arXiv subjects

Lukasz Cincio

Publications and source records attributed to Lukasz Cincio.

At least 73 records · Page 4Linked to original sources

arXiv2021

Variational Quantum Algorithms

Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers due to the extremely high computational cost. Quantum computers promise a solution, although fault-tolerant quantum computers will likely not be available in the near future. Current quantum devices have serious constraints, including limited numbers of qubits and noise processes that limit circuit depth. Variational Quantum Algorithms (VQAs), which use a classical optimizer to train a parametrized quantum circuit, have emerged as a leading strategy to address these constraints. VQAs have now been proposed for essentially all applications that researchers have envisioned for quantum computers, and they appear to the best hope for obtaining quantum advantage. Nevertheless, challenges remain including the trainability, accuracy, and efficiency of VQAs. Here we overview the field of VQAs, discuss strategies to overcome their challenges, and highlight the exciting prospects for using them to obtain quantum advantage.

quant-ph↗

arXiv2021

Effect of barren plateaus on gradient-free optimization

Barren plateau landscapes correspond to gradients that vanish exponentially in the number of qubits. Such landscapes have been demonstrated for variational quantum algorithms and quantum neural networks with either deep circuits or global cost functions. For obvious reasons, it is expected that gradient-based optimizers will be significantly affected by barren plateaus. However, whether or not gradient-free optimizers are impacted is a topic of debate, with some arguing that gradient-free approaches are unaffected by barren plateaus. Here we show that, indeed, gradient-free optimizers do not solve the barren plateau problem. Our main result proves that cost function differences, which are the basis for making decisions in a gradient-free optimization, are exponentially suppressed in a barren plateau. Hence, without exponential precision, gradient-free optimizers will not make progress in the optimization. We numerically confirm this by training in a barren plateau with several gradient-free optimizers (Nelder-Mead, Powell, and COBYLA algorithms), and show that the numbers of shots required in the optimization grows exponentially with the number of qubits.

quant-ph↗

arXiv2021

Single-Qubit Cross Platform Comparison of Quantum Computing Hardware

As a variety of quantum computing models and platforms become available, methods for assessing and comparing the performance of these devices are of increasing interest and importance. Despite being built of the same fundamental computational unit, radically different approaches have emerged for characterizing the performance of qubits in gate-based and quantum annealing computers, limiting and complicating consistent cross-platform comparisons. To fill this gap, this work proposes a single-qubit protocol (Q-RBPN) for measuring some basic performance characteristics of individual qubits in both models of quantum computation. The proposed protocol scales to large quantum computers with thousands of qubits and provides insights into the distribution of qubit properties within a particular hardware device and across families of devices. The efficacy of the Q-RBPN protocol is demonstrated through the analysis of more than 300 gate-based qubits spanning eighteen machines and 2000 annealing-based qubits from one machine, revealing some unexpected differences in qubit performance. Overall, the proposed Q-RBPN protocol provides a new platform-agnostic tool for assessing the performance of a wide range of emerging quantum computing devices.

quant-ph↗

arXiv2021

Unified approach to data-driven quantum error mitigation

Achieving near-term quantum advantage will require effective methods for mitigating hardware noise. Data-driven approaches to error mitigation are promising, with popular examples including zero-noise extrapolation (ZNE) and Clifford data regression (CDR). Here we propose a novel, scalable error mitigation method that conceptually unifies ZNE and CDR. Our approach, called variable-noise Clifford data regression (vnCDR), significantly outperforms these individual methods in numerical benchmarks. vnCDR generates training data first via near-Clifford circuits (which are classically simulable) and second by varying the noise levels in these circuits. We employ a noise model obtained from IBM's Ourense quantum computer to benchmark our method. For the problem of estimating the energy of an 8-qubit Ising model system, vnCDR improves the absolute energy error by a factor of 33 over the unmitigated results and by factors 20 and 1.8 over ZNE and CDR, respectively. For the problem of correcting observables from random quantum circuits with 64 qubits, vnCDR improves the error by factors of 2.7 and 1.5 over ZNE and CDR, respectively.

quant-ph↗

arXiv2021

Long-time simulations with high fidelity on quantum hardware

Moderate-size quantum computers are now publicly accessible over the cloud, opening the exciting possibility of performing dynamical simulations of quantum systems. However, while rapidly improving, these devices have short coherence times, limiting the depth of algorithms that may be successfully implemented. Here we demonstrate that, despite these limitations, it is possible to implement long-time, high fidelity simulations on current hardware. Specifically, we simulate an XY-model spin chain on the Rigetti and IBM quantum computers, maintaining a fidelity of at least 0.9 for over 600 time steps. This is a factor of 150 longer than is possible using the iterated Trotter method. Our simulations are performed using a new algorithm that we call the fixed state Variational Fast Forwarding (fsVFF) algorithm. This algorithm decreases the circuit depth and width required for a quantum simulation by finding an approximate diagonalization of a short time evolution unitary. Crucially, fsVFF only requires finding a diagonalization on the subspace spanned by the initial state, rather than on the total Hilbert space as with previous methods, substantially reducing the required resources. We further demonstrate the viability of fsVFF through large numerical implementations of the algorithm, as well as an analysis of its noise resilience and the scaling of simulation errors.

quant-ph↗

arXiv2021

Variational Quantum Eigensolver with Reduced Circuit Complexity

The variational quantum eigensolver (VQE) is one of the most promising algorithms to find eigenvalues and eigenvectors of a given Hamiltonian on noisy intermediate-scale quantum (NISQ) devices. A particular application is to obtain ground or excited states of molecules. The practical realization is currently limited by the complexity of quantum circuits. Here we present a novel approach to reduce quantum circuit complexity in VQE for electronic structure calculations. Our algorithm, called ClusterVQE, splits the initial qubit space into subspaces (qubit clusters) which are further distributed on individual (shallower) quantum circuits. The clusters are obtained based on quantum mutual information reflecting maximal entanglement between qubits, whereas entanglement between different clusters is taken into account via a new "dressed" Hamiltonian. ClusterVQE therefore allows exact simulation of the problem by using fewer qubits and shallower circuit depth compared to standard VQE at the cost of additional classical resources. In addition, a new gradient measurement method without using an ancillary qubit is also developed in this work. Proof-of-principle demonstrations are presented for several molecular systems based on quantum simulators as well as an IBM quantum device with accompanying error mitigation. The efficiency of the new algorithm is comparable to or even improved over qubit-ADAPT-VQE and iterative Qubit Coupled Cluster (iQCC), state-of-the-art circuit-efficient VQE methods to obtain variational ground state energies of molecules on NISQ hardware. Above all, the new ClusterVQE algorithm simultaneously reduces the number of qubits and circuit depth, making it a potential leader for quantum chemistry simulations on NISQ devices.

quant-ph↗

arXiv2021

Qubit-efficient exponential suppression of errors

Achieving a practical advantage with near-term quantum computers hinges on having effective methods to suppress errors. Recent breakthroughs have introduced methods capable of exponentially suppressing errors by preparing multiple noisy copies of a state and virtually distilling a more purified version. Here we present an alternative method, the Resource-Efficient Quantum Error Suppression Technique (REQUEST), that adapts this breakthrough to much fewer qubits by making use of active qubit resets, a feature now available on commercial platforms. Our approach exploits a space/time trade-off to achieve a similar error reduction using only $2N+1$ qubits as opposed to $MN+1$ qubits, for $M$ copies of an $N$ qubit state. Additionally, we propose a method using near-Clifford circuits to find the optimal number of these copies in the presence of realistic noise, which limits this error suppression. We perform a numerical comparison between the original method and our qubit-efficient version with a realistic trapped-ion noise model. We find that REQUEST can reproduce the exponential suppression of errors of the virtual distillation approach, while out-performing virtual distillation when fewer than $3N+1$ qubits are available. Finally, we examine the scaling of the number of shots $N_S$ required for REQUEST to achieve useful corrections. We find that $N_S$ remains reasonable well into the quantum advantage regime where $N$ is hundreds of qubits.

quant-ph↗

arXiv2021

Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits

Variational quantum algorithms (VQAs) optimize the parameters $\vecθ$ of a parametrized quantum circuit $V(\vecθ)$ to minimize a cost function $C$. While VQAs may enable practical applications of noisy quantum computers, they are nevertheless heuristic methods with unproven scaling. Here, we rigorously prove two results, assuming $V(\vecθ)$ is an alternating layered ansatz composed of blocks forming local 2-designs. Our first result states that defining $C$ in terms of global observables leads to exponentially vanishing gradients (i.e., barren plateaus) even when $V(\vecθ)$ is shallow. Hence, several VQAs in the literature must revise their proposed costs. On the other hand, our second result states that defining $C$ with local observables leads to at worst a polynomially vanishing gradient, so long as the depth of $V(\vecθ)$ is $\mathcal{O}(\log n)$. Our results establish a connection between locality and trainability. We illustrate these ideas with large-scale simulations, up to 100 qubits, of a quantum autoencoder implementation.

quant-ph↗

arXiv2021

Machine learning of noise-resilient quantum circuits

Noise mitigation and reduction will be crucial for obtaining useful answers from near-term quantum computers. In this work, we present a general framework based on machine learning for reducing the impact of quantum hardware noise on quantum circuits. Our method, called noise-aware circuit learning (NACL), applies to circuits designed to compute a unitary transformation, prepare a set of quantum states, or estimate an observable of a many-qubit state. Given a task and a device model that captures information about the noise and connectivity of qubits in a device, NACL outputs an optimized circuit to accomplish this task in the presence of noise. It does so by minimizing a task-specific cost function over circuit depths and circuit structures. To demonstrate NACL, we construct circuits resilient to a fine-grained noise model derived from gate set tomography on a superconducting-circuit quantum device, for applications including quantum state overlap, quantum Fourier transform, and W-state preparation.

quant-ph↗

arXiv2020

State preparation and measurement in a quantum simulation of the O(3) sigma model

Recently, Singh and Chandrasekharan showed that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. In a paper by the NuQS collaboration, the proposal is made to simulate such field theories on a quantum computer using the universal properties of a similar model. In this paper, following that direction, we demonstrate how to prepare the ground state of the model from and measure a dynamical quantity of interest, the O(3) Noether charge, on a quantum computer. In particular, we apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes and use shadow tomography to measure the dynamics of local observables. We then present and analyze a quantum algorithm based on non-unitary randomized simulation methods that may yield an approach suitable for intermediate-term noisy quantum devices.

quant-ph↗

arXiv2020

Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time

Trotterization-based, iterative approaches to quantum simulation are restricted to simulation times less than the coherence time of the quantum computer, which limits their utility in the near term. Here, we present a hybrid quantum-classical algorithm, called Variational Fast Forwarding (VFF), for decreasing the quantum circuit depth of quantum simulations. VFF seeks an approximate diagonalization of a short-time simulation to enable longer-time simulations using a constant number of gates. Our error analysis provides two results: (1) the simulation error of VFF scales at worst linearly in the fast-forwarded simulation time, and (2) our cost function's operational meaning as an upper bound on average-case simulation error provides a natural termination condition for VFF. We implement VFF for the Hubbard, Ising, and Heisenberg models on a simulator. Additionally, we implement VFF on Rigetti's quantum computer to demonstrate simulation beyond the coherence time. Finally, we show how to estimate energy eigenvalues using VFF.

quant-ph↗

arXiv2020

Correlation-Informed Permutation of Qubits for Reducing Ansatz Depth in VQE

The Variational Quantum Eigensolver (VQE) is a method of choice to solve the electronic structure problem for molecules on near-term gate-based quantum computers. However, the circuit depth is expected to grow significantly with problem size. Increased depth can both degrade the accuracy of the results and reduce trainability. In this work, we propose a novel approach to reduce ansatz circuit depth. Our approach, called PermVQE, adds an additional optimization loop to VQE that permutes qubits in order to solve for the qubit Hamiltonian that minimizes long-range correlations in the ground state. The choice of permutations is based on mutual information, which is a measure of interaction between electrons in spin-orbitals. Encoding strongly interacting spin-orbitals into proximal qubits on a quantum chip naturally reduces the circuit depth needed to prepare the ground state. For representative molecular systems, LiH, H$_2$, (H$_2$)$_2$, H$_4$, and H$_3^+$, we demonstrate for linear qubit connectivity that placing entangled qubits in close proximity leads to shallower depth circuits required to reach a given eigenvalue-eigenvector accuracy. This approach can be extended to any qubit connectivity and can significantly reduce the depth required to reach a desired accuracy in VQE. Moreover, our approach can be applied to other variational quantum algorithms beyond VQE.

quant-ph↗

arXiv2020

Variational Hamiltonian Diagonalization for Dynamical Quantum Simulation

Dynamical quantum simulation may be one of the first applications to see quantum advantage. However, the circuit depth of standard Trotterization methods can rapidly exceed the coherence time of noisy quantum computers. This has led to recent proposals for variational approaches to dynamical simulation. In this work, we aim to make variational dynamical simulation even more practical and near-term. We propose a new algorithm called Variational Hamiltonian Diagonalization (VHD), which approximately transforms a given Hamiltonian into a diagonal form that can be easily exponentiated. VHD allows for fast forwarding, i.e., simulation beyond the coherence time of the quantum computer with a fixed-depth quantum circuit. It also removes Trotterization error and allows simulation of the entire Hilbert space. We prove an operational meaning for the VHD cost function in terms of the average simulation fidelity. Moreover, we prove that the VHD cost function does not exhibit a shallow-depth barren plateau, i.e., its gradient does not vanish exponentially. Our proof relies on locality of the Hamiltonian, and hence we connect locality to trainability. Our numerical simulations verify that VHD can be used for fast-forwarding dynamics.

quant-ph↗

arXiv2020

An Adaptive Optimizer for Measurement-Frugal Variational Algorithms

Variational hybrid quantum-classical algorithms (VHQCAs) have the potential to be useful in the era of near-term quantum computing. However, recently there has been concern regarding the number of measurements needed for convergence of VHQCAs. Here, we address this concern by investigating the classical optimizer in VHQCAs. We introduce a novel optimizer called individual Coupled Adaptive Number of Shots (iCANS). This adaptive optimizer frugally selects the number of measurements (i.e., number of shots) both for a given iteration and for a given partial derivative in a stochastic gradient descent. We numerically simulate the performance of iCANS for the variational quantum eigensolver and for variational quantum compiling, with and without noise. In all cases, and especially in the noisy case, iCANS tends to out-perform state-of-the-art optimizers for VHQCAs. We therefore believe this adaptive optimizer will be useful for realistic VHQCA implementations, where the number of measurements is limited.

quant-ph↗

arXiv2020

Information Scrambling and Loschmidt Echo

We demonstrate analytically and verify numerically that the out-of-time order correlator is given by the thermal average of Loschmidt echo signals. This provides a direct link between the out-of-time-order correlator -- a recently suggested measure of information scrambling in quantum chaotic systems -- and the Loschmidt echo, a well-appreciated familiar diagnostic that captures the dynamical aspect of chaotic behavior in the time domain, and is accessible to experimental studies.

quant-ph↗

arXiv2020

Operator Sampling for Shot-frugal Optimization in Variational Algorithms

Quantum chemistry is a near-term application for quantum computers. This application may be facilitated by variational quantum-classical algorithms (VQCAs), although a concern for VQCAs is the large number of measurements needed for convergence, especially for chemical accuracy. Here we introduce a strategy for reducing the number of measurements (i.e., shots) by randomly sampling operators $h_i$ from the overall Hamiltonian $H = \sum_i c_i h_i$. In particular, we employ weighted sampling, which is important when the $c_i$'s are highly non-uniform, as is typical in chemistry. We integrate this strategy with an adaptive optimizer developed recently by our group to construct an improved optimizer called Rosalin (Random Operator Sampling for Adaptive Learning with Individual Number of shots). Rosalin implements stochastic gradient descent while adapting the shot noise for each partial derivative and randomly assigning the shots amongst the $h_i$ according to a weighted distribution. We implement this and other optimizers to find the ground states of molecules H$_2$, LiH, and BeH$_2$, without and with quantum hardware noise, and Rosalin outperforms other optimizers in most cases.

quant-ph↗

arXiv2020

Variational Quantum Fidelity Estimation

Computing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelity $F(ρ,σ)$ based on the "truncated fidelity" $F(ρ_m, σ)$, which is evaluated for a state $ρ_m$ obtained by projecting $ρ$ onto its $m$-largest eigenvalues. Our bounds can be refined, i.e., they tighten monotonically with $m$. To compute our bounds, we introduce a hybrid quantum-classical algorithm, called Variational Quantum Fidelity Estimation, that involves three steps: (1) variationally diagonalize $ρ$, (2) compute matrix elements of $σ$ in the eigenbasis of $ρ$, and (3) combine these matrix elements to compute our bounds. Our algorithm is aimed at the case where $σ$ is arbitrary and $ρ$ is low rank, which we call low-rank fidelity estimation, and we prove that a classical algorithm cannot efficiently solve this problem. Finally, we demonstrate that our bounds can detect quantum phase transitions and are often tighter than previously known computable bounds for realistic situations.

quant-ph↗

arXiv2020

A New Heavy Flavor Program for the Future Electron-Ion Collider

The proposed high-energy and high-luminosity Electron-Ion Collider (EIC) will provide one of the cleanest environments to precisely determine the nuclear parton distribution functions (nPDFs) in a wide $x$-$Q^{2}$ range. Heavy flavor production at the EIC provides access to nPDFs in the poorly constrained high Bjorken-$x$ region, allows us to study the quark and gluon fragmentation processes, and constrains parton energy loss in cold nuclear matter. Scientists at the Los Alamos National Laboratory are developing a new physics program to study heavy flavor production, flavor tagged jets, and heavy flavor hadron-jet correlations in the nucleon/nucleus going direction at the future EIC. The proposed measurements will provide a unique way to explore the flavor dependent fragmentation functions and energy loss in a heavy nucleus. They will constrain the initial-state effects that are critical for the interpretation of previous and ongoing heavy ion measurements at the Relativistic Heavy Ion Collider and the Large Hadron Collider. We show an initial conceptual design of the proposed Forward Silicon Tracking (FST) detector at the EIC, which is essential to carry out the heavy flavor measurements. We further present initial feasibility studies/simulations of heavy flavor hadron reconstruction using the proposed FST.

nucl-ex↗