arXiv subjects

Martin Leib

Publications and source records attributed to Martin Leib.

34 records · Page 2Linked to original sources

arXiv2021

Quantum Approximate Optimization of Non-Planar Graph Problems on a Planar Superconducting Processor

We demonstrate the application of the Google Sycamore superconducting qubit quantum processor to combinatorial optimization problems with the quantum approximate optimization algorithm (QAOA). Like past QAOA experiments, we study performance for problems defined on the (planar) connectivity graph of our hardware; however, we also apply the QAOA to the Sherrington-Kirkpatrick model and MaxCut, both high dimensional graph problems for which the QAOA requires significant compilation. Experimental scans of the QAOA energy landscape show good agreement with theory across even the largest instances studied (23 qubits) and we are able to perform variational optimization successfully. For problems defined on our hardware graph we obtain an approximation ratio that is independent of problem size and observe, for the first time, that performance increases with circuit depth. For problems requiring compilation, performance decreases with problem size but still provides an advantage over random guessing for circuits involving several thousand gates. This behavior highlights the challenge of using near-term quantum computers to optimize problems on graphs differing from hardware connectivity. As these graphs are more representative of real world instances, our results advocate for more emphasis on such problems in the developing tradition of using the QAOA as a holistic, device-level benchmark of quantum processors.

quant-ph↗

arXiv2020

Quantum algorithms with local particle number conservation: noise effects and error correction

Quantum circuits with local particle number conservation (LPNC) restrict the quantum computation to a subspace of the Hilbert space of the qubit register. In a noiseless or fault-tolerant quantum computation, such quantities are preserved. In the presence of noise, however, the evolution's symmetry could be broken and non-valid states could be sampled at the end of the computation. On the other hand, the restriction to a subspace in the ideal case suggest the possibility of more resource efficient error mitigation techniques for circuits preserving symmetries that are not possible for general circuits. Here, we analyze the probability of staying in such symmetry-preserved subspaces under noise, providing an exact formula for local depolarizing noise. We apply our findings to benchmark, under depolarizing noise, the symmetry robustness of XY-QAOA, which has local particle number conserving symmetries, and is a special case of the Quantum Alternating Operator Ansatz. We also analyze the influence of the choice of encoding the problem on the symmetry robustness of the algorithm and discuss a simple adaption of the bit flip code to correct for symmetry-breaking errors with reduced resources.

quant-ph↗

arXiv2020

Forbidden subspaces for level-1 QAOA and IQP circuits

We present a thorough investigation of problems that can be solved exactly with the level-1 Quantum Approximate Optimization Algorithm (QAOA). To this end we implicitly define a class of problem Hamiltonians that employed as phase separator in a level-1 QAOA circuit provide unit overlap with a target subspace spanned by a set of computational basis states. For one-dimensional target subspaces we identify instances within the implicitly defined class of Hamiltonians for which Quantum Annealing (QA) and Simulated Annealing (SA) have an exponentially small probability to find the solution. Consequently, our results define a first demarcation line between QAOA, QA and SA, and highlight the fundamental differences between an interference-based search heuristic such as QAOA and heuristics that are based on thermal and quantum fluctuations like SA and QA respectively. Moreover, for two-dimensional solution subspaces we are able to show that the depth of the QAOA circuit grows linearly with the Hamming distance between the two target states. We further show that there are no genuine solutions for target subspaces of dimension higher than $2$ and smaller than $2^n$. We also transfer these results to Instantaneous Quantum Polynomial (IQP) circuits.

quant-ph↗

arXiv2020

Layerwise learning for quantum neural networks

With the increased focus on quantum circuit learning for near-term applications on quantum devices, in conjunction with unique challenges presented by cost function landscapes of parametrized quantum circuits, strategies for effective training are becoming increasingly important. In order to ameliorate some of these challenges, we investigate a layerwise learning strategy for parametrized quantum circuits. The circuit depth is incrementally grown during optimization, and only subsets of parameters are updated in each training step. We show that when considering sampling noise, this strategy can help avoid the problem of barren plateaus of the error surface due to the low depth of circuits, low number of parameters trained in one step, and larger magnitude of gradients compared to training the full circuit. These properties make our algorithm preferable for execution on noisy intermediate-scale quantum devices. We demonstrate our approach on an image-classification task on handwritten digits, and show that layerwise learning attains an 8% lower generalization error on average in comparison to standard learning schemes for training quantum circuits of the same size. Additionally, the percentage of runs that reach lower test errors is up to 40% larger compared to training the full circuit, which is susceptible to creeping onto a plateau during training.

quant-ph↗

arXiv2019

Training the Quantum Approximate Optimization Algorithm without access to a Quantum Processing Unit

In this paper, we eliminate the classical outer learning loop of the Quantum Approximate Optimization Algorithm (QAOA) and present a strategy to find good parameters for QAOA based on topological arguments of the problem graph and tensor network techniques. Starting from the observation of the concentration of control parameters of QAOA, we find a way to classically infer parameters which scales polynomially in the number of qubits and exponentially with the depth of the circuit. Using this strategy, the quantum processing unit (QPU) is only needed to infer the final state of QAOA. This method paves the way for a variation-free version of QAOA and makes QAOA more practical for applications on NISQ devices. Moreover, we show the applicability of our method beyond the scope of QAOA, in improving schedules for quantum annealing.

quant-ph↗

arXiv2019

Solving Quantum Chemistry Problems with a D-Wave Quantum Annealer

Quantum annealing devices have been subject to various analyses in order to classify their usefulness for practical applications. While it has been successfully proven that such systems can in general be used for solving combinatorial optimization problems, they have not been used to solve chemistry applications. In this paper we apply a mapping, put forward by Xia et al. (The Journal of Physical Chemistry B 122.13 (2017): 3384-3395.), from a quantum chemistry Hamiltonian to an Ising spin glass formulation and find the ground state energy with a quantum annealer. Additionally we investigate the scaling in terms of needed physical qubits on a quantum annealer with limited connectivity. To the best of our knowledge, this is the first experimental study of quantum chemistry problems on quantum annealing devices. We find that current quantum annealing technologies result in an exponential scaling for such inherently quantum problems and that new couplers are necessary to make quantum annealers attractive for quantum chemistry.

quant-ph↗

arXiv2019

Comparison of QAOA with Quantum and Simulated Annealing

We present a comparison between the Quantum Approximate Optimization Algorithm (QAOA) and two widely studied competing methods, Quantum Annealing (QA) and Simulated Annealing (SA). To achieve this, we define a class of optimization problems with respect to their spectral properties which are exactly solvable with QAOA. In this class, we identify instances for which QA and SA have an exponentially small probability to find the solution. Consequently, our results define a first demarcation line between QAOA, Simulated Annealing and Quantum Annealing, and highlight the fundamental differences between an interference-based search heuristic such as QAOA and heuristics that are based on thermal and quantum fluctuations like SA and QA respectively.

quant-ph↗

arXiv2016

A Transmon Quantum Annealer: Decomposing Many-Body Ising Constraints Into Pair Interactions

Adiabatic quantum computing is an analog quantum computing scheme with various applications in solving optimization problems. In the parity picture of quantum optimization, the problem is encoded in local fields that act on qubits which are connected via local 4-body terms. We present an implementation of a parity annealer with Transmon qubits with a specifically tailored Ising interaction from Josephson ring modulators.

quant-ph↗

arXiv2014

Steady-state phase diagram of a driven QED-cavity array with cross-Kerr nonlinearities

We study the properties of an array of QED-cavities coupled by nonlinear elements in the presence of photon leakage and driven by a coherent source. The main effect of the nonlinear couplings is to provide an effective cross-Kerr interaction between nearest-neighbor cavities. Additionally, correlated photon hopping between neighboring cavities arises. We provide a detailed mean-field analysis of the steady-state phase diagram as a function of the system parameters, the leakage, and the external driving, and show the emergence of a number of different quantum phases. A photon crystal associated to a spatial modulation of the photon blockade appears. The steady state can also display oscillating behavior and bistability. In some regions the crystalline ordering may coexist with the oscillating behavior. Furthermore we study the effect of short-range quantum fluctuations by employing a cluster mean-field analysis. Focusing on the corrections to the photon crystal boundaries, we show that, apart for some quantitative differences, the cluster mean field supports the findings of the simple single-site analysis. In the last part of the paper we concentrate on the possibility to build up the class of arrays introduced here, by means of superconducting circuits of existing technology. We consider a realistic choice of the parameters for this specific implementation and discuss some properties of the steady-state phase diagram.

quant-ph↗

arXiv2014

Synchronized Switching in a Josephson Junction Crystal

We consider a superconducting coplanar waveguide resonator where the central conductor is interrupted by a series of uniformly spaced Josephson junctions. The device forms an extended medium that is optically nonlinear on the single photon level with normal modes that inherit the full nonlinearity of the junctions but are nonetheless accessible via the resonator ports. For specific plasma frequencies of the junctions a set of normal modes clusters in a narrow band and eventually become entirely degenerate. Upon increasing the intensity of a red detuned drive on these modes, we observe a sharp and synchronized switching from low occupation quantum states to high occupation classical fields, accompanied by a pronounced jump from low to high output intensity.

cond-mat.mes-hall↗

arXiv2013

A "Single-Photon" Transistor in Circuit Quantum Electrodynamics

We introduce a circuit quantum electrodynamical setup for a "single-photon" transistor. In our approach photons propagate in two open transmission lines that are coupled via two interacting transmon qubits. The interaction is such that no photons are exchanged between the two transmission lines but a single photon in one line can completely block respectively enable the propagation of photons in the other line. High on-off ratios can be achieved for feasible experimental parameters. Our approach is inherently scalable as all photon pulses can have the same pulse shape and carrier frequency such that output signals of one transistor can be input signals for a consecutive transistor.

quant-ph↗

arXiv2013

Photon solid phases in driven arrays of nonlinearly coupled cavities

We introduce and study the properties of an array of QED cavities coupled by nonlinear elements, in the presence of photon leakage and driven by a coherent source. The nonlinear couplings lead to photon hopping and to nearest-neighbor Kerr terms. By tuning the system parameters, the steady state of the array can exhibit a photon crystal associated with a periodic modulation of the photon blockade. In some cases, the crystalline ordering may coexist with phase synchronization. The class of cavity arrays we consider can be built with superconducting circuits of existing technology.

quant-ph↗

arXiv2012

Photon Blockade in the Ultrastrong Coupling Regime

We explore photon coincidence counting statistics in the ultrastrong-coupling regime where the atom-cavity coupling rate becomes comparable to the cavity resonance frequency. In this regime usual normal order correlation functions fail to describe the output photon statistics. By expressing the electric-field operator in the cavity-emitter dressed basis we are able to propose correlation functions that are valid for arbitrary degrees of light-matter interaction. Our results show that the standard photon blockade scenario is significantly modified for ultrastrong coupling. We observe parametric processes even for two-level emitters and temporal oscillations of intensity correlation functions at a frequency given by the ultrastrong photon emitter coupling. These effects can be traced back to the presence of two-photon cascade decays induced by counter-rotating interaction terms.

quant-ph↗

arXiv2012

Many Body Physics with Coupled Transmission Line Resonators

We present the Josephson junction intersected superconducting transmission line resonator. In contrast to the Josephson parametric amplifier, Josephson bifurcation amplifier and Josephson parametric converter we consider the regime of few microwave photons. We review the derivation of eigenmode frequencies and zero point fluctuations of the nonlinear transmission line resonator and the derivation of the eigenmode Kerr nonlinearities. Remarkably these nonlinearities can reach values comparable to Transmon qubits rendering the device ideal for accessing the strongly correlated regime. This is particularly interesting for investigation of quantum many-body dynamics of interacting particles under the influence of drive and dissipation. We provide current profiles for the device modes and investigate the coupling between resonators in a network of nonlinear transmission line resonators.

quant-ph↗

arXiv2012

Networks of nonlinear superconducting transmission line resonators

We investigate a network of coupled superconducting transmission line resonators, each of them made nonlinear with a capacitively shunted Josephson junction coupling to the odd flux modes of the resonator. The resulting eigenmode spectrum shows anticrossings between the plasma mode of the shunted junction and the odd resonator modes. Notably, we find that the combined device can inherit the complete nonlinearity of the junction, allowing for a description as a harmonic oscillator with a Kerr nonlinearity. Using a dc SQUID instead of a single junction, the nonlinearity can be tuned between 10 kHz and 4 MHz while maintaining resonance frequencies of a few gigahertz for realistic device parameters. An array of such nonlinear resonators can be considered a scalable superconducting quantum simulator for a Bose-Hubbard Hamiltonian. The device would be capable of accessing the strongly correlated regime and be particularly well suited for investigating quantum many-body dynamics of interacting particles under the influence of drive and dissipation.

cond-mat.supr-con↗

arXiv2010

Bose-Hubbard dynamics of polaritons in a chain of circuit QED cavities

We investigate a chain of superconducting stripline resonators, each interacting with a transmon qubit, that are capacitively coupled in a row. We show that the dynamics of this system can be described by a Bose-Hubbard Hamiltonian with attractive interactions for polaritons, superpositions of photons and qubit excitations. This setup we envisage constitutes one of the first platforms where all technological components that are needed to experimentally study chains of strongly interacting polaritons have already been realized. By driving the first stripline resonator with a microwave source and detecting the output field of the last stripline resonator one can spectroscopically probe properties of the system in the driven dissipative regime. We calculate the stationary polariton density and density-density correlations $g^{(2)}$ for the last cavity which can be measured via the output field. Our results display a transition from a coherent to a quantum field as the ratio of on site interactions to driving strength is increased.

cond-mat.mes-hall↗