Robust quantum computing
Robust optimal control techniques are provided that may shape driving pulses such that the gates are realised with high fidelity despite experimental uncertainty in all or some of the physical parameters of the qubits, drives, qubit-qubit coupling, and qubit-drive coupling. For example, a method for controlling a quantum system comprising a plurality of coupled qubits may comprise: i) assigning the qubits to a plurality of subgroups, wherein the assigning comprises selecting at least one driven qubit and a plurality of undriven qubits for each subgroup, such that each undriven qubit in a subgroup is coupled to a driven qubit in that subgroup and such that any two adjacent subgroups share at least one undriven qubit and do not share any driven qubit; and ii) applying drive signals to each driven qubit to implement a set of desired quantum gates at the driven qubits, wherein the application of the drive signals to the driven qubits at the same time implements the identity gate at each undriven qubit.
1 . A method for controlling a quantum system comprising a plurality of coupled qubits, comprising:
i) assigning the qubits to a plurality of subgroups, wherein the assigning comprises selecting at least one driven qubit and a plurality of undriven qubits for each subgroup, such that each undriven qubit in a subgroup is coupled to a driven qubit in that subgroup and such that any two adjacent subgroups share at least one undriven qubit and do not share any driven qubit; and
ii) applying drive signals to each driven qubit to implement a set of desired quantum gates at the driven qubits, wherein the application of the drive signals to the driven qubits at the same time implements the identity gate at each undriven qubit through fixed qubit-qubit coupling.
2 . A method according to claim 1 , wherein the qubit-qubit coupling has a form such that the Hamiltonians of the subgroups mutually commute.
3 . A method according to claim 1 , wherein coupling between the qubits comprises ZZ coupling, or any coupling which commutes with the qubit's free evolution Hamiltonian.
4 . A method according to claim 1 , wherein the plurality of coupled qubits are arranged as a 1D, 2D, or 3D array.
5 . A method according to claim 1 , further comprising repeating steps i) and ii) to implement a further set of desired quantum gates.
6 . A method according to claim 5 , wherein repeating step i) comprises selecting different driven qubits.
7 . A method according to claim 5 , wherein the drive signals from an earlier iteration of step ii) continue to be applied until the drive signals from a subsequent iteration of step ii) are applied.
8 . A method according to claim 1 , wherein the set of desired quantum gates comprises the Hadamard gate, the π/8 gate, the identity gate, and the CNOT gate.
9 . A method according to claim 1 , wherein the set of desired quantum gates may comprise at least one two-qubit gate.
10 . A method according to claim 1 , wherein the drive signals are obtained by:
generating a representation of the quantum system;
defining a region reflecting a range of uncertainty for one or more parameters of the quantum system;
identifying, for a point within the region, initial drive signals for which a calculated fidelity is maximised using the representation;
identifying, simultaneously for a plurality of points on the boundary of the region, final drive signals for which a calculated fidelity is maximised using the and the initial drive signal,
wherein the final drive signals are applied to the driven qubits.
11 . A method according to claim 10 , wherein the representation of the quantum system is a tensor network representation.
12 . A method according to claim 10 , further comprising, prior to applying the final drive signals to the driven qubits:
calculating the fidelity of the final drive signals at one or more further points within the region; and
determining a distribution of the fidelity across the region from the calculated fidelities.
13 . A method according to claim 10 , wherein the step of identifying the initial drive signals comprises utilising a gradient ascent/descent method.
14 . A method according to claim 10 , wherein the step of identifying the final drive signals comprises utilising a gradient ascent/descent method starting from the initial drive signals.
15 . A method according to claim 1 , further comprising:
iii) measuring the state of at least one of the qubits.
16 . A method according to claim 1 , wherein the qubits are superconducting qubits.
17 . A method according to claim 16 , wherein the qubits are transmon or flux qubits.
18 . A method for obtaining drive signals to be applied to a quantum system comprising a plurality of qubits, the method comprising:
generating a representation of the quantum system;
defining a region reflecting a range of uncertainty for one or more parameters of the quantum system;
identifying, for a point within the region, initial drive signals for which a calculated fidelity is maximised using the representation;
identifying, simultaneously for a plurality of points on the boundary of the region, final drive signals for which a calculated fidelity is maximised using the representation and the initial drive signal,
wherein the final drive signals are applied to one or more qubits.
19 . A computer program product comprising computer executable instructions which, when the instructions are executed by a computer, cause the computer to carry out the method according to claim 18 .