Two studies show why short quantum circuits can pass some randomness tests but fail others. The allowed operations and the test both matter.
Two research teams have found limits on how short quantum circuits can be while meeting certain randomness tests. Their papers appeared in Nature Communications on November 2, 2026. These are mathematical findings, not tests of a new computer chip. 1 2
What is a quantum circuit?
A quantum computer stores information in quantum bits, called qubits. A gate is an operation that changes qubits. A quantum circuit is a sequence of these operations.
Some gates can run at the same time. Researchers count these steps in layers. The number of layers is called circuit depth. A shallow circuit has few layers. 1 2
Researchers sometimes choose gates at random to help study quantum systems. But looking jumbled is not enough. The circuit must produce the statistical patterns needed for a particular job. These are patterns found by comparing results across many randomly chosen circuits. 1
Different rules give different answers
An approximate design is a collection of operations that closely matches selected statistical patterns of a fully random collection. It does not have to match every possible property. 1 2
Lorenzo Grevink and his colleagues studied several restricted families of operations. They found that circuits cannot be too shallow for some design targets. The limit can depend on which qubits can interact. 1
They also found shorter routes for some weaker targets. These include preparing quantum states with a less demanding error rule. A quantum state describes a quantum system's condition. For several cases, the needed layer count grows slowly as more qubits are added. This is not the same as making the operations pass every randomness test. 1
Maxwell West and his colleagues proved another set of limits. They used certain quantum states that the allowed operations preserve. Under the paper's conditions, circuits using nearby operations need a minimum depth to meet the chosen design target. Different arrangements of qubits can give different bounds. The result does not ban every short circuit. 2
Why this matters
Random choices can help scientists measure quantum systems. One method, called classical shadows, makes a compact record on an ordinary computer. Scientists can use it to estimate many selected properties of a quantum state. 3
A shorter circuit may look like an attractive replacement in a measurement recipe. But researchers must check that it still meets that recipe's randomness requirements. 1 2
The two papers help identify which shortcuts can work and which face mathematical limits. They do not show that quantum computers now run faster. 1 2
Read the research
[1] Short-depth designs beyond the unitary group — Nature Communications, November 2, 2026
[2] No-go theorems for sublinear-depth group designs — Nature Communications, November 2, 2026