Real Quantum Computers Sources Richard Spillman Mike Frank Mike Frank Julian Miller Isaac Chuang, M. Steffen, L.M.K. Vandersypen, G. Breyta, C.S. Yannoni, M. Sherwood C.S. Yannoni, M. Sherwood

Requirements for quantum computation 1. Robust representation of quantum information1. Robust representation of quantum information 2. Perform universal family of unitary transformations2. Perform universal family of unitary transformations 3. Prepare a fiducial initial state3. Prepare a fiducial initial state 4. Measure the output result4. Measure the output result

Outline Hurdles to building quantum computersHurdles to building quantum computers –Decoherence –Error Correction Requirements for workable quantum computersRequirements for workable quantum computers NMR quantum computersNMR quantum computers Other quantum computersOther quantum computers

Where is the market? Banks? Military? Security agencies? Physicists? Simulation of quantum systems for drug design? Why build a quantum computer?

Why not build a quantum computer?

Implications of building a quantum computer

Why is building a quantum computer so difficult?

Ion traps, 2 & 3 qubit systemsIon traps, 2 & 3 qubit systems Nuclear spins in NMR devices, 4 (5?, 6?) qubitsNuclear spins in NMR devices, 4 (5?, 6?) qubits So far: very few qubits, impracticalSo far: very few qubits, impractical A lot of current researchA lot of current research Physical implementation Two 9Be+ Ions in an Ion Trap Wineland’s group, NIST

Main Contenders 1. NMR (nuclear magnetic resonance), invented in the 1940's and widely used in chemistry and medicine today1. NMR (nuclear magnetic resonance), invented in the 1940's and widely used in chemistry and medicine today 2. Ion traps - single atoms2. Ion traps - single atoms 3. Optical lattices3. Optical lattices 4. Quantum dots4. Quantum dots 5. Electrons on liquid helium5. Electrons on liquid heliumetc.

Quantum Technology Requirements for Physical Implementation Quantum Technology Requirements [Di Vicenzo ‘01] 1. A Scalable physical system with well-characterized (well-defined) qubits1. A Scalable physical system with well-characterized (well-defined) qubits 2. An ability to initialize the system to Initializable to a pure basis states such as  00…0 2. An ability to initialize the system to Initializable to a pure basis states such as  00…0  3. Relatively long decoherence time, longer than the gate operation times.3. Relatively long decoherence time, longer than the gate operation times. 4. “Universal” set of quantum gates4. “Universal” set of quantum gates 5. Qubit-specific measurement capability5. Qubit-specific measurement capability Ability to faithfully communicate qubitsAbility to faithfully communicate qubits

Di Vincenzo Criteria Additional Di Vincenzo Criteria

Decoherence Quantum computations rely on being able to operate on a set of qubits in an entangled/superimposed stateQuantum computations rely on being able to operate on a set of qubits in an entangled/superimposed state –Allows computation on all possible inputs to a computation in parallel Problem: Interaction of qubits with environment affects their state, causing them to not be entangled/superimposedProblem: Interaction of qubits with environment affects their state, causing them to not be entangled/superimposed –Can partially address this by designing computer to reduce interaction with environment, but this may make it impractical (for example, running at very low temperatures) General result: a quantum computation can only proceed for a limited period of time before a measurement must be performedGeneral result: a quantum computation can only proceed for a limited period of time before a measurement must be performed –Measurement forces the system into a more-stable classical state –Measurement destroys superposition –System limited by ratio of decoherence time to operation latency

Decoherence

Decoherence

Decoherence

How decoherence happens

Decoherence-related Figure of Merit

Quantum Computer uses a single molecule Protons and Neutrons have spin. In a normal atoms these spins cancel out. In isotopes there are extra neutrons. These extra neutrons create a net positive or negative spin in an atom.

Spins and Coherence Most advanced demonstrated technology for quantum computationMost advanced demonstrated technology for quantum computation Use nuclei with spin ½ as qubitsUse nuclei with spin ½ as qubits –Spin straight up = |0> –Spin straight down = |1> –Other directions indicate superpositions of |0> and |1> –Long coherence times (seconds) Electron spins (alternate technology) have coherence times of nanosecondsElectron spins (alternate technology) have coherence times of nanoseconds –In a magnetic field, spin direction precesses about the field’s axis at a rate that is proportional to the field strength

Quantum Computer uses a single molecule A nearly ideal physical system that can be used as quantum computer is a single molecule, in which nuclear spins of individual atoms represent qubits.A nearly ideal physical system that can be used as quantum computer is a single molecule, in which nuclear spins of individual atoms represent qubits. Using NMR techniques, these spins can be manipulated, initialized and measured.Using NMR techniques, these spins can be manipulated, initialized and measured. The quantum behavior of the spins can be exploited to perform quantum computation; for example, the carbon and hydrogen nuclei in a chloroform molecule (as shown) represent two qubits.The quantum behavior of the spins can be exploited to perform quantum computation; for example, the carbon and hydrogen nuclei in a chloroform molecule (as shown) represent two qubits. Single molecule or ensamble?