Early Fault-Tolerant Quantum Computing

Abstract

Over the past decade, research in quantum computing has tended to fall into one of two camps: near-term intermediate scale quantum (NISQ) and fault-tolerant quantum computing (FTQC). Yet, a growing body of work has been investigating how to use quantum computers in transition between these two eras. This envisions operating with tens of thousands to millions of physical qubits, able to support fault-tolerant protocols, though operating close to the fault-tolerant threshold. Two challenges emerge from this picture: how to model the performance of devices that are continually improving and how to design algorithms to make the most use of these devices? In this work we develop a model for the performance of early fault-tolerant quantum computing (EFTQC) architectures and use this model to elucidate the regimes in which algorithms suited to such architectures are advantageous. As a concrete example, we show that, for the canonical task of phase estimation, in a regime of moderate scalability and using just over one million physical qubits, the ``reach'' of the quantum computer can be extended (compared to the standard approach) from 90-qubit instances to over 130-qubit instances using a simple early fault-tolerant quantum algorithm, which reduces the number of operations per circuit by a factor of 100 and increases the number of circuit repetitions by a factor of 10,000. This clarifies the role that such algorithms might play in the era of limited-scalability quantum computing.

arXiv comment20 pages, 8 figures with desmos links, plus appendix

References in corpus (73)

• Quantum Computing in the NISQ era and beyond
• Fault-tolerant quantum computation by anyons
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• A variational eigenvalue solver on a quantum processor
• Quantum Mechanics helps in searching for a needle in a haystack
• Surface codes: Towards practical large-scale quantum computation
• Topological quantum memory
• Quantum Amplitude Amplification and Estimation
• Error mitigation for short-depth quantum circuits
• Quantum Algorithms Revisited
• Suppressing quantum errors by scaling a surface code logical qubit
• Logical quantum processor based on reconfigurable atom arrays
• Quantum Error Correction and Orthogonal Geometry
• Demonstration of a small programmable quantum computer with atomic qubits
• Qubit architecture with high coherence and fast tunable coupling
• Computing with spin qubits at the surface code error threshold
• Quantum generative adversarial networks
• Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography
• A fault-tolerant one-way quantum computer
• A random compiler for fast Hamiltonian simulation
• Quantum computing with nearest neighbor interactions and error rates over 1%
• The Future of Quantum Computing with Superconducting Qubits
• Quantum Low-Density Parity-Check Codes
• Active stabilisation, quantum computation and quantum state synthesis
• Demonstration of fault-tolerant universal quantum gate operations
• Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors
• Differentiable Learning of Quantum Circuit Born Machine
• Fault-tolerant quantum computation with long-range correlated noise
• Accelerated Variational Quantum Eigensolver
• Magic State Distillation: Not as Costly as You Think
• Optimal Quantum Measurements of Expectation Values of Observables
• Fault-tolerant quantum computation against biased noise
• Heisenberg-limited ground state energy estimation for early fault-tolerant quantum computers
• Digital zero noise extrapolation for quantum error mitigation
• Tunable Superconducting Qubits with Flux-Independent Coherence
• Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments
• Realisation of a programmable two-qubit quantum processor
• Efficient tensor network simulation of IBM's Eagle kicked Ising experiment
• Ground state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices
• Reliably assessing the electronic structure of cytochrome P450 on today's classical computers and tomorrow's quantum computers
• Quantum error mitigation as a universal error-minimization technique: applications from NISQ to FTQC eras
• Measurements as a roadblock to near-term practical quantum advantage in chemistry: resource analysis
• Neutral Atom Quantum Computing Hardware: Performance and End-User Perspective
• Fault-Tolerance of "Bad" Quantum Low-Density Parity Check Codes
• Low-overhead fault-tolerant quantum computing using long-range connectivity
• Circuit knitting with classical communication
• Fault-tolerant resource estimate for quantum chemical simulations: Case study on Li-ion battery electrolyte molecules
• A randomized quantum algorithm for statistical phase estimation
• Real time evolution for ultracompact Hamiltonian eigenstates on quantum hardware
• Even shorter quantum circuit for phase estimation on early fault-tolerant quantum computers with applications to ground-state energy estimation
• Quantum logic and entanglement by neutral Rydberg atoms: methods and fidelity
• Minimizing estimation runtime on noisy quantum computers
• Exact and efficient Lanczos method on a quantum computer
• Low depth algorithms for quantum amplitude estimation
• Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision
• Simple proof of fault tolerance in the graph-state model
• Proof of finite surface code threshold for matching
• Limitations in quantum computing from resource constraints
• Efficient quantum computation of molecular forces and other energy gradients
• Computing Ground State Properties with Early Fault-Tolerant Quantum Computers
• Effective quantum volume, fidelity and computational cost of noisy quantum processing experiments
• Entangling an arbitrary pair of qubits in a long ion crystal
• Optimal control of superconducting gmon qubits using Pontryagin's minimum principle: preparing a maximally entangled state with singular bang-bang protocols
• Heisenberg-limited quantum phase estimation of multiple eigenvalues with few control qubits
• Sampling Frequency Thresholds for Quantum Advantage of Quantum Approximate Optimization Algorithm
• State Preparation Boosters for Early Fault-Tolerant Quantum Computation
• A stochastic quantum Krylov protocol with double factorized Hamiltonians
• Overhead-constrained circuit knitting for variational quantum dynamics
• Quantifying $T$-gate-count improvements for ground-state-energy estimation with near-optimal state preparation
• Robust measurement of wave function topology on NISQ quantum computers
• Foundations for Bayesian inference with engineered likelihood functions for robust amplitude estimation
• Pulse optimization for high-precision motional-mode characterization in trapped-ion quantum computers

Cited by in corpus (41)

• Rapid initial state preparation for the quantum simulation of strongly correlated molecules
• Quantum Multiple Eigenvalue Gaussian filtered Search: an efficient and versatile quantum phase estimation method
• Simulating Non-Markovian Quantum Dynamics on NISQ Computers Using the Hierarchical Equations of Motion
• Fault-tolerant quantum algorithms for quantum molecular systems: A survey
• Multiscale Embedding for Quantum Computing
• Quantum computing through the lens of control: A tutorial introduction
• Option pricing under stochastic volatility on a quantum computer
• Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation
• Near-Term Spin-Qubit Architecture Design via Multipartite Maximally-Entangled States
• Distributed quantum machine learning via classical communication
• Efficient Strategies for Reducing Sampling Error in Quantum Krylov Subspace Diagonalization
• Quantum Computing for Discrete Optimization: A Highlight of Three Technologies
• Halving the Cost of Quantum Algorithms with Randomization
• Symmetric Clifford twirling for cost-optimal quantum error mitigation in early FTQC regime
• Parameter Setting Heuristics Make the Quantum Approximate Optimization Algorithm Suitable for the Early Fault-Tolerant Era
• Unlocking early fault-tolerant quantum computing with mitigated magic dilution
• Efficient fault-tolerant code switching via one-way transversal CNOT gates
• Statistics of topological defects across a phase transition in a digital superconducting quantum processor
• Comparison of encoding schemes for quantum computing of $S>1/2$ spin chains
• Error mitigation and circuit division for early fault-tolerant quantum phase estimation
• Extending Quantum Computing through Subspace, Embedding and Classical Molecular Dynamics Techniques
• Bridging Quantum Computing and Nuclear Structure: Atomic Nuclei on a Trapped-Ion Quantum Computer
• Stabilizer configuration interaction: Finding molecular subspaces with error detection properties
• Simulating quantum collision models with Hamiltonian simulations using early fault-tolerant quantum computers
• High-precision and low-depth quantum algorithm design for eigenstate problems
• Estimates of loss function concentration in noisy parametrized quantum circuits
• Averaging gate approximation error and performance of Unitary Coupled Cluster ansatz in Pre-FTQC Era
• Mitigating photon loss in linear optical quantum circuits
• Rovibrational energy levels of H${}_2$O by quantum computing
• Architectural Approaches to Fault-Tolerant Distributed Quantum Computing and Their Entanglement Overheads
• Double-bracket quantum algorithms for high-fidelity ground state preparation
• Weakly Fault-Tolerant Computation in a Quantum Error-Detecting Code
• Exact and Efficient Stabilizer Simulation of Thermal-Relaxation Noise for Quantum Error Correction
• Pinball: A Cryogenic Predecoder for Surface Code Decoding Under Circuit-Level Noise
• Deterministic Ground State Preparation via Power-Cosine Filtering of Time Evolution Operators
• iSwitch: QEC on Demand via In-Situ Encoding of Bare Qubits for Ion Trap Architectures
• All-to-all connectivity of Rydberg-atom-based quantum processors with messenger qubits
• Introducing UNIQuE: The Unconventional Noiseless Intermediate Quantum Emulator
• Unbiased observable estimation with approximate channels in fault-tolerant quantum computation
• Quantum Imaginary-Time Evolution with Polynomial Resources in Evolution Time
• Information Processing in Quantum Thermodynamic Systems: an Autonomous Hamiltonian Approach