-ph↗

arXiv2009

Classical Ising model test for quantum circuits

We exploit a recently constructed mapping between quantum circuits and graphs in order to prove that circuits corresponding to certain planar graphs can be efficiently simulated classically. The proof uses an expression for the Ising model partition function in terms of quadratically signed weight enumerators (QWGTs), which are polynomials that arise naturally in an expansion of quantum circuits in terms of rotations involving Pauli matrices. We combine this expression with a known efficient classical algorithm for the Ising partition function of any planar graph in the absence of an external magnetic field, and the Robertson-Seymour theorem from graph theory. We give as an example a set of quantum circuits with a small number of non-nearest neighbor gates which admit an efficient classical simulation.

quant-ph↗