Quantum annealing correction at finite temperature: ferromagnetic $p$-spin models

Abstract

The performance of open-system quantum annealing is adversely affected by thermal excitations out of the ground state. While the presence of energy gaps between the ground and excited states suppresses such excitations, error correction techniques are required to ensure full scalability of quantum annealing. Quantum annealing correction (QAC) is a method that aims to improve the performance of quantum annealers when control over only the problem (final) Hamiltonian is possible, along with decoding. Building on our earlier work [S. Matsuura et al., Phys. Rev. Lett. 116, 220501 (2016)], we study QAC using analytical tools of statistical physics by considering the effects of temperature and a transverse field on the penalty qubits in the ferromagnetic $p$-body infinite-range transverse-field Ising model. We analyze the effect of QAC on second ($p=2$) and first ($p\ge 3$) order phase transitions, and construct the phase diagram as a function of temperature and penalty strength. Our analysis reveals that for sufficiently low temperatures and in the absence of a transverse field on the penalty qubit, QAC breaks up a single, large free energy barrier into multiple smaller ones. We find theoretical evidence for an optimal penalty strength in the case of a transverse field on the penalty qubit, a feature observed in QAC experiments. Our results provide further compelling evidence that QAC provides an advantage over unencoded quantum annealing.

arXiv comment19 pages, 12 figures

References in corpus (55)

• Quantum Annealing in the Transverse Ising Model
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Quantum annealing with more than one hundred qubits
• Theory of Quantum Annealing of an Ising Spin Glass
• Quantum Annealing and Analog Quantum Computation
• Quantum Annealing: A New Method for Minimizing Multidimensional Functions
• Robustness of adiabatic quantum computation
• Bounds for the adiabatic approximation with applications to quantum computation
• Architectural considerations in the design of a superconducting quantum annealing processor
• Quantum Adiabatic Markovian Master Equations
• Experimental Investigation of an Eight Qubit Unit Cell in a Superconducting Optimization Processor
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Adiabatic Quantum Computation in Open Systems
• Error corrected quantum annealing with hundreds of qubits
• Decoherence in adiabatic quantum computation
• Error correcting codes for adiabatic quantum computation
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• Towards Fault Tolerant Adiabatic Quantum Computation
• Tunable Quantum Tunneling of Magnetic Domain Walls
• Quantum annealing with antiferromagnetic fluctuations
• Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve
• Thermally assisted adiabatic quantum computation
• Understanding Quantum Tunneling through Quantum Monte Carlo Simulations
• Quantum annealing correction for random Ising problems
• Quantum accuracy threshold for concatenated distance-3 codes
• Reexamining classical and quantum models for the D-Wave One processor
• Quantum Annealing Correction with Minor Embedding
• Adiabaticity in open quantum systems
• How "Quantum" is the D-Wave Machine?
• Decoherence in adiabatic quantum computation
• Finite-temperature mutual information in a simple phase transition
• Many-body transverse interactions in the quantum annealing of the p-spin ferromagnet
• On quantum mean-field models and their quantum annealing
• Adiabatic theorems for generators of contracting evolutions
• General Adiabatic Evolution with a Gap Condition
• Error suppression and error correction in adiabatic quantum computation I: techniques and challenges
• Unraveling Quantum Annealers using Classical Hardness
• Unification and limitations of error suppression techniques for adiabatic quantum computing
• Adiabatic quantum optimization with the wrong Hamiltonian
• Quantum phase transitions in fully connected spin models: an entanglement perspective
• Nested Quantum Annealing Correction
• Error suppression and error correction in adiabatic quantum computation II: non-equilibrium dynamics
• Adiabatic Markovian Dynamics
• Performance of two different quantum annealing correction codes
• Mean Field Analysis of Quantum Annealing Correction
• Error suppression for Hamiltonian-based quantum computation using subsystem codes
• High Fidelity Adiabatic Quantum Computation via Dynamical Decoupling
• Quantum and Classical in Adiabatic Computation
• Hearing the Shape of the Ising Model with a Programmable Superconducting-Flux Annealer
• Energy gap at first-order quantum phase transitions: An anomalous case
• Quantum error suppression with commuting Hamiltonians: Two-local is too local
• A family of [[6k, 2k, 2]] codes for practical, scalable adiabatic quantum computation
• Exponential suppression of decoherence and relaxation of quantum systems using energy penalty
• Critical properties of dissipative quantum spin systems in finite dimensions

Cited by in corpus (31)

• Prospects for Quantum Enhancement with Diabatic Quantum Annealing
• Temperature scaling law for quantum annealing optimizers
• Counterdiabatic driving in the quantum annealing of the $p$-spin model: a variational approach
• Quantum annealing of the $p$-spin model under inhomogeneous transverse field driving
• Genetic optimization of quantum annealing
• Phase space geometry and optimal state preparation in quantum metrology with collective spins
• Dissipative phase transitions in the fully-connected Ising model with $p$-spin interaction
• Nonlinear dynamics and quantum chaos of a family of kicked $p$-spin models
• Scaling Advantage in Approximate Optimization with Quantum Annealing
• Floquet time crystals in driven spin systems with all-to-all $p$-body interactions
• Scalable effective temperature reduction for quantum annealers via nested quantum annealing correction
• Trotter errors from dynamical structural instabilities of Floquet maps in quantum simulation
• Simulation of complex dynamics of mean-field $p$-spin models using measurement-based quantum feedback control
• Nested Quantum Annealing Correction at Finite Temperature: $p$-spin models
• Adiabatic theorem for closed quantum systems initialized at finite temperature
• Error suppression in adiabatic quantum computing with qubit ensembles
• Dynamics of Order Parameters of Non-stoquastic Hamiltonians in the Adaptive Quantum Monte Carlo Method
• Balancing coherent and dissipative dynamics in a central-spin system
• Perils of Embedding for Quantum Sampling
• 4-clique Network Minor Embedding for Quantum Annealers
• Quantum annealing speedup of embedded problems via suppression of Griffiths singularities
• Quantum annealing with a nonvanishing final value of the transverse field
• Bifurcation-based quantum annealing with nested spins
• Demonstration of error-suppressed quantum annealing via boundary cancellation
• Using copies to improve precision in continuous-time quantum computing
• Non-linearity and chaos in the kicked top
• Analog Errors in Quantum Annealing: Doom and Hope
• Benchmarking Embedded Chain Breaking in Quantum Annealing
• Effects of dynamical paths on the energy gap and the corrections to free energy in path integrals of mean-field quantum spin systems
• Structural Comparison of Error Mitigation Methods for Ising Machines: Penalty-Spin Model versus Stacked Model
• Frustration-enhanced quantum annealing correction models with additional inter-replica interactions