Blueprint for fault-tolerant quantum computation with Rydberg atoms

We present a blueprint for building a fault-tolerant universal quantum computer with Rydberg atoms. Our scheme, which is based on the surface code, uses individually addressable, optically trapped atoms as qubits and exploits electromagnetically induced transparency to perform the multiqubit gates required for error correction and computation. We discuss the advantages and challenges of using Rydberg atoms to build such a quantum computer, and we perform error correction simulations to obtain an error threshold for our scheme. Our findings suggest that Rydberg atoms are a promising candidate for quantum computation, but gate fidelities need to improve before fault-tolerant universal quantum computation can be achieved.

Figure 1

A distance $d=5$ planar code (black dots represent physical data qubits). (a) Primal lattice showing a star stabilizer generator $A_s$, a plaquette stabilizer generator $B_p$, and a logical Pauli operator $\overline{Z}$. (b) Dual lattice showing the same stabilizer generators and a logical Pauli operator $\overline{X}$ that anticommutes with the logical $\overline{Z}$ operator in (a).

Figure 2

Using EIT to perform a cnot gate with the method in Ref. [25] (control qubit always on the left, target qubit always on the right). (a) Shows the order of the pulses, (b) shows EIT blocking the ${|0\rangle }_t\leftrightarrow {|1\rangle }_t$ transition on the target qubit, and (c) shows the dipole blockade shifting the EIT out of resonance and allowing the ${|0\rangle }_t\leftrightarrow {|1\rangle }_t$ transition on the target qubit.

Figure 3

Measuring a star operator using a multitarget EIT cnot gate. The top qubit is the ancilla syndrome qubit and is used only for syndrome measurement. The method for measuring a plaquette stabilizer generator involves applying Hadamard gates to each data qubit before and after the entangling operation but is otherwise identical.

Figure 4

Arrangement of Rydberg atoms for a planar code. Green shaded qubits denote ancilla syndrome qubits used to measure stabilizer generators, and solid black qubits denote data qubits of the planar code. Using different species of atoms for syndrome and data qubits may help to reduce crosstalk during measurement [32].

Figure 5

Stabilizer generators must be measured in at least four stages to ensure that each data qubit is involved in only a single interaction at any time. Each of the subfigures represents one stage of measurement, with all four stages required for one complete round of syndrome measurement. (a, b) Measurements of star stabilizer generators, (c, d) measurements of plaquette stabilizer generators.

Figure 6

Leakage detection circuit from [35]. If the top qubit is in the computational basis, then the bottom qubit (an ancilla) will be observed in the $|1\rangle$ state. If the top qubit has leaked or been lost, the bottom qubit will be observed in the $|0\rangle$ state. The top qubit can be reinitialized if leakage or loss occurs.

Figure 7

Logical error rates from error simulations for code distances 8, 10, 12, and 14. The crossing point gives the resulting error threshold of 1.25%.