An important challenge in superconducting quantum computing is the need to physically couple many devices using quasi-two-dimensional fabrication processes. Recent advances in the design and fabrication of quantum annealing processors have enabled an increase in pairwise connectivity among thousands of qubits. One benefit of this is the ability to minor-embed optimization problems using fewer physical qubits for each logical spin. Here we demonstrate the benefit of this progress in the problem of minimizing the energy of three-dimensional spin glasses. Comparing the previous generation D-Wave 2000Q system to the new Advantage system, we observe improved scaling of solution time and improved consistency over multiple graph embeddings.

# Scientific Publications

D-Wave is the world’s first commercial supplier of quantum computers. Learn more about the science behind our cutting-edge quantum technology and the use cases it can be applied to. Visit our resource library to read our technical white papers.

**2024**

Publication

#### Quantum fluctuations drive nonmonotonic correlations in a qubit lattice

**2023**

Publication

#### Kagome qubit ice

Publication

#### Quantum error mitigation in quantum annealing

Publication

#### Tutorial: calibration refinement in quantum annealing

Publication

#### Milestones on the Quantum Utility Highway

Publication

#### Quantum Critical Dynamics in a 5,000-Qubit Programmable Spin Glass

Publication

#### Probing Flux and Charge Noise with Macroscopic Resonant Tunneling

**2022**

Publication

#### Multilevel Resonant Tunneling in the Presence of Flux and Charge Noise

Publication

#### Coherent Quantum Annealing in a Programmable 2,000 Qubit Ising Chain

Publication

#### Annealing-based Quantum Computing for Combinatorial Optimal Power Flow

Publication

#### Hybrid Quantum Annealing for Larger-than-QPU Lattice-Structured Problems

**2021**

Publication

#### Essentially Exact Numerical Modelling of Flux Qubit Chains Subject to Charge and Flux Noise

Publication

#### Architectural Considerations in the Design of a Third-Generation Superconducting Quantum Annealing Processor

Publication

#### Qubit Spin Ice

Publication

#### Improving Nonstoquastic Quantum Annealing with Spin-Reversal Transformations

Publication

#### Scaling Advantage Over Path-Integral Monte Carlo in Quantum Simulation of Geometrically Frustrated Magnets

Publication

#### Quantum Annealing Simulation of Out-of-Equilibrium Magnetization in a Spin-Chain Compound

**2020**

Publication

#### Simulating the Shastry-Sutherland Ising Model Using Quantum Annealing

Publication

#### Improving Performance of Logical Qubits by Parameter Tuning and Topology Compensation

Publication

#### Performance Benefits of Increased Qubit Connectivity in Quantum Annealing 3-Dimensional Spin Glasses

Publication

#### Theory Versus Practice in Annealing-Based Quantum Computing

Publication

#### Probing Environmental Spin Polarization with Superconducting Flux Qubits

Publication

#### Demonstration of a Nonstoquastic Hamiltonian in Coupled Superconducting Flux Qubits

**2019**

Publication

#### A Path Towards Quantum Advantage in Training Deep Generative Models with Quantum Annealers

Publication

#### PixelVAE++: Improved PixelVAE with Discrete Prior

Publication

#### Quantum-Assisted Genetic Algorithm

Publication

#### The Mathematics of Quantum-Enabled Applications on the D-Wave Quantum Computer

Publication

#### Demonstration of Nonstoquastic Hamiltonian in Coupled Superconducting Flux Qubits

**2018**

Publication

#### Solving SAT and MaxSAT with a Quantum Annealer: Foundations, Encodings, and Preliminary Results

Publication

#### Computing Wasserstein Distance for Persistence Diagrams on a Quantum Computer

Publication

#### Theory of Open Quantum Dynamics with Hybrid Noise

Publication

#### Observation of Topological Phenomena in a Programmable Lattice of 1,800 Qubits

Publication

#### Phase Transitions in a Programmable Quantum Spin Glass Simulator

Publication

#### GumBolt: Extending Gumbel Trick to Boltzmann Priors

Publication

#### DVAE#: Discrete Variational Autoencoders with Relaxed Boltzmann Priors

Publication

#### Toward Robustness Against Label Noise in Training Deep Discriminative Neural Networks

Publication

#### Quantum Variational Autoencoder

Publication

#### DVAE++: Discrete Variational Autoencoders with Overlapping Transformations

**2017**

Publication

#### From Near to Eternity: Spin-Glass Planting, Tiling Puzzles, and Constraint Satisfaction Problems

Publication

#### Experimental Demonstration of Perturbative Anticrossing Mitigation using Non-Uniform Driver Hamiltonians

Publication

#### Can Quantum Monte Carlo Simulate Quantum Annealing?

Publication

#### Quantum Eigenstate Tomography with Qubit Tunneling Spectroscopy

**2016**

Publication

#### Benchmarking Quantum Hardware for Training of Fully Visible Boltzmann Machines

Publication

#### Discrete Variational Autoencoders

Publication

#### Global Warming: Temperature Estimation in Annealers

Publication

#### Mapping Constrained Optimization Problems to Quantum Annealing with Application to Fault Diagnosis

Publication

#### Quantum Boltzmann Machine

Publication

#### A Frequency and Sensitivity Tunable Microresonator Array for High-Speed Quantum Processor Readout

**2015**

Publication

#### Degeneracy, Degree, and Heavy Tails in Quantum Annealing

Publication

#### Fast Clique Minor Generation in Chimera Qubit Connectivity Graphs

Publication

#### Constructing SAT Filters with a Quantum Annealer

Publication

#### Performance of a Quantum Annealer on Range-Limited Constraint Satisfaction Problems

Publication

#### Benchmarking a Quantum Annealing Processor with the Time-to-Target Metric

Publication

#### Searching for Quantum Speedup in Quasistatic Quantum Annealers

Publication

#### Computational Role of Collective Tunneling in a Quantum Annealer

**2014**

Publication

#### Discrete Optimization Using Quantum Annealing on Sparse Ising Models

Publication

#### A Practical Heuristic for Finding Graph Minors

Publication

#### Entanglement in a Quantum Annealing Processor

Publication

#### Architectural Considerations in the Design of a Superconducting Quantum Annealing Processor

**2013**

Publication

#### Evidence for Temperature Dependent Spin-Diffusion as a Mechanism of Intrinsic Flux Noise in SQUIDs

Publication

#### Tunneling Spectroscopy Using a Probe Qubit

Publication

#### Thermally Assisted Quantum Annealing of a 16-Qubit Problem

Publication

#### Adiabatic Quantum Optimization with Qudits

**2012**

Publication

#### Algorithmic Approach to Adiabatic Quantum Optimization

Publication

#### Approximate Diagonalization Method for Large-Scale Hamiltonian

**2011**

Publication

#### Probing High-Frequency Noise with Macroscopic Resonant Tunneling

Publication

#### Does Adiabatic Quantum Optimization Fail for NP-Complete Problems?

Publication

#### Importance of Explicit Vectorization for CPU and GPU Software Performance

Publication

#### The Ising Model: Teaching an Old Problem New Tricks

Publication

#### Investigating the Performance of an Adiabatic Quantum Optimization Processor

Publication

#### Quantum Annealing with Manufactured Spins

**2010**

Publication

#### A Scalable Control System for a Superconducting Adiabatic Quantum Optimization Processor

Publication

#### Experimental Demonstration of a Robust and Scalable Flux Qubit

Publication

#### High-Performance Physics Simulations Using Multi-Core CPUs and GPGPUs in a Volunteer Computing Context

Publication

#### Robust Parameter Selection for Parallel Tempering

Publication

#### Experimental Investigation of an Eight Qubit Unit Cell in a Superconducting Optimization Processor

Publication

#### Cotunneling in Pairs of Coupled Flux Qubits

Publication

#### A Scalable Readout System for a Superconducting Adiabatic Quantum Optimization System

**2009**

Publication

#### Geometrical Dependence of the Low-Frequency Noise in Superconducting Flux Qubits

Publication

#### Non-Markovian Incoherent Quantum Dynamics of a Two-State System

Publication

#### Decoherence in Adiabatic Quantum Computation

Publication

#### A Compound Josephson Junction Coupler for Flux Qubits With Minimal Crosstalk

Publication

#### Landau-Zener Transitions in an Adiabatic Quantum Computer

Publication

#### Consistency of the Adiabatic Theorem

Publication

#### Landau-Zener Transitions in the Presence of Spin Environment

Publication

#### First Order Quantum Phase Transition in Adiabatic Quantum Computation

Publication

#### The Role of Single Qubit Decoherence Time in Adiabatic Quantum Computation

**2008**

Publication

#### Minor-Embedding in Adiabatic Quantum Computation: I. The Parameter Setting Problem

Publication

#### Macroscopic Resonant Tunneling in the Presence of Low Frequency Noise

Publication

#### On the Construction of Model Hamiltonians for Adiabatic Quantum Computing and its Application to Finding Low Energy Conformations of Lattice Protein Models

Publication

#### Effect of Local Minima on Adiabatic Quantum Optimization

Publication

#### Thermally Assisted Adiabatic Quantum Computation

Publication

#### Probing Noise in Flux Qubits via Macroscopic Resonant Tunneling

Publication

#### Realizable Hamiltonians for Universal Adiabatic Quantum Computers

**2007**

Publication

#### Sign- and Magnitude-Tunable Coupler for Superconducting Flux Qubits

Publication

#### A Characterization of Global Entanglement

**2006**

Publication

#### Rabi Oscillations in Systems with Small Anharmonicity

Publication

#### Four-Qubit Device with Mixed Couplings

Publication

#### Adiabatic Quantum Computation with Flux Qubits, First Experimental Results

**2005**

Publication

#### Silent Phase Qubit Based on D-Wave Josephson Junctions

Publication

#### Flux Qubit in Charge-Phase regime

Publication

#### Mediated Tunable Coupling of Flux Qubits

Publication

#### Direct Josephson Coupling Between Superconducting Flux Qubits

Publication

#### Simulated Quantum Computation of Molecular Energies

Publication

#### Hamiltonian for Coupled Flux Qubits

Publication

#### Quantum Nondemolition Charge Measurement of a Josephson Qubit

**2004**

Publication

#### Evidence for Entangled States of Two Coupled Flux Qubits

Publication

#### Low-Frequency Measurement of the Tunneling Amplitude in a Flux Qubit

Publication

#### Quasiparticle Decoherence in D-Wave Superconducting Qubits

Publication

#### Observation of Macroscopic Landau-Zener Tunneling in a Superconducting Device

Publication

#### Wigner Distribution Function Formalism for Superconductors and Collisionless Dynamics of the Superconducting Order Parameter

Publication

#### Dephasing-Insensitive Quantum Information Storage and Processing with Superconducting Qubits

**2003**

Publication

#### Non-Equilibrium Quasiclassical Theory for Josephson Structures

Publication

#### Josephson-Phase Qubit without Tunneling

Publication

#### Dynamical Effects of an Unconventional Current-Phase Relation in YBCO dc SQUIDs

Publication

#### Anomalous Current-Phase Relation as Basis for HTS Qubit

Publication

#### Nonequilibrium Quasiclassical Theory for Josephson Structures

Publication

#### Quasiclassical Calculations of Spontaneous Current in Restricted Geometries

Publication

#### Continuous Monitoring of Rabi Oscillations in a Josephson Flux Qubit

Publication

#### Theory of Weak Continuous Measurements in a Strongly Driven Quantum Bit

Publication

#### Tunable Coupling of Superconducting Qubits

Publication

#### Dynamical Effects of an Unconventional Current-Phase Relation in YBCO dc-SQUIDs

**2002**

Publication

#### Low-Frequency Characterization of Quantum Tunneling in Flux Qubits

Publication

#### Multi-Terminal Superconducting Phase Qubit

Publication

#### High Temperature PI/2-SQUID

Publication

#### Time Reversal Breaking States and Spontaneous Current Pattern in Josephson Junctions of D-Wave Superconductors

Publication

#### Quasiclassical Theory of Spontaneous Currents at Surfaces and Interfaces of D-Wave Superconductors

Publication

#### d+is Versus d+id Time Reversal Symmetry Breaking States in Finite Size Systems

Publication

#### DC-SQUID Based on the Mesoscopic Multi-Terminal Josephson Junction

**2001**

Publication

#### Mesoscopic Multi-Terminal Josephson Structures. I. Effects of Nonlocal Weak Coupling

Publication

#### Degenerate Ground State in a Mesoscopic YBa2CuO Grain Boundary Josephson Junction

Publication