Adiabatic quantum computation with superconducting qubits

Abstract

A method for computing using a quantum system comprising a plurality of superconducting qubits is provided. Quantum system can be in any one of at least two configurations including (i) an initialization Hamiltonian H 0 and (ii) a problem Hamiltonian H P . The plurality of superconducting qubits are arranged with respect to one another, with a predetermined number of couplings between respective pairs of superconducting qubits in the plurality of qubits, such that the plurality of superconducting qubits, coupled by the predetermined number of couplings, collectively define a computational problem to be solved. In the method, quantum system is initialized to the initialization Hamiltonian H O . Quantum system is then adiabatically changed until it is described by the ground state of the problem Hamiltonian H P . The quantum state of quantum system is then readout thereby solving the computational problem to be solved.

1 - 23 . (canceled) 
     
     
         24 . A method for quantum computing using a quantum system comprising a plurality of superconducting qubits, the plurality of superconducting qubits including at least one pair of superconducting qubits, wherein the quantum system is characterized by an impedance and wherein the quantum system is capable of being in any one of at least two configurations at any given time, the at least two configurations comprising:
 a first configuration characterized by an initialization Hamiltonian H O , and   a second configuration characterized by a problem Hamiltonian H P  having a ground state, and wherein for each pair of superconducting qubits a first superconducting qubit in a respective one of the pairs of superconducting qubits is arranged with respect to a second superconducting qubit in the respective pair of superconducting qubits such that the first superconducting qubit and the second superconducting qubit define a predetermined coupling strength, and wherein the predetermined coupling strengths collectively define a computational problem to be solved, the method comprising:   initializing the quantum system to the initialization Hamiltonian H O ,   adiabatically changing the quantum system until it is described by a ground state of the problem Hamiltonian H P ; and   reading out a state of the quantum system.   
     
     
         25 . The method of  claim 24  wherein reading out a state of the quantum system includes probing an observable of at least one of a σ x  Pauli matrix operator and a σ z  Pauli matrix operator. 
     
     
         26 . The method of  claim 24  wherein reading out a state of the quantum system includes determining a state of a superconducting qubit in the plurality of superconducting qubits. 
     
     
         27 . The method of  claim 26  wherein reading out a state of the quantum system includes differentiating a ground state of the superconducting qubit from an excited state of the superconducting qubit. 
     
     
         28 . The method of  claim 24  wherein a superconducting qubit in the plurality of superconducting qubits is a persistent current qubit. 
     
     
         29 . The method of  claim 24  wherein reading out a state of the quantum system includes measuring a quantum state of the superconducting qubit based on a presence or an absence of a voltage. 
     
     
         30 . The method of  claim 24  wherein a superconducting qubit in the plurality of superconducting qubits is capable of tunneling between a first state and a second state when the quantum system is in the first configuration. 
     
     
         31 . The method of  claim 24  wherein adiabatically changing the quantum system until it is described by a ground state of the problem Hamiltonian H P  includes a superconducting qubit in the plurality of superconducting qubits tunneling between a first stable state and a second stable state. 
     
     
         32 . The method of  claim 24  wherein adiabatically changing the quantum system until it is described by a ground state of the problem Hamiltonian H P  has a duration between about 1 nanosecond and 100 microseconds. 
     
     
         33 . The method of  claim 24  wherein initializing the quantum system to the initialization Hamiltonian H O  includes applying a magnetic field to the plurality of superconducting qubits in a direction of a vector that is perpendicular to a plane defined by the plurality of superconducting qubits. 
     
     
         34 . A method for adiabatic quantum computing using a quantum system comprising a plurality of superconducting qubits, wherein the quantum system is capable of being in any one of at least two quantum configurations at any given time, the at least two quantum configurations comprising:
 a first configuration described by an initialization Hamiltonian H O ; and   a second configuration described by a problem Hamiltonian H P  having a ground state, the method comprising:
 initializing the quantum system to the first configuration; 
 adiabatically changing the quantum system until it is described by the ground state of the problem Hamiltonian Hp; and 
 reading out a state of the quantum system. 
   
     
     
         35 . The method of  claim 34  wherein the plurality of superconducting qubits includes at least one pair of superconducting qubits wherein for each pair of superconducting qubits, a first superconducting qubit in a respective one of the pairs of superconducting qubits is arranged with respect to a second superconducting qubit in the respective pair of superconducting qubits such that the first superconducting qubit and the second superconducting qubit define a predetermined coupling strength, and wherein the predetermined coupling strengths respectively define a computational problem to be solved. 
     
     
         36 . The method of  claim 34  wherein the problem Hamiltonian H P  comprises a tunneling term for each of the respective superconducting qubits in the plurality of superconducting qubits, and wherein an energy of a tunneling term for each respective superconducting qubit in the plurality of superconducting qubits is less than an average of the predetermined coupling strengths. 
     
     
         37 . The method of  claim 34  wherein the reading out step comprises probing an observable of at least one of a σ x  Pauli matrix operator and a σ z  Pauli matrix operator for a superconducting qubit in the plurality of superconducting qubits. 
     
     
         38 . The method of  claim 34  wherein a superconducting qubit in the plurality of superconducting qubits is a persistent current qubit. 
     
     
         39 . A computer program product for use in conjunction with a computer system, the computer program product comprising a computer readable storage medium and a computer program mechanism embedded therein, the computer program mechanism comprising:
 instructions for initializing a quantum system comprising a plurality of superconducting qubits to an initialization Hamiltonian H o , wherein the plurality of superconducting qubits includes at least one pair of qubits and wherein the quantum system is capable of being in one of at least two configurations at any given time, the at least two configurations including:
 a first configuration characterized by the initialization Hamiltonian H O , and 
 a second configuration characterized by a problem Hamiltonian H P , and wherein for each pair of superconducting qubits in the plurality of superconducting qubits, a first superconducting qubit in a respective one of the pairs of superconducting qubits is arranged with respect to a second superconducting qubit in the respective pair of superconducting qubits such that the first superconducting qubit and the second superconducting qubit define a predetermined coupling strength, and wherein the predetermined coupling strengths collectively define a computational problem to be solved; 
   instructions for adiabatically changing the quantum system until it is described by a ground state of the problem Hamiltonian H P ; and   instructions for reading out a state of the quantum system.