Non-Clifford gate

A quantum computer performs computations by applying so-called gates to qubits — the basic building blocks of a quantum computer, comparable to bits in an ordinary computer. Gates are individual computational steps that change the state of a qubit. Most gates used by quantum computers can be divided into two groups: Clifford gates and non-Clifford gates. Clifford gates are fast, easy to simulate, and make up the majority of operations used. Non-Clifford gates, on the other hand, are rarer, more costly — and indispensable. Only by adding them does a quantum computer become truly powerful: with Clifford gates alone, an ordinary laptop could easily mimic any quantum computer.

The boundary to true quantum advantage

A quantum computer is supposed to solve problems that classical computers fail at — such as breaking certain encryption schemes or simulating molecules for drug research. But it can only do this if it fully masters a particular set of gates, the so-called universal gate set. Clifford gates alone are demonstrably not sufficient for this; this has been mathematically proven.

Non-Clifford gates close this gap. The best-known example is the T-gate, which performs a rotation of the qubit state by a specific angle — specifically by 45 degrees on the so-called Bloch sphere, a geometric model used to represent qubit states. Together with Clifford gates, this yields a complete set with which, in principle, any conceivable quantum computation can be carried out. Non-Clifford gates are therefore not the heart of every computation, but the crucial key that unlocks the door in the first place.

Why non-Clifford gates are so expensive

The central problem: non-Clifford gates are extremely difficult to execute without errors. Quantum computers are sensitive to disturbances — heat, vibrations, or electromagnetic fields can knock qubits out of their desired state. To deal with this, quantum error correction is used: many physical qubits are wired together to form a single, reliable “logical qubit.” Clifford gates can be executed directly and efficiently on logical qubits. Non-Clifford gates, however, cannot.

For them, a complex procedure called magic state distillation is needed. In this process, a single, highly pure state is obtained from many flawed qubit states, the so-called magic states, through repeated filtering — similar to how crude oil is refined into clean fuel through many distillation steps. This process consumes an enormous amount of additional qubits and computing time. According to estimates, more than 90 percent of all qubits in a fault-tolerant quantum computer may be needed solely to provide T-gates. The number of non-Clifford gates in an algorithm — the so-called T-complexity — is therefore a crucial measure of how demanding a quantum program actually is.

An important misconception is the assumption that more non-Clifford gates automatically mean better algorithms. The opposite is often true: a major field of research is concerned with rewriting algorithms so that they require as few T-gates as possible without losing their computational power.

Non-Clifford gates in practice and in the news

When tech companies like Google, IBM, or Microsoft report on the progress of their quantum computers, the term often appears indirectly. Reports about new records in error correction or more efficient quantum algorithms are usually about how well a system can handle non-Clifford gates. Microsoft’s approach using so-called topological qubits aims, among other things, to make non-Clifford gates inherently more robust from the ground up, rather than correcting them afterward through distillation.

Non-Clifford gates also play a role in cryptography. The best-known quantum algorithm for breaking encryption, the so-called Shor’s algorithm, requires non-Clifford gates. Exactly how many, and how to reduce that number, is an active area of research — because it determines when and whether a quantum computer could threaten real-world encryption schemes. For anyone reading news about quantum computing, it is therefore worth knowing: behind many milestones ultimately lies the question of how well a machine copes with these few but crucial gates.