The method of claim 12, further comprising selecting one or more of a duration, frequency, and amplitude of each of the drive signals to implement the error-transparent quantum gate with the first and second logical qubits.ġ4. A method for implementing an error-transparent quantum gate with first and second logical qubits, the first logical qubit including a first plurality of physical qubits, the second logical qubit including a second plurality of physical qubits, comprising: off-resonantly driving one or more tunable couplers with one or more corresponding drive signals to entangle the first plurality of physical qubits with the second plurality of physical qubits, the drive signals being configured to implement with the first and second logical qubits an error-transparent quantum gate that operates independently of single errors in the first and second logical qubits.ġ3. The error-transparent two-qubit quantum circuit of claim 10, each of the first, second, third, and fourth shadow qubits being a resonator and each of the first, second, third, and fourth physical qubits being a superconducting qubit.ġ2. The error-transparent two-qubit quantum circuit of claim 9, each of the first, second, third, and fourth shadow qubits being a superconducting qubit and each of the first, second, third, and fourth physical qubits being a superconducting qubit.ġ1. The error-transparent two-qubit quantum circuit of claim 4, further comprising: first, second, third, and fourth shadow qubits a third tunable coupler for coupling the first shadow qubit and the first logical qubit a fourth tunable coupler for coupling the second shadow qubit and the first logical qubit a fifth tunable coupler for coupling the third shadow qubit and the second logical qubit and a sixth tunable coupler for coupling the fourth shadow qubit and the second logical qubit.ġ0. The error-transparent two-qubit quantum circuit of claim 4, each of the first and second tunable couplers being a gmon coupler.ĩ. The error-transparent two-qubit quantum circuit of claim 6, wherein: the first and second transmons share a first common bridged ground and the third and fourth transmons share a second common bridged ground.Ĩ. The error-transparent two-qubit quantum circuit of claim 5, wherein: each of the first, second, third, and fourth superconducting qubits is a transmon the first logical qubit further includes a first SQUID for coupling the first and second transmons and the second logical qubit further includes a second SQUID for coupling the third and fourth transmons.ħ. The error-transparent two-qubit quantum circuit of claim 4, each of the first, second, third, and fourth physical qubits being a superconducting qubit.Ħ. The error-transparent two-qubit quantum circuit of claim 3, each of the first and second logical qubits being a very small logical qubit (VSLQ).ĥ. The error-transparent two-qubit quantum circuit of claim 1, the first plurality of physical qubits comprising first and second physical qubits and the second plurality of physical qubits comprising third and fourth physical qubits.Ĥ. The error-transparent two-qubit quantum circuit of claim 1, the error-transparent quantum gate being an error-transparent controlled-Z quantum gate.ģ. An error-transparent two-qubit quantum circuit, comprising: a first logical qubit formed from a first plurality of physical qubits a second logical qubit formed from a second plurality of physical qubits and one or more tunable couplers for entangling the first plurality of physical qubits with the second plurality of physical qubits, the one or more tunable couplers being driven to implement with the first and second logical qubits an error-transparent quantum gate that operates independently of single errors in the first and second logical qubits.Ģ.
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