Real Quantum Real Quantum ComputersComputers

SourcesSourcesRichard SpillmanRichard Spillman

Mike FrankMike FrankJulian MillerJulian Miller

Isaac Chuang, M. Steffen, L.M.K. Vandersypen, G. Breyta, Isaac Chuang, M. Steffen, L.M.K. Vandersypen, G. Breyta, C.S. Yannoni, M. SherwoodC.S. Yannoni, M. Sherwood

Requirements for quantumRequirements for quantumcomputationcomputation

• 1. Robust representation of quantum 1. Robust representation of quantum informationinformation

• 2. Perform universal family of unitary 2. Perform universal family of unitary transformationstransformations

• 3. Prepare a fiducial initial state3. Prepare a fiducial initial state• 4. Measure the output result4. Measure the output result

OutlineOutline• Hurdles to building quantum computersHurdles to building quantum computers

– DecoherenceDecoherence– Error CorrectionError Correction

• Requirements for workable quantum computersRequirements for workable quantum computers• NMR quantum computersNMR quantum computers• Other quantum computersOther quantum computers

Where is the market?Where is the market?

Banks? Military? Security agencies? Physicists? Simulation of quantum systems for drug design?

Why build a quantum computer?Why build a quantum computer?

Why not build a quantum Why not build a quantum computer?computer?

Implications of building a Implications of building a quantum computerquantum computer

Why is building a quantum Why is building a quantum computer so difficult?computer so difficult?

• Ion traps, 2 & 3 qubit systems Ion traps, 2 & 3 qubit systems • Nuclear spins in NMR devices, 4 (5?, 6?) qubits Nuclear spins in NMR devices, 4 (5?, 6?) qubits • So far: very few qubits, impractical So far: very few qubits, impractical • A lot of current researchA lot of current research

Physical Physical implementationimplementation

•Two 9Be+ Ions in an Ion Trap •Wineland’s group, NIST

Main ContendersMain Contenders• 1.1. NMR (nuclear magnetic resonance) NMR (nuclear magnetic resonance) , invented , invented

in the 1940's and widely used in chemistry and in the 1940's and widely used in chemistry and medicine todaymedicine today

• 2.2. Ion traps - single atoms Ion traps - single atoms• 3.3. Optical lattices Optical lattices• 4.4. Quantum dots Quantum dots• 5.5. Electrons on liquid helium Electrons on liquid helium

etc.etc.

Quantum Technology Quantum Technology Requirements for Physical Requirements for Physical

ImplementationImplementationQuantum Technology RequirementsQuantum Technology Requirements [Di Vicenzo ‘01][Di Vicenzo ‘01]• 1. A Scalable1. A Scalable physical system with physical system with well-characterizedwell-characterized (well- (well-

defined) qubitsdefined) qubits• 2. An ability to initialize the system to Initializable2. An ability to initialize the system to Initializable to a pure to a pure

basis states such as basis states such as 00…000…0• 3.3. Relatively Relatively long decoherencelong decoherence time, longer than the gate time, longer than the gate

operation times.operation times.• 4. “Universal”4. “Universal” set of quantum gates set of quantum gates• 5.5. Qubit-specific Qubit-specific measurement measurement capabilitycapability• Ability to faithfully Ability to faithfully communicate qubitscommunicate qubits

Di Vincenzo CriteriaDi Vincenzo Criteria

Additional Di Vincenzo CriteriaAdditional Di Vincenzo Criteria

DecoherenceDecoherence• Quantum computations rely on being able to operate on a Quantum computations rely on being able to operate on a set of qubitsset of qubits

in an in an entangled/superimposed stateentangled/superimposed state– Allows computation on all possible inputs to a computation in parallelAllows computation on all possible inputs to a computation in parallel

• ProblemProblem: Interaction of qubits with environment : Interaction of qubits with environment affects their stateaffects their state, , causing them causing them to not be entangledto not be entangled/superimposed/superimposed– Can partially address this by designing computer to Can partially address this by designing computer to reduce interaction with reduce interaction with

environmentenvironment, but this may make it, but this may make it impractical impractical (for example, running at very (for example, running at very low temperatureslow temperatures))

• General result:General result: a quantum computation can only proceed for a a quantum computation can only proceed for a limited period of timelimited period of time before a measurementbefore a measurement must be performed must be performed– Measurement forces the system into a more-stable classical stateMeasurement forces the system into a more-stable classical state– Measurement destroys superpositionMeasurement destroys superposition– System limited by System limited by ratio ofratio of decoherence time to operation latency decoherence time to operation latency

DecoherenceDecoherence

DecoherenceDecoherence

DecoherenceDecoherence

How decoherence happensHow decoherence happens

Decoherence-related Decoherence-related Figure of MeritFigure of Merit

Quantum Computer uses a single moleculeQuantum Computer uses a single molecule

Protons and Neutrons have Protons and Neutrons have spin.spin.

In a normal atoms these spins cancel out.In a normal atoms these spins cancel out.

In isotopes there are In isotopes there are extra neutronsextra neutrons. .

These extra neutrons create a net These extra neutrons create a net positive or positive or negative spin in an atom.negative spin in an atom.

Spins and CoherenceSpins and Coherence• Most advanced Most advanced demonstrated technologydemonstrated technology for for

quantum computationquantum computation• Use nuclei with spin ½ as qubitsUse nuclei with spin ½ as qubits

– Spin straight up = |0>Spin straight up = |0>– Spin straight down = |1>Spin straight down = |1>– Other directions indicate superpositions of |0> and |1>Other directions indicate superpositions of |0> and |1>– LongLong coherence times (seconds) coherence times (seconds)

• Electron spins (alternate technology) have coherence times of Electron spins (alternate technology) have coherence times of nanosecondsnanoseconds

– In a magnetic field, In a magnetic field, spin direction precesses about the spin direction precesses about the field’s axisfield’s axis at a at a rate that is proportional to the field rate that is proportional to the field strengthstrength

Quantum Computer uses a single moleculeQuantum Computer uses a single molecule

• A nearly ideal physical system that can be used as A nearly ideal physical system that can be used as quantum computer is a quantum computer is a single moleculesingle molecule, in which , in which nuclear spins of individual atomsnuclear spins of individual atoms represent qubits. represent qubits.

• Using NMR techniques, these spins can be Using NMR techniques, these spins can be manipulated, initialized and measured. manipulated, initialized and measured.

• The quantum behavior of the spins The quantum behavior of the spins can be exploitedcan be exploited to perform quantum computationto perform quantum computation; for example, the ; for example, the carbon and hydrogen nuclei in a chloroform molecule carbon and hydrogen nuclei in a chloroform molecule (as shown) represent two qubits. (as shown) represent two qubits.

Single molecule or Single molecule or ensamble?ensamble?