[Paper Review] Quantum Supremacy Is Both Closer and Farther than It Appears

Igor L. Markov, Aneeqa Fatima+2 more|arXiv (Cornell University)|Jul 27, 2018

Quantum Computing Algorithms and Architecture31 references50 citations

TL;DR

The paper introduces Rollright, a massively parallel Schrödinger–Feynman hybrid quantum circuit simulator, and demonstrates that approximate sampling of Google-style quantum-supremacy circuits can be achieved at lower costs and with less memory than prior supercomputer simulations, while also showing new circuits that are harder to simulate.

ABSTRACT

As quantum computers improve in the number of qubits and fidelity, the question of when they surpass state-of-the-art classical computation for a well-defined computational task is attracting much attention. The leading candidate task for this milestone entails sampling from the output distribution defined by a random quantum circuit. We develop a massively-parallel simulation tool Rollright that does not require inter-process communication (IPC) or proprietary hardware. We also develop two ways to trade circuit fidelity for computational speedups, so as to match the fidelity of a given quantum computer --- a task previously thought impossible. We report massive speedups for the sampling task over prior software from Microsoft, IBM, Alibaba and Google, as well as supercomputer and GPU-based simulations. By using publicly available Google Cloud Computing, we price such simulations and enable comparisons by total cost across hardware platforms. We simulate approximate sampling from the output of a circuit with 7x8 qubits and depth 1+40+1 by producing one million bitstring probabilities with fidelity 0.5%, at an estimated cost of $35184. The simulation costs scale linearly with fidelity, and using this scaling we estimate that extending circuit depth to 1+48+1 increases costs to one million dollars. Scaling the simulation to 10M bitstring probabilities needed for sampling 1M bitstrings helps comparing simulation to quantum computers. We describe refinements in benchmarks that slow down leading simulators, halving the circuit depth that can be simulated within the same time.

Motivation & Objective

• Assess the feasibility of classically simulating quantum-supremacy circuits at scale with limited memory.
• Develop a fidelity-controlled approximate simulation framework to match near-term quantum computer fidelities.
• Benchmark Rollright against prior simulators and quantify cost and resource tradeoffs.
• Propose protocols for validating quantum-supremacy simulations without exact answers.
• Explore circuit-design choices that affect classical simulability and introduce harder benchmarks.

Proposed method

• Develop Rollright, a massively-parallel Schrödinger–Feynman hybrid simulator that requires no inter-process communication (IPC).
• Partition qubit layouts into blocks and decompose cross-block gates into tensor terms to reduce memory usage.
• Use gate clustering, bitmask-encoded gate positions, and cache-efficient amplitude updates to optimize performance.
• Apply a cross-block decomposition for xCZ gates to manage runtime growth with circuit depth.
• Introduce two approximate-simulation approaches: fidelity-controlled amplitude generation and approximate sampling with tunable statistical error.
• Provide a protocol for interactive validation of quantum-supremacy simulations using approximate fidelity and inner-product estimation.

Experimental results

Research questions

• RQ1 Can approximate simulation of random quantum-circuit outputs be achieved with linear scaling in fidelity?
• RQ2 How does the fidelity control affect runtime and cost for simulating Google-style quantum-supremacy circuits?
• RQ3 What are the memory and computational tradeoffs when using Schrödinger–Feynman hybrids for near-term quantum circuits?
• RQ4 How do circuit design choices (gate libraries, depths, and topologies) influence classical simulability?
• RQ5 Can cloud-based, preemptible resources outperform traditional supercomputers for these simulations in terms of cost and accessibility?

Key findings

• Rollright achieves significant speedups over prior simulators (e.g., 31x vs Microsoft QDK and 16x vs IBM QISKit-Terra/QASM on comparable tasks).
• A single Google Cloud n1-highcpu-96 server can produce one million probabilities for certain circuits at relatively low cost (e.g., 4.7 hours, $3.34 for 6×7, depth 1+25).
• Simulations for 9×5 and 7×6/7×7 layouts show substantial memory savings (GiB) and favorable runtimes, with costs scalable by fidelity.
• Approximate simulation with fidelity f yields runtime that scales linearly with f, enabling speedups (e.g., fidelity 0.1 is 10× faster than exact simulation).
• Extending depth to 1+48+1 or higher can raise estimated costs to around one million dollars for 7×7/7×8 circuits, illustrating tight cost–fidelity–depth tradeoffs.
• The authors present frugal rejection sampling techniques that bound statistical distance while reducing the number of probabilities needed per sampled bitstring.