Quantum operations with passive noise suppression

Patent metadata

Field	Value
Publication number	US-10074056-B2
Application number	US-201615225210-A
Country	US
Kind code	B2
Filing date	Aug 1, 2016
Priority date	Aug 1, 2016
Publication date	Sep 11, 2018
Grant date	Sep 11, 2018

Abstract

Systems and methods are provided for performing noise-resilient quantum operations. A set of control signals are applied to a system to provide a first Hamiltonian for the system. The system includes an array of physical qubits and a plurality of coupling mechanisms configured such that each pair of neighboring physical qubits within the array is coupled by an associated coupling mechanism. The first Hamiltonian represents, for each coupling mechanism, a coupling strength between zero and a maximum value. An adiabatic interpolation of the Hamiltonian of the system from the first Hamiltonian to a second Hamiltonian is performed. The second Hamiltonian represents, for at least one of the plurality of coupling mechanisms, a coupling strength different from that of the first Hamiltonian.

First claim

What is claimed is:

1. A method for performing a quantum operation on a logical qubit, comprising a plurality of physical qubits, that is resilient to noise on control signals, on the individual physical qubits, and on the coupling strengths between physical qubits, the method comprising:
applying a set of control signals to provide a first Hamiltonian for a system comprising an array of physical qubits, the array of physical qubits including at least the plurality of physical qubits, and a plurality of coupling mechanisms, each coupling mechanism operatively coupling only an associated pair of neighboring physical qubits within the array, the first Hamiltonian representing, for each coupling mechanism, a coupling strength between zero and a maximum value;
performing an adiabatic interpolation of the Hamiltonian of the system from the first Hamiltonian to a second Hamiltonian, the second Hamiltonian representing, for at least one of the plurality of coupling mechanisms, a coupling strength different from that of the first Hamiltonian.

2. The method of claim 1 , wherein the quantum operation is a state preparation for the logical qubit, comprising a plurality of physical qubits from the array of physical qubits, to an eigenstate associated with a Pauli operator and the first Hamiltonian comprises a set of single qubit terms representing a splitting of the energy state of each physical qubit comprising the logical qubit into eigenstates of the Pauli operator and the second Hamiltonian represents a non-zero coupling strength for each coupling mechanism connecting two physical qubits in the logical qubit.

3. The method of claim 2 , wherein the Pauli operator is the X operator and the eigenstate is one of the plus and the minus states.

4. The method of claim 2 , wherein the Pauli operator is the Z operator and the eigenstate is one of the |0 and |1 states.

5. The method of claim 1 , wherein the quantum operation is a read operation on the logical qubit, comprising a plurality of physical qubits from the array of physical qubits, and the first Hamiltonian represents a non-zero coupling strength for each coupling mechanism connecting two physical qubits in the logical qubit and the second Hamiltonian comprises a set of single qubit terms representing a splitting of the energy state of each physical qubit comprising the logical qubit into eigenstates of a Pauli operator.

6. The method of claim 1 , wherein the quantum operation is an elongation of the logical qubit, comprising a plurality of physical qubits from the array of physical qubits, into a defined elongation region and the first Hamiltonian comprises a set of single qubit terms representing a splitting of the ground energy state of each physical qubit within the elongation region into eigenstates of a Pauli operator and the second Hamiltonian represents a non-zero coupling strength for each coupling mechanism connecting two physical qubits in the elongation region.

7. The method of claim 1 , wherein the quantum operation is a contraction of the logical qubit, comprising a plurality of physical qubits from the array of physical qubits, and the first Hamiltonian represents a non-zero coupling strength for each coupling mechanism connecting two physical qubits in the logical qubit and the second Hamiltonian comprises a set of single qubit terms representing a splitting of the ground energy state of each physical qubit within a region to be contracted into eigenstates of a Pauli operator and a set of two-qubit qubit terms defining a non-zero coupling strength for each coupling mechanism connecting two physical qubits in a remainder of the logical qubit.

8. The method of claim 1 , wherein the quantum operation is a CNOT gate on a target logical qubit, comprising the logical qubit, using a control logical qubit, comprising a second plural set of physical qubits from the array of physical qubits, the first Hamiltonian comprising a set of two-qubit terms representing a non-zero coupling strength for each coupling mechanism connecting two physical qubits in each of the control qubit and the target qubit, and the second Hamiltonian comprises a term representing a zero coupling strength for at least one coupling mechanism connecting two physical qubits in the control qubit and a non-zero coupling strength for at least one coupling mechanism connecting at least one physical qubit in the control qubit to corresponding physical qubits in the target qubit, such that a portion of the control qubit is decoupled from the control qubit and coupled to the target qubit.

9. The method of claim 1 , wherein the quantum operation is a non-Clifford rotation gate on the logical qubit and the first Hamiltonian comprises a set of two-qubit terms representing a non-zero coupling strength for each coupling mechanism connecting two physical qubits in each of the control qubit and the second Hamiltonian comprises a single qubit term representing a splitting of the ground energy state around an axis on the Bloch sphere defined by a desired angle of the non-Clifford rotation for a physical qubit in the logical qubit and a two-qubit qubit term defining a non-zero coupling strength for a coupling mechanism connecting two physical qubits in a remainder of the logical qubit.

10. The method of claim 9 , wherein the axis on the Bloch sphere comprises each of the Y axis and the Z axis, and the rotation can be represented by an operator A=aY+bZ, where a 2 +b 2 =1 and b is the cosine of the desired angle.

11. The method of claim 1 , wherein the quantum operation is a Hadamard gate on the logical qubit, comprising a plurality of physical qubits from the array of physical qubits, a first set of XX coupling mechanisms of the plurality of coupling mechanisms that couple each physical qubit to a nearest neighbor in a first direction on the array, and a first set of ZZ coupling mechanisms of the plurality of coupling mechanisms that couple each physical qubit to a nearest neighbor in a second direction on the array, where the first Hamiltonian comprises a set of single qubit terms representing a splitting of the ground energy state of a plurality of physical qubits within an elongation region of the array outside the logical qubit into eigenstates of a Pauli operator and non-zero coupling values for each of the first set of XX coupling mechanisms and the first set of ZZ coupling mechanisms, and the second Hamiltonian represents a non-zero coupling for a second set of at least one ZZ coupling mechanism that couple at least two physical qubits in the elongation region in the first direction.

12. The method of claim 11 , further comprising performing an adiabatic interpolation of the Hamiltonian of the system from the second Hamiltonian to a third Hamiltonian comprising a set of single qubit terms representing a splitting of the ground energy state of each physical qubit comprising the original logical qubit into eigenstates of a Pauli operator and a set of two-qubit qubit terms defining a non-zero coupling strength for each coupling mechanism in the second set of at least one ZZ coupling mechanism and second set of at least one XX coupling mechanism of the plurality of coupling mechanisms that couple at least two physical qubits in the elongation region in the second direction.

13. The method of claim 11 , further comprising:
performing an adiabatic interpolation of the Hamiltonian of the system from the second Hamiltonian to a third Hamiltonian comprising a set of single qubit terms representing a splitting of the ground energy state of a proper subset of the physical qubits comprising the original logical qubit into eigenstates of a Pauli X operator and a set of two-qubit qubit

Assignees

• Epstein Ryan J
• Northrop Grumman Systems Corp

Inventors

• Epstein Ryan J

Classifications

• H03K19/195

  using superconductive devices · CPC title

• G06N99/002 Primary

  Physics · mapped topic

• G06N10/20

  Models of quantum computing, e.g. quantum circuits or universal quantum computers · CPC title

• G06N10/40

  Physical realisations or architectures of quantum processors or components for manipulating qubits, e.g. qubit coupling or qubit control · CPC title

• G06N10/70 Primary

  Quantum error correction, detection or prevention, e.g. surface codes or magic state distillation · CPC title