arXiv subjects

Wim van Dam

Publications and source records attributed to Wim van Dam.

At least 19 recordsLinked to original sources

arXiv2025

Roadmap to fault tolerant quantum computation using topological qubit arrays

We describe a concrete device roadmap towards a fault-tolerant quantum computing architecture based on noise-resilient, topologically protected Majorana-based qubits. Our roadmap encompasses four generations of devices: a single-qubit device that enables a measurement-based qubit benchmarking protocol; a two-qubit device that uses measurement-based braiding to perform single-qubit Clifford operations; an eight-qubit device that can be used to show an improvement of a two-qubit operation when performed on logical qubits rather than directly on physical qubits; and a topological qubit array supporting lattice surgery demonstrations on two logical qubits. Devices that enable this path require a superconductor-semiconductor heterostructure that supports a topological phase, quantum dots and coupling between those quantum dots that can create the appropriate loops for interferometric measurements, and a microwave readout system that can perform fast, low-error single-shot measurements. We describe the key design components of these qubit devices, along with the associated protocols for demonstrations of single-qubit benchmarking, Clifford gate execution, quantum error detection, and quantum error correction, which differ greatly from those in more conventional qubits. Finally, we comment on implications and advantages of this architecture for utility-scale quantum computation.

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arXiv2025

Fault-tolerant quantum computation with a neutral atom processor

Quantum computing experiments are transitioning from running on physical qubits to using encoded, logical qubits. Fault-tolerant computation can identify and correct errors, and has the potential to enable the dramatically reduced logical error rates required for valuable algorithms. However, it requires flexible control of high-fidelity operations performed on large numbers of qubits. We demonstrate fault-tolerant quantum computation on a quantum processor with 256 qubits, each an individual neutral Ytterbium atom. The operations are designed so that key error sources convert to atom loss, which can be detected by imaging. Full connectivity is enabled by atom movement. We demonstrate the entanglement of 24 logical qubits encoded into 48 atoms, at once catching errors and correcting for, on average 1.8, lost atoms. We also implement the Bernstein-Vazirani algorithm with up to 28 logical qubits encoded into 112 atoms, showing better-than-physical error rates. In both cases, "erasure conversion," changing errors into a form that can be detected independently from qubit state, improves circuit performance. These results begin to clear a path for achieving scientific quantum advantage with a programmable neutral atom quantum processor.

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arXiv2024

Demonstration of quantum computation and error correction with a tesseract code

A critical milestone for quantum computers is to demonstrate fault-tolerant computation that outperforms computation on physical qubits. The tesseract subsystem color code protects four logical qubits in 16 physical qubits, to distance four. Using the tesseract code on Quantinuum's trapped-ion quantum computers, we prepare high-fidelity encoded graph states on up to 12 logical qubits, beneficially combining for the first time fault-tolerant error correction and computation. We also protect encoded states through up to five rounds of error correction. Using performant quantum software and hardware together allows moderate-depth logical quantum circuits to have an order of magnitude less error than the equivalent unencoded circuits.

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arXiv2024

End-to-End Quantum Simulation of a Chemical System

We demonstrate the first end-to-end integration of high-performance computing (HPC), reliable quantum computing, and AI in a case study on catalytic reactions producing chiral molecules. We present a hybrid computation workflow to determine the strongly correlated reaction configurations and estimate, for one such configuration, its active site's ground state energy. We combine 1) the use of HPC tools like AutoRXN and AutoCAS to systematically identify the strongly correlated chemistry within a large chemical space with 2) the use of logical qubits in the quantum computing stage to prepare the quantum ground state of the strongly correlated active site, demonstrating the advantage of logical qubits compared to physical qubits, and 3) the use of optimized quantum measurements of the logical qubits with so-called classical shadows to accurately predict various properties of the ground state including energies. The combination of HPC, reliable quantum computing, and AI in this demonstration serves as a proof of principle of how future hybrid chemistry applications will require integration of large-scale quantum computers with classical computing to be able to provide a measurable quantum advantage.

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arXiv2024

Using Azure Quantum Resource Estimator for Assessing Performance of Fault Tolerant Quantum Computation

The resource estimation tools provided by Azure Quantum and Azure Quantum Development Kit are described. Using these tools one can automatically evaluate the logical and physical resources required to run algorithms on fault-tolerant quantum computers. An example is given of obtaining resource estimates for quantum fault-tolerant implementations of three different multiplication algorithms.

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arXiv2022

Expectation Values from the Single-Layer Quantum Approximate Optimization Algorithm on Ising Problems

We report on the energy-expectation-value landscapes produced by the single-layer ($p=1$) Quantum Approximate Optimization Algorithm (QAOA) when being used to solve Ising problems. The landscapes are obtained using an analytical formula that we derive. The formula allows us to predict the landscape for any given Ising problem instance and consequently predict the optimal QAOA parameters for heuristically solving that instance using the single-layer QAOA. We have validated our analytical formula by showing that it accurately reproduces the landscapes published in recent experimental reports. We then applied our methods to address the question: how well is the single-layer QAOA able to solve large benchmark problem instances? We used our analytical formula to calculate the optimal energy-expectation values for benchmark MAX-CUT problems containing up to $7\,000$ vertices and $41\,459$ edges. We also calculated the optimal energy expectations for general Ising problems with up to $100\,000$ vertices and $150\,000$ edges. Our results provide an estimate for how well the single-layer QAOA may work when run on a quantum computer with thousands of qubits. In addition to providing performance estimates when optimal angles are used, we are able to use our analytical results to investigate the difficulties one may encounter when running the QAOA in practice for different classes of Ising instances. We find that depending on the parameters of the Ising Hamiltonian, the expectation-value landscapes can be rather complex, with sharp features that necessitate highly accurate rotation gates in order for the QAOA to be run optimally on quantum hardware. We also present analytical results that explain some of the qualitative landscape features that are observed numerically.

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arXiv2022

Quantum Optimization Heuristics with an Application to Knapsack Problems

This paper introduces two techniques that make the standard Quantum Approximate Optimization Algorithm (QAOA) more suitable for constrained optimization problems. The first technique describes how to use the outcome of a prior greedy classical algorithm to define an initial quantum state and mixing operation to adjust the quantum optimization algorithm to explore the possible answers around this initial greedy solution. The second technique is used to nudge the quantum exploration to avoid the local minima around the greedy solutions. To analyze the benefits of these two techniques we run the quantum algorithm on known hard instances of the Knapsack Problem using unit depth quantum circuits. The results show that the adjusted quantum optimization heuristics typically perform better than various classical heuristics.

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arXiv2021

Instance Independence of Single Layer Quantum Approximate Optimization Algorithm on Mixed-Spin Models at Infinite Size

This paper studies the application of the Quantum Approximate Optimization Algorithm (QAOA) to spin-glass models with random multi-body couplings in the limit of a large number of spins. We show that for such mixed-spin models the performance of depth $1$ QAOA is independent of the specific instance in the limit of infinite sized systems and we give an explicit formula for the expected performance. We also give explicit expressions for the higher moments of the expected energy, thereby proving that the expected performance of QAOA concentrates.

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arXiv2020

Prospects and challenges of quantum finance

Quantum computers are expected to have substantial impact on the finance industry, as they will be able to solve certain problems considerably faster than the best known classical algorithms. In this article we describe such potential applications of quantum computing to finance, starting with the state-of-the-art and focusing in particular on recent works by the QC Ware team. We consider quantum speedups for Monte Carlo methods, portfolio optimization, and machine learning. For each application we describe the extent of quantum speedup possible and estimate the quantum resources required to achieve a practical speedup. The near-term relevance of these quantum finance algorithms varies widely across applications - some of them are heuristic algorithms designed to be amenable to near-term prototype quantum computers, while others are proven speedups which require larger-scale quantum computers to implement. We also describe powerful ways to bring these speedups closer to experimental feasibility - in particular describing lower depth algorithms for Monte Carlo methods and quantum machine learning, as well as quantum annealing heuristics for portfolio optimization. This article is targeted at financial professionals and no particular background in quantum computation is assumed.

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arXiv2018

Evolution-Time Dependence in Near-Adiabatic Quantum Evolutions

We expand upon the standard quantum adiabatic theorem, examining the time-dependence of quantum evolution in the near-adiabatic limit. We examine a Hamiltonian that evolves along some fixed trajectory from $\hat{H}_0$ to $\hat{H}_1$ in a total evolution-time $τ$, and our goal is to determine how the final state of the system depends on $τ$. If the system is initialized in a non-degenerate ground state, the adiabatic theorem says that in the limit of large $τ$, the system will stay in the ground state. We examine the near-adiabatic limit where the system evolves slowly enough that most but not all of the final state is in the ground state, and we find that the probability of leaving the ground state oscillates in $τ$ with a frequency determined by the integral of the spectral gap along the trajectory of the Hamiltonian, so long as the gap is big. If the gap becomes exceedingly small, the final probability is the sum of oscillatory behavior determined by the integrals of the gap before and after the small gap. We confirm these analytic predictions with numerical evidence from barrier tunneling problems in the context of quantum adiabatic optimization.

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arXiv2018

Two-Qubit Stabilizer Circuits with Recovery I: Existence

Understanding how a stabilizer circuit responds to different input is important to formulating an effective strategy for resource management. In this paper, we further investigate the many ways of using stabilizer operations to generate a single qubit output from a two-qubit state. In particular, by restricting the input to certain product states, we discover probabilistic operations capable of transforming stabilizer circuit outputs back into stabilizer circuit inputs. These secondary operations are ideally suited for recovery purposes and require only one extra resource ancilla to succeed. As a result of reusing qubits in this manner, we present an alternative to the original state preparation process that can lower the overall costs of executing any two-qubit stabilizer procedure involving non-stabilizer resources.

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arXiv2017

Necessary Adiabatic Run Times in Quantum Optimization

Quantum annealing is guaranteed to find the ground state of optimization problems in the adiabatic limit. Recent work [Phys. Rev. X 6, 031010 (2016)] has found that for some barrier tunneling problems, quantum annealing can be run much faster than is adiabatically required. Specifically, an $n$-qubit optimization problem was presented for which a non-adiabatic, or diabatic, annealing algorithm requires only constant runtime, while an adiabatic annealing algorithm requires a runtime polynomial in $n$. Here we show that this non-adiabatic speed-up is a direct result of a specific symmetry in the studied problems. In the more general case, no such non-adiabatic speed-up occurs. We furthermore show why the special case achieves this speed-up compared to the general case. We conclude with the observation that the adiabatic annealing algorithm has a necessary and sufficient runtime that is quadratically better than the standard quantum adiabatic condition suggests.

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arXiv2016

Discrepancies between Asymptotic and Exact Spectral Gap Analyses of Quantum Adiabatic Barrier Tunneling

We study the asymptotic behavior of the spectral gap of simple barrier tunneling problems, which are related to using quantum annealing to find the global optimum of cost functions defined over n bits. Specifically we look at the problem of having an n qubit system tunnel through a barrier of width and height proportional to n^a. We show that with these quantum annealing problems, the asymptotic, $n\to\infty$, behavior of the spectral gap does not accurately describe the behavior of the gap at finite n until extremely large values of n (n>10^{12}). We prove that this deficiency of the asymptotic expression is a feature of simple one-dimensional tunneling problems themselves, casting doubt on whether asymptotic analysis is an appropriate tool for studying tunneling problems in quantum annealing for reasonably sized systems.

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arXiv2016

Spectral Gap Analysis for Efficient Tunneling in Quantum Adiabatic Optimization

We investigate the efficiency of Quantum Adiabatic Optimization when overcoming potential barriers to get from a local to a global minimum. Specifically we look at n qubit systems with symmetric cost functions f:{0, 1}^n->R where the ground state must tunnel through a potential barrier of width n^a and height n^b. By the quantum adiabatic theorem the time delay sufficient to ensure tunneling grows quadratically with the inverse spectral gap during this tunneling process. We analyze barrier sizes with 1/2 < a + b and a < 1/2 and show that the minimum gap scales polynomially as n^{1/2-a-b} when 2a+b < 1 and exponentially as n^{-b/2} exp(-C n^{(2a+b-1)/2} ) when 1 < 2a+b. Our proof uses elementary techniques and confirms and extends an unpublished folklore result by Goldstone, which used large spin and instanton methods. Parts of our result also refine recent results by Kong and Crosson and Jiang et al. about the exponential gap scaling.

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arXiv2016

Optimal quantum algorithm for polynomial interpolation

We consider the number of quantum queries required to determine the coefficients of a degree-d polynomial over GF(q). A lower bound shown independently by Kane and Kutin and by Meyer and Pommersheim shows that d/2+1/2 quantum queries are needed to solve this problem with bounded error, whereas an algorithm of Boneh and Zhandry shows that d quantum queries are sufficient. We show that the lower bound is achievable: d/2+1/2 quantum queries suffice to determine the polynomial with bounded error. Furthermore, we show that d/2+1 queries suffice to achieve probability approaching 1 for large q. These upper bounds improve results of Boneh and Zhandry on the insecurity of cryptographic protocols against quantum attacks. We also show that our algorithm's success probability as a function of the number of queries is precisely optimal. Furthermore, the algorithm can be implemented with gate complexity poly(log q) with negligible decrease in the success probability. We end with a conjecture about the quantum query complexity of multivariate polynomial interpolation.

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arXiv2015

Quantum Monte Carlo Simulations of Tunneling in Quantum Adiabatic Optimization

We explore to what extent path-integral quantum Monte Carlo methods can efficiently simulate the tunneling behavior of quantum adiabatic optimization algorithms. Specifically we look at symmetric cost functions defined over n bits with a single potential barrier that a successful optimization algorithm will have to tunnel through. The height and width of this barrier depend on n, and by tuning these dependencies, we can make the optimization algorithm succeed or fail in polynomial time. In this article we compare the strength of quantum adiabatic tunneling with that of path-integral quantum Monte Carlo methods. We find numerical evidence that quantum Monte Carlo algorithms will succeed in the same regimes where quantum adiabatic optimization succeeds.

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arXiv2013

Decoherent histories of quantum searching

The theory of decoherent histories is an attempt to derive classical physics from positing only quantum laws at the fundamental level without notions of a classical apparatus or collapse of the wave-function. Searching for a marked target in a list of N items requires Ω(N) oracle queries when using a classical computer, while a quantum computer can accomplish the same task in O{\sqrt{N}} queries using Grover's quantum algorithm. We study a closed quantum system executing Grover algorithm in the framework of decoherent histories and find it to be an exactly solvable model, thus yielding an alternate derivation of Grover's famous result. We also subject the Grover-executing computer to a generic external influence without needing to know the specifics of the Hamiltonian insofar as the histories decohere. Depending on the amount of decoherence, which is captured in our model by a single parameter related to the amount of information obtained by the environment, the search time can range from quantum to classical. Thus, we identify a key effect induced by the environment that can adversely affect a quantum computer's performance and demonstrate exactly how classical computing can emerge from quantum laws.

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arXiv2012

Minimum Energy-Surface Required by Quantum Memory Devices

We address the question what physical resources are required and sufficient to store classical information. While there is no lower bound on the required energy or space to store information, we find that there is a nonzero lower bound for the product (P = ) of these two resources. Specifically, we prove that any physical system of mass m and d degrees of freedom that stores S bits of information will have lower bound on the product P that is proportional to d^2/m (exp(S/d)-1)^2. This result is obtained in a non-relativistic, quantum mechanical setting and it is independent from earlier thermodynamical results such as the Bekenstein bound on the entropy of black holes.

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