arXiv subjects

Daniel A. Lidar

Publications and source records attributed to Daniel A. Lidar.

At least 37 records · Page 2Linked to original sources

arXiv2024

Beating the Ramsey limit on sensing with deterministic qubit control

Quantum sensors promise revolutionary advances in medical imaging, energy production, mass detection, geodesy, foundational physics research, and a host of other fields. In many sensors, the signal takes the form of a changing qubit frequency, which is detected with an interference measurement. Unfortunately, environmental noise decoheres the qubit state, reducing signal-to-noise ratio (SNR). Here we introduce a protocol for enhancing the sensitivity of a measurement of a qubit's frequency in the presence of decoherence. We use a continuous drive to stabilize one component of the qubit's Bloch vector, enhancing the effect of a small static frequency shift. We demonstrate our protocol on a superconducting qubit, enhancing SNR per measurement shot by 1.65$\times$ and SNR per qubit evolution time by 1.09$\times$ compared to standard Ramsey interferometry. We explore the protocol theoretically and numerically, finding maximum enhancements of 1.96$\times$ and 1.18$\times$, respectively. We also show that the protocol is robust to parameter miscalibrations. Our protocol provides an unconditional enhancement in signal-to-noise ratio compared to standard Ramsey interferometry. It requires no feedback and no extra control or measurement resources, and can be immediately applied in a wide variety of quantum computing and quantum sensor technologies to enhance their sensitivities.

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arXiv2024

Quantum Property Preservation

Quantum property preservation (QPP) is the problem of maintaining a target property of a quantum system for as long as possible. This problem arises naturally in the context of open quantum systems subject to decoherence. Here, we develop a general theory to formalize and analyze QPP. We characterize properties encoded as scalar functions of the system state that can be preserved time-locally via continuous control using smoothly varying, time-dependent control Hamiltonians. The theory offers an intuitive geometric interpretation involving the level sets of the target property and the stable and unstable points related to the noise channel. We present solutions for various noise channels and target properties, which are classified as trivially controllable, uncontrollable, or controllable. In the controllable scenario, we demonstrate the existence of control Hamiltonian singularities and breakdown times, beyond which property preservation fails. QPP via Hamiltonian control is complementary to quantum error correction, as it does not require ancilla qubits or rely on measurement and feedback. It is also complementary to dynamical decoupling, since it uses only smooth Hamiltonians without pulsing and works in the regime of Markovian open system dynamics. From the perspective of control theory, this work addresses the challenge of tracking control for open quantum systems.

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arXiv2024

Simulating Chemistry on Bosonic Quantum Devices

Bosonic quantum devices offer a novel approach to realize quantum computations, where the quantum two-level system (qubit) is replaced with the quantum (an)harmonic oscillator (qumode) as the fundamental building block of the quantum simulator. The simulation of chemical structure and dynamics can then be achieved by representing or mapping the system Hamiltonians in terms of bosonic operators. In this perspective, we review recent progress and future potential of using bosonic quantum devices for addressing a wide range of challenging chemical problems, including the calculation of molecular vibronic spectra, the simulation of gas-phase and solution-phase adiabatic and nonadiabatic chemical dynamics, the efficient solution of molecular graph theory problems, and the calculations of electronic structure.

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arXiv2024

Qudit Dynamical Decoupling on a Superconducting Quantum Processor

Multi-level qudit systems are increasingly being explored as alternatives to traditional qubit systems due to their denser information storage and processing potential. However, qudits are more susceptible to decoherence than qubits due to increased loss channels, noise sensitivity, and crosstalk. To address these challenges, we develop protocols for dynamical decoupling (DD) of qudit systems based on the Heisenberg-Weyl group. We implement and experimentally verify these DD protocols on a superconducting transmon processor that supports qudit operation based on qutrits $(d=3)$ and ququarts $(d=4)$. Specifically, we demonstrate single-qudit DD sequences to decouple qutrits and ququarts from system-bath-induced decoherence. We also introduce two-qudit DD sequences designed to suppress the detrimental cross-Kerr couplings between coupled qudits. This allows us to demonstrate a significant improvement in the fidelity of time-evolved qutrit Bell states. Our results highlight the utility of leveraging DD to enable scalable qudit-based quantum computing.

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arXiv2024

Scaling Advantage in Approximate Optimization with Quantum Annealing

Quantum annealing is a heuristic optimization algorithm that exploits quantum evolution to approximately find lowest energy states. Quantum annealers have scaled up in recent years to tackle increasingly larger and more highly connected discrete optimization and quantum simulation problems. Nevertheless, despite numerous attempts, a computational quantum advantage in exact optimization using quantum annealing hardware has so far remained elusive. Here, we present evidence for a quantum annealing scaling advantage in approximate optimization. The advantage is relative to the top classical heuristic algorithm: parallel tempering with isoenergetic cluster moves (PT-ICM). The setting is a family of 2D spin-glass problems with high-precision spin-spin interactions. To achieve this advantage, we implement quantum annealing correction (QAC): an embedding of a bit-flip error-correcting code with energy penalties that leverages the properties of the D-Wave Advantage quantum annealer to yield over 1,300 error-suppressed logical qubits on a degree-5 interaction graph. We generate random spin-glass instances on this graph and benchmark their time-to-epsilon, a generalization of the time-to-solution metric for low-energy states. We demonstrate that with QAC, quantum annealing exhibits a scaling advantage over PT-ICM at sampling low energy states with an optimality gap of at least 1.0%. This amounts to the first demonstration of an algorithmic quantum speedup in approximate optimization.

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arXiv2023

Dynamical decoupling for superconducting qubits: a performance survey

Dynamical Decoupling (DD) is perhaps the simplest and least resource-intensive error suppression strategy for improving quantum computer performance. Here we report on a large-scale survey of the performance of 60 different DD sequences from 10 families, including basic as well as advanced sequences with high order error cancellation properties and built-in robustness. The survey is performed using three different superconducting-qubit IBMQ devices, with the goal of assessing the relative performance of the different sequences in the setting of arbitrary quantum state preservation. We find that the high-order universally robust (UR) and quadratic DD (QDD) sequences generally outperform all other sequences across devices and pulse interval settings. Surprisingly, we find that DD performance for basic sequences such as CPMG and XY4 can be made to nearly match that of UR and QDD by optimizing the pulse interval, with the optimal interval being substantially larger than the minimum interval possible on each device.

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arXiv2023

Quantum trajectories for time-dependent adiabatic master equations

We describe a quantum trajectories technique for the unraveling of the quantum adiabatic master equation in Lindblad form. By evolving a complex state vector of dimension $N$ instead of a complex density matrix of dimension $N^2$, simulations of larger system sizes become feasible. The cost of running many trajectories, which is required to recover the master equation evolution, can be minimized by running the trajectories in parallel, making this method suitable for high performance computing clusters. In general, the trajectories method can provide up to a factor $N$ advantage over directly solving the master equation. In special cases where only the expectation values of certain observables are desired, an advantage of up to a factor $N^2$ is possible. We test the method by demonstrating agreement with direct solution of the quantum adiabatic master equation for $8$-qubit quantum annealing examples. We also apply the quantum trajectories method to a $16$-qubit example originally introduced to demonstrate the role of tunneling in quantum annealing, which is significantly more time consuming to solve directly using the master equation. The quantum trajectories method provides insight into individual quantum jump trajectories and their statistics, thus shedding light on open system quantum adiabatic evolution beyond the master equation.

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arXiv2023

Which differential equations correspond to the Lindblad equation?

The Lindblad master equation can always be transformed into a first-order linear ordinary differential equation (1ODE) for the coherence vector. We pose the inverse problem: given a finite-dimensional, non-homogeneous 1ODE, does a corresponding Lindblad equation exist? If so, what are the corresponding Hamiltonian and Lindblad operators? We provide a general solution to this problem, including a complete positivity test in terms of the parameters of the 1ODE. We also derive a host of properties relating the two representations (master equation and 1ODE), which are of independent interest.

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arXiv2023

Modeling low- and high-frequency noise in transmon qubits with resource-efficient measurement

Transmon qubits experience open system effects that manifest as noise at a broad range of frequencies. We present a model of these effects using the Redfield master equation with a hybrid bath consisting of low and high-frequency components. We use two-level fluctuators to simulate 1/f-like noise behavior, which is a dominant source of decoherence for superconducting qubits. By measuring quantum state fidelity under free evolution with and without dynamical decoupling (DD), we can fit the low- and high-frequency noise parameters in our model. We train and test our model using experiments on quantum devices available through IBM quantum experience. Our model accurately predicts the fidelity decay of random initial states, including the effect of DD pulse sequences. We compare our model with two simpler models and confirm the importance of including both high-frequency and 1/f noise in order to accurately predict transmon behavior.

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arXiv2022

Quantum adiabatic theorem for unbounded Hamiltonians with a cutoff and its application to superconducting circuits

We present a new quantum adiabatic theorem that allows one to rigorously bound the adiabatic timescale for a variety of systems, including those described by unbounded Hamiltonians. Our bound is geared towards the qubit approximation of superconducting circuits, and presents a sufficient condition for remaining within the $2^n$-dimensional qubit subspace of a circuit model of $n$ qubits. The novelty of this adiabatic theorem is that unlike previous rigorous results, it does not contain $2^n$ as a factor in the adiabatic timescale, and it allows one to obtain an expression for the adiabatic timescale independent of the cutoff of the infinite-dimensional Hilbert space of the circuit Hamiltonian. As an application, we present an explicit dependence of this timescale on circuit parameters for a superconducting flux qubit, and demonstrate that leakage out of the qubit subspace is inevitable as the tunnelling barrier is raised towards the end of a quantum anneal. We also discuss a method of obtaining a $2^n\times 2^n$ effective Hamiltonian that best approximates the true dynamics induced by slowly changing circuit control parameters.

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arXiv2022

Demonstration of algorithmic quantum speedup

Quantum algorithms theoretically outperform classical algorithms in solving problems of increasing size, but computational errors must be kept to a minimum to realize this potential. Despite the development of increasingly capable quantum computers (QCs), an experimental demonstration of a provable algorithmic quantum speedup employing today's non-fault-tolerant, noisy intermediate-scale quantum (NISQ) devices has remained elusive. Here, we unequivocally demonstrate such a speedup, quantified in terms of the scaling with the problem size of the time-to-solution metric. We implement the single-shot Bernstein-Vazirani algorithm, which solves the problem of identifying a hidden bitstring that changes after every oracle query, utilizing two different 27-qubit IBM Quantum (IBMQ) superconducting processors. The speedup is observed on only one of the two QCs (ibmq_montreal) when the quantum computation is protected by dynamical decoupling (DD) -- a carefully designed sequence of pulses applied to the QC that suppresses its interaction with the environment, but not without DD. In contrast to recent quantum supremacy demonstrations, the quantum speedup reported here does not rely on any additional assumptions or complexity-theoretic conjectures and solves a bona fide computational problem, in the setting of a game with an oracle and a verifier.

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arXiv2022

HOQST: Hamiltonian Open Quantum System Toolkit

We present an open-source software package called "Hamiltonian Open Quantum System Toolkit" (HOQST), a collection of tools for the investigation of open quantum system dynamics in Hamiltonian quantum computing, including both quantum annealing and the gate-model of quantum computing. It features the key master equations (MEs) used in the field, suitable for describing the reduced system dynamics of an arbitrary time-dependent Hamiltonian with either weak or strong coupling to infinite-dimensional quantum baths. This includes the Redfield ME, the polaron-transformed Redfield ME, the adiabatic ME, the coarse-grained ME, and the universal Lindblad ME. HOQST also includes the stochastic Schrodinger equation with spin-fluctuators. We present an overview of the theories behind the various MEs and provide examples to illustrate typical workflows in HOQST. We present an example that shows that HOQST can provide order of magnitude speedups compared to QuTiP, for problems with time-dependent Hamiltonians. The package is ready to be deployed on high-performance computing (HPC) clusters and is aimed at providing reliable open-system analysis tools for noisy intermediate-scale quantum (NISQ) devices. The HOQST Github repository (https://github.com/USCqserver/OpenQuantumTools.jl) provides the starting point for users. Detailed information can be found in the README file.

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arXiv2022

Breakdown of the weak coupling limit in quantum annealing

Reverse annealing is a variant of quantum annealing, in which the system is prepared in a classical state, reverse-annealed to an inversion point, and then forward-annealed. We report on reverse annealing experiments using the D-Wave 2000Q device, with a focus on the $p=2$ $p$-spin problem, which undergoes a second order quantum phase transition with a gap that closes polynomially in the number of spins. We concentrate on the total and partial success probabilities, the latter being the probabilities of finding each of two degenerate ground states of all spins up or all spins down, the former being their sum. The empirical partial success probabilities exhibit a strong asymmetry between the two degenerate ground states, depending on the initial state of the reverse anneal. To explain these results, we perform open-system simulations using master equations in the limits of weak and strong coupling to the bath. The former, known as the adiabatic master equation (AME), with decoherence in the instantaneous energy eigenbasis, predicts perfect symmetry between the two degenerate ground states, thus failing to agree with the experiment. In contrast, the latter, known as the polaron transformed Redfield equation (PTRE), is in close agreement with experiment. Thus our results present a challenge to the sufficiency of the weak system-bath coupling limit in describing the dynamics of current experimental quantum annealers, at least for reverse annealing on timescales of a microsecond or longer.

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arXiv2022

Customized quantum annealing schedules

In a typical quantum annealing protocol, the system starts with a transverse field Hamiltonian which is gradually turned off and replaced by a longitudinal Ising Hamiltonian. The ground state of the Ising Hamiltonian encodes the solution to the computational problem of interest, and the state overlap with this ground state gives the success probability of the annealing protocol. The form of the annealing schedule can have a significant impact on the ground state overlap at the end of the anneal, so precise control over these annealing schedules can be a powerful tool for increasing success probabilities of annealing protocols. Here we show how superconducting circuits, in particular capacitively shunted flux qubits (CSFQs), can be used to construct quantum annealing systems by providing tools for mapping circuit flux biases to Pauli coefficients. We use this mapping to find customized annealing schedules: appropriate circuit control biases that yield a desired annealing schedule, while accounting for the physical limitations of the circuitry. We then provide examples and proposals that utilize this capability to improve quantum annealing performance.

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arXiv2022

Coherent quantum annealing in a programmable 2000-qubit Ising chain

Quantum simulation has emerged as a valuable arena for demonstrating and understanding the capabilities of near-term quantum computers. Quantum annealing has been used successfully in simulating a range of open quantum systems, both at equilibrium and out of equilibrium. However, in all previous experiments, annealing has been too slow to simulate a closed quantum system coherently, due to the onset of thermal effects from the environment. Here we demonstrate coherent evolution through a quantum phase transition in the paradigmatic setting of the 1D transverse-field Ising chain, using up to 2000 superconducting flux qubits in a programmable quantum annealer. In large systems we observe the quantum Kibble-Zurek mechanism with theoretically predicted kink statistics, as well as characteristic positive kink-kink correlations, independent of system temperature. In small chains, excitation statistics validate the picture of a Landau-Zener transition at a minimum gap. In both cases, results are in quantitative agreement with analytical solutions to the closed-system quantum model. For slower anneals we observe anti-Kibble-Zurek scaling in a crossover to the open quantum regime. These experiments demonstrate that large-scale quantum annealers can be operated coherently, paving the way to exploiting coherent dynamics in quantum optimization, machine learning, and simulation tasks.

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arXiv2022

3-Regular 3-XORSAT Planted Solutions Benchmark of Classical and Quantum Heuristic Optimizers

With current semiconductor technology reaching its physical limits, special-purpose hardware has emerged as an option to tackle specific computing-intensive challenges. Optimization in the form of solving Quadratic Unconstrained Binary Optimization (QUBO) problems, or equivalently Ising spin glasses, has been the focus of several new dedicated hardware platforms. These platforms come in many different flavors, from highly-efficient hardware implementations on digital-logic of established algorithms to proposals of analog hardware implementing new algorithms. In this work, we use a mapping of a specific class of linear equations whose solutions can be found efficiently, to a hard constraint satisfaction problem (3-regular 3-XORSAT, or an Ising spin glass) with a 'golf-course' shaped energy landscape, to benchmark several of these different approaches. We perform a scaling and prefactor analysis of the performance of Fujitsu's Digital Annealer Unit (DAU), the D-Wave Advantage quantum annealer, a Virtual MemComputing Machine, Toshiba's Simulated Bifurcation Machine (SBM), the SATonGPU algorithm from Bernaschi et al., and our implementation of parallel tempering. We identify the SATonGPU and DAU as currently having the smallest scaling exponent for this benchmark, with SATonGPU having a small scaling advantage and in addition having by far the smallest prefactor thanks to its use of massive parallelism. Our work provides an objective assessment and a snapshot of the promise and limitations of dedicated optimization hardware relative to a particular class of optimization problems.

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arXiv2022

Suppression of crosstalk in superconducting qubits using dynamical decoupling

Currently available superconducting quantum processors with interconnected transmon qubits are noisy and prone to various errors. The errors can be attributed to sources such as open quantum system effects and spurious inter-qubit couplings (crosstalk). The ZZ-coupling between qubits in fixed frequency transmon architectures is always present and contributes to both coherent and incoherent crosstalk errors. Its suppression is therefore a key step towards enhancing the fidelity of quantum computation using transmons. Here we propose the use of dynamical decoupling to suppress the crosstalk, and demonstrate the success of this scheme through experiments performed on several IBM quantum cloud processors. In particular, we demonstrate improvements in quantum memory as well as the performance of single-qubit and two-qubit gate operations. We perform open quantum system simulations of the multi-qubit processors and find good agreement with the experimental results. We analyze the performance of the protocol based on a simple analytical model and elucidate the importance of the qubit drive frequency in interpreting the results. In particular, we demonstrate that the XY4 dynamical decoupling sequence loses its universality if the drive frequency is not much larger than the system-bath coupling strength. Our work demonstrates that dynamical decoupling is an effective and practical way to suppress crosstalk and open system effects, thus paving the way towards higher-fidelity logic gates in transmon-based quantum computers.

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arXiv2022

Standard quantum annealing outperforms adiabatic reverse annealing with decoherence

We study adiabatic reverse annealing (ARA) in an open system. In the closed system (unitary) setting, this annealing protocol allows avoidance of first-order quantum phase transitions of selected models, resulting in an exponential speedup compared with standard quantum annealing, provided that the initial state of the algorithm is close in Hamming distance to the target one. Here, we show that decoherence can significantly modify this conclusion: by resorting to the adiabatic master equation approach, we simulate the dynamics of the ferromagnetic $p$-spin model with $p=3$ under independent and collective dephasing. For both models of decoherence, we show that the performance of open system ARA is far less sensitive to the choice of the initial state than its unitary counterpart, and, most significantly, that open system ARA by and large loses its time to solution advantage compared to standard quantum annealing. These results suggest that as a stand-alone strategy, ARA is unlikely to experimentally outperform standard "forward" quantum annealing, and that error mitigation strategies will likely be required in order to realize the benefits of ARA in realistic, noisy settings.

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