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Quantum Supremacy Achieved?

Google researchers claimed to achieved “quantum supremacy” in a 2019 Nature article.

Specifically, their 53-qubit quantum processor solved a problem in 200 seconds that would have taken a state-of-the-art classical supercomputer 10,000 years to solve

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Abstract

Google built a 54-qubit quantum processor (only 53 working qubits) called “Sycamore” using programmable superconducting qubits

This quantum computer (QC) operates on quantum states in a 2⁵³ = 10¹⁶ dimensional Hilbert space

The QC took 200 seconds to solve a problem that would take a classical computer 10,000 years, demonstrating a dramatic increase in speed compared to known classical algorithms

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Background: Why did Google do this?

Physicist Richard Feynman (1982) and others proposed a quantum computer (QC) could solve or dramatically speed up intractable problems in physics and chemistry.

Challenges:

Can such a quantum system actually be built with high fidelity?
What problems are hard for classic computers but easy for a QC?
How is this measurement benchmarked and verified?

QCs require fault-tolerant qubits that can be operated simultaneously, a technical engineering feat. Google used a 53-qubit processor to demonstrate the feasibility of QCs at scale, and developed a cross-entropy benchmark to measure its performance.

(real answer: they wanted to flex their tech leadership)

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Conducting the Research (I)

Task: sampling a random quantum circuit

Qubits were entangled using random one- and two-qubit logic gates in quantum circuit

The sampling process was repeated millions of times with new random selections

Each random circuit produces a probability distribution for each bitstring (0011010, 1101001…) due to quantum interference

Cross-entropy benchmarking compares the expected probability of each bitstring with its actual measured frequency

For large enough circuit, calculating fidelity F_XEB on a classical computer is prohibitively expensive

F_XEB = 2ⁿ⟨P(x_i)⟩_i-1

F_XEB = fidelity

n = number of qubits

P(x_I) = probability of bitstring x_i

⟨⟩ = average value (ideal case)

Cross-entropy benchmarking

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Conducting the Research (II)

The random sampling task requires qubits with low error rates because even a single bit flip will destroy the interference pattern, resulting in near-zero fidelity

The Sycamore chip used a 2D array of 53 superconducting transmon qubits, acting as nonlinear resonators at 5-7GHz. Each qubit is coupled to the 4 nearest qubits in a lattice, and connected to a linear resonator to read out the qubit state

Qubit states |0⟩ and |1⟩ are encoded as the two lowest energy eigenstates and logic gates are encoded using resonant microwave pulses

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Error Correction (I)

Surface codes are a quantum error correction approach, working on a 2D grid with only nearest-neighbor interactions

Physical qubits are arranged in a square lattice, and extra qubits measure stabilizers to detect errors without disturbing the encoded logical qubit information

Surface codes are robust and scalable, with high tolerances (error threshold ~1%), providing a path to fault-tolerant quantum computing

Surface codes: Towards practical large-scale quantum computation

Fowler, et al. Phys. Rev. A 86

https://doi.org/10.1103/PhysRevA.86.032324

Example of surface code 2D array

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Error Correction (II)

Google did not have full fault-tolerant QEC, but they demonstrated small-scale surface code primitives:

(1) repeated stabilizer measurements

(2) detection of bit-flip and phase-flip errors

They also validated that hardware quality was approaching theoretical thresholds needed for surface-code QEC, especially:

Gate optimization
Improved coherence
Tunable couplers
Reduced crosstalk

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What are the Final Results?

Google built the world’s first physical proof of quantum computation principles at scale:

Performed task in 200s, where there is NO efficient classical algorithm that can match within 10,000 years, i.e. QUANTUM SUPREMACY
Developed fast, high fidelity gates that can be executed simultaneously across a 2D qubit array. Moving beyond single gate isolated operations.
Used component level fidelities to accurately predict system fidelity.
Processor is an entanglement amplifier. Gates scramble amplitudes (amplified interference) across a real 2⁵³ dimensional Hilbert Space

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Connection to EE 225

One- and two-qubit logic gates

NOT, CNOT, CZ, SWAP, and the Pauli matrices
They also used √X and W = (X+Y)/√2

Qubit states |0⟩ and |1⟩ as eigenstates of physical observables
Quantum state in a Hilbert space, N=2ⁿ states for n qubits with |𝜓⟩ ∈ ℂ^{2^n} dimensionality
The probabilistic nature of measurement outcomes
Error correction codes with stabilizers

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We Still Don’t Understand…

The circuit doesn’t seem to simulate a “real” quantum system. How do we know the QC would be useful on a real problem?

e.g. simulating quantum materials (Feynman), or Shor’s algorithm

If the problem is too difficult for a classical computer to solve, how do we verify the QC results?

i.e. how do we know the QC actually worked rather than noise?

Has anyone surpassed this result since publication? Research from China and private sector (D-Wave) have also claimed similar results. What metrics apply across industry?
The actual hardware is something of a black box to us, which should be covered in EE 226 - Cryogenic Nanoelectronics!

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Improvements and Suggestions We Have

The paper is written for a technical audience, who may not be familiar with the statistical methods employed

It would be great to see the researchers design a more useful NISQ algorithm and run it on this hardware

More information on near-term development and applications, rather than abstract statements about mathematical theses

A stronger statement about how this research connects to the broader goals of quantum computing, e.g. simulating quantum materials or meaningful progress on implementing Shor’s algorithm

Google should hire us

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Summary and Future Directions

Google set out to achieve quantum supremacy and did so using quantum superconducting qubits.

Future directions:

Sycamore marks the start of the NISQ era – real, but noisy quantum devices
Upgrade physical qubits -> logical qubit devices via error correction. Smarter controls and smarter devices.
Improve fidelity, coherence time, and connectivity between qubits to scale quantum systems
Fault-tolerant architectures in coding
Expected continuation of Moore’s law

2024, Google released “Willow” processor (105-qubits).
Next major goal - long-lived logical qubits.