* * 22 Jan 2024

In this article, we establish a mathematical framework that utilizes concepts from graph theory to define the parity transformation as a mapping that encompasses all possible compiled hypergraphs, and investigate uniqueness properties of this mapping in more detail. By introducing so-called loop labelings, we derive an alternative expression of the preimage of any set of compiled hypergraphs under this encoding procedure when all equivalences classes of graphs are being considered. We then deduce equivalent conditions for the injectivity of the parity transformation on any subset of all equivalences classes of graphs. Moreover, we show concrete examples of optimization problems demonstrating that the parity transformation is not an injective mapping, and also introduce an important class of plaquette layouts and their corresponding set of constraints whose preimage is uniquely determined. In addition, we provide an algorithm which is based on classical algorithms from theoretical computer science and computes a compiled physical layout in this class in polynomial time.

* * 10 Jan 2024

https://doi.org/10.1038/s41467-023-43957-x

Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that fault-tolerant quantum computing could possibly provide provably efficient resolutions for generic (stochastic) gradient descent algorithms, scaling as O(T^2 polylog(n)), where n is the size of the models and T is the number of iterations in the training, as long as the models are both sufficiently dissipative and sparse, with small learning rates. Based on earlier efficient quantum algorithms for dissipative differential equations, we find and prove that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. In practice, we benchmark instances of large machine learning models from 7 million to 103 million parameters. We find that, in the context of sparse training, a quantum enhancement is possible at the early stage of learning after model pruning, motivating a sparse parameter download and re-upload scheme. Our work shows solidly that fault-tolerant quantum algorithms could potentially contribute to most state-of-the-art, large-scale machine-learning problems.

* * 30 Nov 2023

In the realm of advanced computing and signal processing, the need for optimized data processing methodologies is steadily increasing. With the world producing vast quantities of data, computing architectures necessitate to be swifter and more energy efficient. Edge computing architectures such as the NetCast architecture [1] combine the strength of electronic and photonic computing by outsourcing multiply-accumulate operations (MAC) to the optical domain. Herein we demonstrate a hybrid architecture, combining the advantages of FPGA data processing facilitating an ultra-low power electro-optical “smart transceiver” comprised of a lithium-niobate on insulator photonic circuit. The as-demonstrated device combines potential GHz speed data processing, with a power consumption in the order of 6.63 fJ per bit. Our device provides a blueprint of a unit cell for a TFLN smart transceiver alongside a variety of optical computing architectures, such as optical neural networks, as it provides a low power, reconfigurable memory unit.

* * 15 Nov 2023

In the near term, programming quantum computers will remain severely limited by low quantum volumes. Therefore, it is desirable to implement quantum circuits with the fewest resources possible. For the common Clifford+T circuits, most research is focused on reducing the number of T gates, since they are an order of magnitude more expensive than Clifford gates in quantum error corrected encoding schemes. However, this optimization sometimes leads to more 2-qubit gates, which, even though they are less expensive in terms of fault-tolerance, contribute significantly to the overall circuit cost. Approaches based on the ZX-calculus have recently gained some popularity in the field, but reduction of 2-qubit gates is not their focus. In this work, we present an alternative for improving 2-qubit gate count of a quantum circuit with the ZX-calculus by using heuristics in ZX-diagram simplification. Our approach maintains the good reduction of the T gate count provided by other strategies based on ZX-calculus, thus serving as an extension for other optimization algorithms. Our results show that combining the available ZX-calculus-based optimizations with our algorithms can reduce the number of 2-qubit gates by as much as 40% compared to current approaches using ZX-calculus. Additionally, we improve the results of the best currently available optimization technique of Nam et. al for some circuits by up to 15%.

* * 3 Nov 2023

arXiv:2308.12358 [cond-mat.str-el]

Tensor networks capture large classes of ground states of phases of quantum matter faithfully and efficiently. Their manipulation and contraction has remained a challenge over the years, however. For most of the history, ground state simulations of two-dimensional quantum lattice systems using (infinite) projected entangled pair states have relied on what is called a time-evolving block decimation. In recent years, multiple proposals for the variational optimization of the quantum state have been put forward, overcoming accuracy and convergence problems of previously known methods. The incorporation of automatic differentiation in tensor networks algorithms has ultimately enabled a new, flexible way for variational simulation of ground states and excited states. In this work, we review the state of the art of the variational iPEPS framework. We present and explain the functioning of an efficient, comprehensive and general tensor network library for the simulation of infinite two-dimensional systems using iPEPS, with support for flexible unit cells and different lattice geometries.

* * 30 Oct 2023

arXiv:2309.13118 [cond-mat.str-el]

The ground state of the toric code, that of the two-dimensional class D superconductor, and the partition sum of the two-dimensional Ising model are dual to each other. This duality is remarkable inasmuch as it connects systems commonly associated to different areas of physics -- that of long range entangled topological order, (topological) band insulators, and classical statistical mechanics, respectively. Connecting fermionic and bosonic systems, the duality construction is intrinsically non-local, a complication that has been addressed in a plethora of different approaches, including dimensional reduction to one dimension, conformal field theory methods, and operator algebra. In this work, we propose a unified approach to this duality, whose main protagonist is a tensor network (TN) assuming the role of an intermediate translator. Introducing a fourth node into the net of dualities offers several advantages: the formulation is integrative in that all links of the duality are treated on an equal footing, (unlike in field theoretical approaches) it is formulated with lattice precision, a feature that becomes key in the mapping of correlation functions, and their possible numerical implementation. Finally, the passage from bosons to fermions is formulated entirely within the two-dimensional TN framework where it assumes an intuitive and technically convenient form. We illustrate the predictive potential of the formalism by exploring the fate of phase transitions, point and line defects, topological boundary modes, and other structures under the mapping between system classes. Having condensed matter readerships in mind, we introduce the construction pedagogically in a manner assuming only minimal familiarity with the concept of TNs.

* * 22 Sept 2023

Schemes of classical shadows have been developed to facilitate the read-out of digital quantum devices, but similar tools for analog quantum simulators are scarce and experimentally impractical. In this work, we provide a measurement scheme for fermionic quantum devices that estimates second and fourth order correlation functions by means of free fermionic, translationally invariant evolutions - or quenches - and measurements in the mode occupation number basis. We precisely characterize what correlation functions can be recovered and equip the estimates with rigorous bounds on sample complexities, a particularly important feature in light of the difficulty of getting good statistics in reasonable experimental platforms, with measurements being slow. Finally, we demonstrate how our procedure can be approximately implemented with just nearest-neighbour, translationally invariant hopping quenches, a very plausible procedure under current experimental requirements, and requiring only random time-evolution with respect to a single native Hamiltonian. On a conceptual level, this work brings the idea of classical shadows to the realm of large scale analog quantum simulators.

* *15 Sept 2023

Neutral Atom Quantum Computing (NAQC) emerges as a promising hardware platform primarily due to its long coherence times and scalability. Additionally, NAQC offers computational advantages encompassing potential long-range connectivity, native multi-qubit gate support, and the ability to physically rearrange qubits with high fidelity. However, for the successful operation of a NAQC processor, one additionally requires new software tools to translate high-level algorithmic descriptions into a hardware executable representation, taking maximal advantage of the hardware capabilities. Realizing new software tools requires a close connection between tool developers and hardware experts to ensure that the corresponding software tools obey the corresponding physical constraints. This work aims to provide a basis to establish this connection by investigating the broad spectrum of capabilities intrinsic to the NAQC platform and its implications on the compilation process. To this end, we first review the physical background of NAQC and derive how it affects the overall compilation process by formulating suitable constraints and figures of merit. We then provide a summary of the compilation process and discuss currently available software tools in this overview. Finally, we present selected case studies and employ the discussed figures of merit to evaluate the different capabilities of NAQC and compare them between two hardware setups.

* * 13 Sept 2023

Combinatorial optimization - a field of research addressing problems that feature strongly in a wealth of scientific and industrial contexts - has been identified as one of the core potential fields of applicability of quantum computers. It is still unclear, however, to what extent quantum algorithms can actually outperform classical algorithms for this type of problems. In this work, by resorting to computational learning theory and cryptographic notions, we prove that quantum computers feature an in-principle super-polynomial advantage over classical computers in approximating solutions to combinatorial optimization problems. Specifically, building on seminal work by Kearns and Valiant and introducing a new reduction, we identify special types of problems that are hard for classical computers to approximate up to polynomial factors. At the same time, we give a quantum algorithm that can efficiently approximate the optimal solution within a polynomial factor. The core of the quantum advantage discovered in this work is ultimately borrowed from Shor's quantum algorithm for factoring. Concretely, we prove a super-polynomial advantage for approximating special instances of the so-called integer programming problem. In doing so, we provide an explicit end-to-end construction for advantage bearing instances. This result shows that quantum devices have, in principle, the power to approximate combinatorial optimization solutions beyond the reach of classical efficient algorithms. Our results also give clear guidance on how to construct such advantage-bearing problem instances.

* * 12 Sept 2023

arXiv:2309.04717 [physics.atom-ph]

Recent advances in quantum simulation based on neutral atoms have largely benefited from high-resolution, single-atom sensitive imaging techniques. A variety of approaches have been developed to achieve such local detection of atoms in optical lattices or optical tweezers. For alkaline-earth and alkaline-earth-like atoms, the presence of narrow optical transitions opens up the possibility of performing novel types of Sisyphus cooling, where the cooling mechanism originates from the capability to spatially resolve the differential optical level shifts in the trap potential. Up to now, it has been an open question whether high-fidelity imaging could be achieved in a "repulsive Sisyphus" configuration, where the trap depth of the ground state exceeds that of the excited state involved in cooling. Here, we demonstrate high-fidelity (99.9995(3)%) and high-survival (99.80(5)%) imaging of strontium atoms using repulsive Sisyphus cooling. We use an optical lattice as a pinning potential for atoms in a large-scale tweezer array with up to 399 tweezers and show repeated, high-fidelity lattice-tweezer-lattice transfers. We furthermore demonstrate the scalability of the platform by directly loading more than 10000 atoms in a single plane of the optical lattice, which can be used as a locally addressable and sortable reservoir for continuous refilling of optical tweezer arrays in the future.

* * 24 Aug 2023

The study of many-body quantum dynamics in strongly-correlated systems is extremely challenging. To date few numerical methods exist which are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, in part reflecting complexity theoretic obstructions. In this work, we present a new technique able to overcome this obstacle, by combining continuous unitary flow techniques with the newly developed method of scrambling transforms. We overcome the prejudice that approximately diagonalizing the Hamiltonian cannot lead to reliable predictions for relatively long times. To the contrary, we show that the method works well in both localized and delocalized phases, and makes reliable predictions for a number of quantities including infinite-temperature autocorrelation functions. We complement our findings with rigorous incremental bounds on the truncation error. This approach shows that in practice, the exploration of intermediate-scale time evolution may be more feasible than is commonly assumed, challenging near-term quantum simulators.

* * 19 Aug 2023

doi: 10.1038/s41467-023-39382-9

Schemes of classical shadows have been developed to facilitate the read-out of digital quantum devices, but similar tools for analog quantum simulators are scarce and experimentally impractical. In this work, we provide a measurement scheme for fermionic quantum devices that estimates second and fourth order correlation functions by means of free fermionic, translationally invariant evolutions - or quenches - and measurements in the mode occupation number basis. We precisely characterize what correlation functions can be recovered and equip the estimates with rigorous bounds on sample complexities, a particularly important feature in light of the difficulty of getting good statistics in reasonable experimental platforms, with measurements being slow. Finally, we demonstrate how our procedure can be approximately implemented with just nearest-neighbour, translationally invariant hopping quenches, a very plausible procedure under current experimental requirements, and requiring only random time-evolution with respect to a single native Hamiltonian. On a conceptual level, this work brings the idea of classical shadows to the realm of large scale analog quantum simulators.

* *7 Aug 2023

We propose a novel variational ansatz for the ground state preparation of the Z2 lattice gauge theory (LGT) in quantum simulators (QSs). It combines dissipative and unitary operations in a completely deterministic scheme with a circuit complexity that does not scale with the size of the considered lattice. We find that, with very few variational parameters, the ansatz is able to achieve >99% fidelity with the true ground state in both the confined and deconfined phase of the Z2 LGT. We benchmark our proposal against the unitary Hamiltonian variational ansatz (HVA), and find a clear advantage of our scheme, especially for few variational parameters as well as for large system sizes. After performing a finite-size scaling analysis, we show that our dissipative variational ansatz is able to predict critical exponents with accuracies that surpass the capabilities of the HVA. Furthermore, we investigate the ground-state preparation algorithm in the presence of circuit-level noise and determine variational error thresholds, which determine error rates *p**L*, below which it would be beneficial to increase the number of layers *L*↦*L*+1. Comparing those values to quantum gate errors *p* of state-of-the-art quantum processors, we provide a detailed assessment of the prospects of our scheme to explore the Z2 LGT on near-term devices.

* * 26 Jul 2023

Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing tools for verifying that a quantum device indeed performed the classically intractable sampling task are either impractical or not scalable to the quantum advantage regime. The verification problem thus remains an outstanding challenge. Here, we experimentally demonstrate efficiently verifiable quantum random sampling in the measurement-based model of quantum computation on a trapped-ion quantum processor. We create random cluster states, which are at the heart of measurement-based computing, up to a size of 4 x 4 qubits. Moreover, by exploiting the structure of these states, we are able to recycle qubits during the computation to sample from entangled cluster states that are larger than the qubit register. We then efficiently estimate the fidelity to verify the prepared states--in single instances and on average--and compare our results to cross-entropy benchmarking. Finally, we study the effect of experimental noise on the certificates. Our results and techniques provide a feasible path toward a verified demonstration of a quantum advantage.

* *25 Jul 2023

Logical qubits can be protected from decoherence by performing QEC cycles repeatedly. Algorithms for fault-tolerant QEC must be compiled to the specific hardware platform under consideration in order to practically realize a quantum memory that operates for in principle arbitrary long times. All circuit components must be assumed as noisy unless specific assumptions about the form of the noise are made. Modern QEC schemes are challenging to implement experimentally in physical architectures where in-sequence measurements and feed-forward of classical information cannot be reliably executed fast enough or even at all. Here we provide a novel scheme to perform QEC cycles without the need of measuring qubits that is fully fault-tolerant with respect to all components used in the circuit. Our scheme can be used for any low-distance CSS code since its only requirement towards the underlying code is a transversal CNOT gate. Similarly to Steane-type EC, we coherently copy errors to a logical auxiliary qubit but then apply a coherent feedback operation from the auxiliary system to the logical data qubit. The logical auxiliary qubit is prepared fault-tolerantly without measurements, too. We benchmark logical failure rates of the scheme in comparison to a flag-qubit based EC cycle. We map out a parameter region where our scheme is feasible and estimate physical error rates necessary to achieve the break-even point of beneficial QEC with our scheme. We outline how our scheme could be implemented in ion traps and with neutral atoms in a tweezer array. For recently demonstrated capabilities of atom shuttling and native multi-atom Rydberg gates, we achieve moderate circuit depths and beneficial performance of our scheme while not breaking fault tolerance. These results thereby enable practical fault-tolerant QEC in hardware architectures that do not support mid-circuit measurements.

* * 23 Jun 2023

Quantum machine learning models have shown successful generalization performance even when trained with few data. In this work, through systematic randomization experiments, we show that traditional approaches to understanding generalization fail to explain the behavior of such quantum models. Our experiments reveal that state-of-the-art quantum neural networks accurately fit random states and random labeling of training data. This ability to memorize random data defies current notions of small generalization error, problematizing approaches that build on complexity measures such as the VC dimension, the Rademacher complexity, and all their uniform relatives. We complement our empirical results with a theoretical construction showing that quantum neural networks can fit arbitrary labels to quantum states, hinting at their memorization ability. Our results do not preclude the possibility of good generalization with few training data but rather rule out any possible guarantees based only on the properties of the model family. These findings expose a fundamental challenge in the conventional understanding of generalization in quantum machine learning and highlight the need for a paradigm shift in the design of quantum models for machine learning tasks.

* *20 Jun 2023

The competition between non-commuting projective measurements in discrete quantum circuits can give rise to entanglement transitions. It separates a regime where initially stored quantum information survives the time evolution from a regime where the measurements destroy the quantum information. Here we study one such system - the projective transverse field Ising model - with a focus on its capabilities as a quantum error correction code. The idea is to interpret one type of measurement as an error and the other type as a syndrome measurement. We demonstrate that there is a finite threshold below which quantum information encoded in an initially entangled state can be retrieved reliably. In particular, we implement the maximum likelihood decoder to demonstrate that the error correction threshold is distinct from the entanglement transition. This implies that there is a finite regime where quantum information is protected by the projective dynamics, but cannot be retrieved by using syndrome measurements.

* * 8 Jun 2023

Saddle points constitute a crucial challenge for first-order gradient descent algorithms. In notions of classical machine learning, they are avoided for example by means of stochastic gradient descent methods. In this work, we provide evidence that the saddle points problem can be naturally avoided in variational quantum algorithms by exploiting the presence of stochasticity. We prove convergence guarantees of the approach and its practical functioning at hand of examples. We argue that the natural stochasticity of variational algorithms can be beneficial for avoiding strict saddle points, i.e., those saddle points with at least one negative Hessian eigenvalue. This insight that some noise levels could help in this perspective is expected to add a new perspective to notions of near-term variational quantum algorithms.

* * 8 Jun 2023

Saddle points constitute a crucial challenge for first-order gradient descent algorithms. In notions of classical machine learning, they are avoided for example by means of stochastic gradient descent methods. In this work, we provide evidence that the saddle points problem can be naturally avoided in variational quantum algorithms by exploiting the presence of stochasticity. We prove convergence guarantees and present practical examples in numerical simulations and on quantum hardware. We argue that the natural stochasticity of variational algorithms can be beneficial for avoiding strict saddle points, i.e., those saddle points with at least one negative Hessian eigenvalue. This insight that some levels of shot noise could help is expected to add a new perspective to notions of near-term variational quantum algorithms.

* * 8 May 2023

arXiv:2208.14432 [cond-mat.dis-nn]

Many-body localisation in disordered systems in one spatial dimension is typically understood in terms of the existence of an extensive number of (quasi)-local integrals of motion (LIOMs) which are thought to decay exponentially with distance and interact only weakly with one another. By contrast, little is known about the form of the integrals of motion in disorder-free systems which exhibit localisation. Here, we explicitly compute the LIOMs for disorder-free localised systems, focusing on the case of a linearly increasing potential. We show that while in the absence of interactions, the LIOMs decay faster than exponentially, the addition of interactions leads to the formation of a spatially extended plateau. We study how varying the linear slope affects the localisation properties of the LIOMs, finding that there is a significant finite-size dependence, and present evidence that adding a weak harmonic potential does not result in typical many-body localisation phenomenology. By contrast, the addition of disorder has a qualitatively different effect, dramatically modifying the properties of the LIOMs.

* *11 Apr 2023

We provide practical and powerful schemes for learning many properties of an unknown n-qubit quantum state using a sparing number of copies of the state. Specifically, we present a depth-modulated randomized measurement scheme that interpolates between two known classical shadows schemes based on random Pauli measurements and random Clifford measurements. These can be seen within our scheme as the special cases of zero and infinite depth, respectively. We focus on the regime where depth scales logarithmically in n and provide evidence that this retains the desirable properties of both extremal schemes whilst, in contrast to the random Clifford scheme, also being experimentally feasible. We present methods for two key tasks; estimating expectation values of certain observables from generated classical shadows and, computing upper bounds on the depth-modulated shadow norm, thus providing rigorous guarantees on the accuracy of the output estimates. We consider observables that can be written as a linear combination of poly(n) Paulis and observables that can be written as a low bond dimension matrix product operator. For the former class of observables both tasks are solved efficiently in n. For the latter class, we do not guarantee efficiency but present a method that works in practice; by variationally computing a heralded approximate inverses of a tensor network that can then be used for efficiently executing both these tasks.

* *10 Mar 2023

Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently, first large-scale implementations of quantum random sampling have arguably surpassed the boundary of what can be simulated on existing classical hardware. In this article, we comprehensively review the theoretical underpinning of quantum random sampling in terms of computational complexity and verifiability, as well as the practical aspects of its experimental implementation using superconducting and photonic devices and its classical simulation. We discuss in detail open questions in the field and provide perspectives for the road ahead, including potential applications of quantum random sampling.

* *9 Mar 2023

arXiv:2303.05317 [cond-mat.stat-mech]

The role of quantum fluctuations in modifying the critical behavior of non-equilibrium phase transitions is a fundamental but unsolved question. In this study, we examine the absorbing state phase transition of a 1D chain of qubits undergoing a contact process that involves both coherent and classical dynamics. We adopt a discrete-time quantum model with states that can be described in the stabilizer formalism, and therefore allows for an efficient simulation of large system sizes. The extracted critical exponents indicate that the absorbing state phase transition of this Clifford circuit model belongs to the directed percolation universality class. This suggests that the inclusion of quantum fluctuations does not necessarily alter the critical behavior of non-equilibrium phase transitions of purely classical systems. Finally, we extend our analysis to a non-Clifford circuit model, where a tentative scaling analysis in small systems reveals critical exponents that are also consistent with the directed percolation universality class.

* *22 Jan 2023

Variational methods play an important role in the study of quantum many body problems, both in the flavour of classical variational principles based on tensor networks as well as of quantum variational principles in near-term quantum computing. This brief pedagogical note stresses that for translationally invariant lattice Hamiltonians, one can easily derive efficiently computable lower bounds to ground state energies that can and should be compared with variational principles providing upper bounds. As small technical results, it is shown that (i) the Anderson bound and a (ii) common hierarchy of semi-definite relaxations both provide approximations with performance guarantees that scale like a constant in the energy density for cubic lattices. (iii) Also, the Anderson bound is systematically improved as a hierarchy of semi-definite relaxations inspired by the marginal problem.

* * 26 Feb 2023

Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing using no or few additional quantum resources, in contrast to fault-tolerant schemes that come along with heavy overheads. Error mitigation has been successfully applied to reduce noise in near-term applications. In this work, however, we identify strong limitations to the degree to which quantum noise can be effectively `undone' for larger system sizes. We set up a framework that rigorously captures large classes of error mitigation schemes in use today. The core of our argument combines fundamental limits of statistical inference with a construction of families of random circuits that are highly sensitive to noise. We show that even at poly log log n depth, a super-polynomial number of samples is needed in the worst case to estimate the expectation values of noiseless observables, the principal task of error mitigation. Notably, our construction implies that scrambling due to noise can kick in at exponentially smaller depths than previously thought. They also impact other near-term applications, constraining kernel estimation in quantum machine learning, causing an earlier emergence of noise-induced barren plateaus in variational quantum algorithms and ruling out exponential quantum speed-ups in estimating expectation values in the presence of noise or preparing the ground state of a Hamiltonian.

* *4 Jan 2023

arXiv:2301.01787[cond-mat.dis-nn]

Quasi-local integrals of motion are a key concept underpinning the modern understanding of many-body localisation, an intriguing phenomenon in which interactions and disorder come together. Despite the existence of several numerical ways to compute them - and astoundingly in the light of the observation that much of the phenomenology of many properties can be derived from them - it is not obvious how to directly measure aspects of them in real quantum simulations; in fact, the smoking gun of their experimental observation is arguably still missing. In this work, we propose a way to extract the real-space properties of such quasi-local integrals of motion based on a spatially-resolved entanglement probe able to distinguish Anderson from many-body localisation from non-equilibrium dynamics. We complement these findings with a new rigorous entanglement bound and compute the relevant quantities using tensor networks. We demonstrate that the entanglement gives rise to a well-defined length scale that can be measured in experiments.

* * 4 Dec 2022

arXiv:2211.16932 [cond-mat.str-el]

We investigate the ground state of the spin S=1/2 Heisenberg anti-ferromagnet on the Shuriken lattice, also in the presence of an external magnetic field. To this end, we employ two-dimensional tensor network techniques based on infinite projected entangled pair and simplex states considering states with different sizes of the unit cells. We show that a valence bond crystal with resonances over length six loops emerges as the ground state (at any given finite bond dimension) yielding the lowest reported estimate of the ground state energy E0/J=−0.4410±0.0001 for this model, estimated in the thermodynamic limit. We also study the model in the presence of an external magnetic field and find the emergence of 0, 1/3 and 2/3 magnetization plateaus with states respecting translation and point group symmetries that feature loop-four plaquette resonances instead.

* * 2 Nov 2022

Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently, first large-scale implementations of quantum random sampling have arguably surpassed the boundary of what can be simulated on existing classical hardware. In this article, we comprehensively review the theoretical underpinning of quantum random sampling in terms of computational complexity and verifiability, as well as the practical aspects of its experimental implementation using superconducting and photonic devices and its classical simulation. We discuss in detail open questions in the field and provide perspectives for the road ahead, including potential applications of quantum random sampling.

* * 31 Oct 2022

arXiv:2211.00121 [cond-mat.str-el]

Aimed at a more realistic classical description of natural quantum systems, we present a two-dimensional tensor network algorithm to study finite temperature properties of frustrated model quantum systems and real quantum materials. For this purpose, we introduce the infinite projected entangled simplex operator ansatz to study thermodynamic properties. To obtain state-of-the-art benchmarking results, we explore the highly challenging spin-1/2 Heisenberg anti-ferromagnet on the Kagome lattice, a system for which we investigate the melting of the magnetization plateaus at finite magnetic field and temperature. Making close connection to actual experimental data of real quantum materials, we go on to studying the finite temperature properties of Ca10Cr7O28. We compare the magnetization curve of this material in the presence of an external magnetic field at finite temperature with classically simulated data. As a first theoretical tool that incorporates both thermal fluctuations as well as quantum correlations in the study of this material, our work contributes to settling the existing controversy between the experimental data and previous theoretical works on the magnetization process.

* *17 Oct 2022

Photons are a natural resource in quantum information, and the last decade showed significant progress in high-quality single photon generation and detection. Furthermore, photonic qubits are easy to manipulate and do not require particularly strongly sealed environments, making them an appealing platform for quantum computing. With the one-way model, the vision of a universal and large-scale quantum computer based on photonics becomes feasible. In one-way computing, the input state is not an initial product state, but a so-called cluster state. A series of measurements on the cluster state's individual qubits and their temporal order, together with a feed-forward procedure, determine the quantum circuit to be executed. We propose a pipeline to convert a QASM circuit into a graph representation named measurement-graph (m-graph), that can be directly translated to hardware instructions on an optical one-way quantum computer. In addition, we optimize the graph using ZX-Calculus before evaluating the execution on an experimental discrete variable photonic platform.

* * 9 Oct 2022

With quantum computing devices increasing in scale and complexity, there is a growing need for tools that obtain precise diagnostic information about quantum operations. However, current quantum devices are only capable of short unstructured gate sequences followed by native measurements. We accept this limitation and turn it into a new paradigm for characterizing quantum gate-sets. A single experiment - random sequence estimation - solves a wealth of estimation problems, with all complexity moved to classical post-processing. We derive robust channel variants of shadow estimation with close-to-optimal performance guarantees and use these as a primitive for partial, compressive and full process tomography as well as the learning of Pauli noise. We discuss applications to the quantum gate engineering cycle, and propose novel methods for the optimization of quantum gates and diagnosing cross-talk.

* * 28 Sept 2022

The physics of a closed quantum mechanical system is governed by its Hamiltonian. However, in most practical situations, this Hamiltonian is not precisely known, and ultimately all there is are data obtained from measurements on the system. In this work, we introduce a highly scalable, data-driven approach to learning families of interacting many-body Hamiltonians from dynamical data, by bringing together techniques from gradient-based optimization from machine learning with efficient quantum state representations in terms of tensor networks. Our approach is highly practical, experimentally friendly, and intrinsically scalable to allow for system sizes of above 100 spins. In particular, we demonstrate on synthetic data that the algorithm works even if one is restricted to one simple initial state, a small number of single-qubit observables, and time evolution up to relatively short times. For the concrete example of the one-dimensional Heisenberg model our algorithm exhibits an error constant in the system size and scaling as the inverse square root of the size of the data set.

* * 19 Sept 2022

arXiv:2209.09132 [cond-mat.quant-gas]

We investigate signal propagation in a quantum field simulator of the Klein-Gordon model realized by two strongly coupled parallel one-dimensional quasi-condensates. By measuring local phononic fields after a quench, we observe the propagation of correlations along sharp light-cone fronts. If the local atomic density is inhomogeneous, these propagation fronts are curved. For sharp edges, the propagation fronts are reflected at the system's boundaries. By extracting the space-dependent variation of the front velocity from the data, we find agreement with theoretical predictions based on curved geodesics of an inhomogeneous metric. This work extends the range of quantum simulations of non-equilibrium field dynamics in general spacetime metrics.

* * Jul - Aug 2022

With quantum computing (QC) maturing, high-performance computing (HPC) centers are already preparing to host early-phase production versions of such systems. Unlike their experimental predecessors in physics laboratories, with a very small and dedicated user community, this next generation of systems needs to serve a wider user community and must work in concert with existing HPC systems and software stacks. This article describes our vision for an integrated ecosystem that combines existing HPC and evolving quantum software stacks into a single system to enable a common and continuous user experience. This integration comes with several major challenges as quantum systems pose significantly different requirements including increased need for compilation at run time, long optimization times, statistical evaluations of results, and the need to work with few centralized resources. To overcome these challenges, new scheduling approaches on the HPC side and new programming approaches on the QC side are required.

* * 26 Jul 2022

We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction of replicas, which requires an effort exponential in the number of replicas and which is costly in terms of memory. In contrast, our method requires the stochastic sampling of matrix elements of the classically represented reduced states with respect to random states drawn from simple product probability measures constituting frames. Even though not corresponding to physical operations, such matrix elements are straightforward to calculate for tensor network states, and their moments provide the Rényi entropies and negativities as well as their symmetry-resolved components. We test our method on the one-dimensional critical XX chain and the two-dimensional toric code in a checkerboard geometry. Although the cost is exponential in the subsystem size, it is sufficiently moderate so that - in contrast with other approaches - accurate results can be obtained on a personal computer for relatively large subsystem sizes.

* * 16 Jun 2022

Randomized benchmarking (RB) refers to a collection of protocols that in the past decade have become central methods for characterizing quantum gates. These protocols aim at efficiently estimating the quality of a set of quantum gates in a way that is resistant to state preparation and measurement errors. Over the years many versions have been developed, however, a comprehensive theoretical treatment of RB has been missing. In this work, we develop a rigorous framework of RB general enough to encompass virtually all known protocols as well as novel, more flexible extensions. Overcoming previous limitations on error models and gate sets, this framework allows us, for the first time, to formulate realistic conditions under which we can rigorously guarantee that the output of any RB experiment is well-described by a linear combination of matrix exponential decays. We complement this with a detailed analysis of the fitting problem associated with RB data. We introduce modern signal processing techniques to RB, prove analytical sample complexity bounds, and numerically evaluate performance and limitations. In order to reduce the resource demands of this fitting problem, we introduce novel, scalable post-processing techniques to isolate exponential decays, significantly improving the practical feasibility of a large set of RB protocols. These post-processing techniques overcome shortcomings in efficiency of several previously proposed methods such as character benchmarking and linear-cross entropy benchmarking. Finally, we discuss, in full generality, how and when RB decay rates can be used to infer quality measures like the average fidelity. On the technical side, our work substantially extends the recently developed Fourier-theoretic perspective on RB by making use of the perturbation theory of invariant subspaces, as well as ideas from signal processing.

* * 2022

Quantum Processing and Languages (QPL22), 27. Jun. - 01. Jul. 2022, Oxford, UK

In the near term, programming quantum computers will remain severely limited by low quantum volumes. Therefore, it is desirable to implement quantum circuits with the fewest resources possible. For the common Clifford+T circuits, most research is focused on reducing the number of T gates, since they are an order of magnitude more expensive than Clifford gates in quantum error corrected encoding schemes. However, this optimization sometimes leads to more 2-qubit gates, which, even though they are less expensive in terms of fault-tolerance, contribute significantly to the overall circuit cost. Approaches based on the ZX-calculus have recently gained some popularity in the field, but reduction of 2-qubit gates is not their focus. In this work, we present an alternative for improving 2-qubit gate count of a quantum circuit with the ZX-calculus by using heuristics in ZX-diagram simplification. Our approach maintains the good reduction of the T gate count provided by other strategies based on ZX-calculus, thus serving as an extension for other optimization algorithms. Our results show that combining the available ZX-calculus-based optimizations with our algorithms can reduce the number of 2-qubit gates by as much as 40 % compared to current approaches using ZX-calculus. Additionally, we improve the results of the best currently available optimization technique of Nam et. al [22] for some circuits by up to 15 %

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In a world shifting towards sustainable growth, high-performance computing has an important challenge: delivering on a growing demand for increased computational power, while keeping energy consumption at bay. Quantum computers promise to meet these challenges with an exponential performance improvement for key applications and are anticipated to be the next big technological breakthrough in the field. This paper discusses part of the road ahead to integrate quantum acceleration into supercomputers, as well as the critical steps and decisions required in order to build the quantum future of high-performance computing and make important strides towards green computing.