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Wednesday, 17 December 2025

what is Quantum Volume (QV) in quantum computing. explain with examples

 Quantum Volume (QV) is a single-number metric used to measure the overall power and performance of a quantum computer.1

It was developed (primarily by IBM) to solve a major problem in the industry: counting "qubits" is misleading.2 A computer with 100 "noisy" qubits (prone to errors) is often less powerful than a computer with 50 "clean" qubits.3

Quantum Volume accounts for both the number of qubits and the quality of operations they can perform before errors ruin the calculation.4


1. The Core Concept: The "Square" Circuit5

To understand Quantum Volume, imagine a square grid where:

  • Width = The number of Qubits involved.6

  • Depth = The number of operations (gates) performed in a sequence (time steps).7

Quantum Volume measures the largest Square Circuit a computer can successfully run.8 This means if you have a computer that can successfully run a program using 9$N$ qubits for 10$N$ steps, its Quantum Volume is 11$2^N$.12

The Formula:

$$QV = 2^N$$

Where $N$ is the maximum number of qubits that can run a circuit of depth $N$ with reliable results.

2. Why is this difficult? (The Example Scenario)

Imagine you have a quantum computer with 100 qubits. You might think its Volume is huge ($2^{100}$). However, quantum states are fragile.

  • Scenario A (High Qubit, Low Quality): You try to use 50 qubits. But the error rate is high. By the time you reach the 10th step of the calculation, the noise has scrambled the data. You cannot reach a "depth" of 50. Therefore, your "useful" square is small.

  • Scenario B (Low Qubit, High Quality): You have a machine with only 12 qubits, but they are very stable. You can easily run 12 steps of operations on all 12 qubits without errors.

    • Since $N=12$, your Quantum Volume is $2^{12} = 4096$.

Result: The machine with 12 stable qubits (Scenario B) might actually have a higher Quantum Volume than the machine with 100 noisy qubits (Scenario A).

3. Factors Influencing Quantum Volume

It is a "holistic" metric because improving ANY of the following increases the score:

FactorWhy it matters
Number of QubitsYou need physical qubits to build the "width" of the circuit.
Gate Fidelity (Low Error)If gates (operations) are error-prone, you can't go "deep" into the circuit.
ConnectivityIf Qubit A needs to talk to Qubit Z, but they aren't connected, you have to add extra "SWAP" steps to move data. This wastes "depth" and lowers volume.
Compiler SoftwareBetter software can optimize the code to run fewer steps, effectively increasing the volume.

4. Real-World Examples

To give you a sense of scale, here is how Quantum Volume has progressed in real hardware. Note that because the formula is exponential ($2^N$), the numbers get big very quickly.

  • QV 32 ($N=5$):

    • Meaning: The computer can reliably run a circuit using 5 qubits for 5 steps.

    • Example: Early IBM machines (approx. 2019).

  • QV 128 ($N=7$):

    • Meaning: The computer can reliably use 7 qubits for 7 steps.

    • Example: This requires significantly lower error rates than QV 32.

  • QV 8,388,608 (13$N=23$):14

    • Meaning: The computer can reliably use 23 qubits for 23 complex sequential steps.

    • Example: Quantinuum (Model H2) achieved this record in 2025.15 This is massive because maintaining coherence across 23 qubits for 23 steps is incredibly difficult.

5. Simple Analogy: The "Tower of Blocks"

Think of Quantum Volume like building a square tower of blocks.

  • Width: How many blocks wide the base is (Qubits).

  • Height: How many blocks high you can build (Time/Depth).

  • The Rule: You must build a perfect square (Width = Height).

If you have 100 blocks (Qubits) for the base, but your hands are shaky (Noise/Errors), the tower falls over after just 3 levels.

  • Your "effective" tower is only $3 \times 3$.

  • Your score is low, even though you had 100 blocks available.

If you have steady hands (Low Noise) and 10 blocks, you can build a stable $10 \times 10$ tower.

  • Your score is higher ($10 \times 10$), even though you started with fewer blocks.

Summary

Quantum Volume tells you how much useful quantum computing you can actually do.16 It proves that a quantum processor is not just a collection of qubits, but a system capable of sustaining complex calculations without collapsing due to errors.17

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