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.

20 pages, 8 figures with desmos links, plus appendix

References in corpus (25)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Surface codes: Towards practical large-scale quantum computation
• Suppressing quantum errors by scaling a surface code logical qubit
• Logical quantum processor based on reconfigurable atom arrays
• Quantum computing with nearest neighbor interactions and error rates over 1%
• The Future of Quantum Computing with Superconducting Qubits
• Fault-tolerant quantum computation against biased noise
• Optimal Quantum Measurements of Expectation Values of Observables
• 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
• Neutral Atom Quantum Computing Hardware: Performance and End-User Perspective
• Fault-Tolerance of "Bad" Quantum Low-Density Parity Check Codes
• Circuit knitting with classical communication
• 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
• Exact and efficient Lanczos method on a quantum computer
• 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
• Effective quantum volume, fidelity and computational cost of noisy quantum processing experiments
• Sampling Frequency Thresholds for Quantum Advantage of Quantum Approximate Optimization Algorithm
• 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
• Pulse optimization for high-precision motional-mode characterization in trapped-ion quantum computers

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• Near-Term Spin-Qubit Architecture Design via Multipartite Maximally-Entangled States
• Distributed quantum machine learning via classical communication
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• Quantum Computing for Discrete Optimization: A Highlight of Three Technologies
• Halving the Cost of Quantum Algorithms with Randomization
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• 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
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• 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